Wikipedia:Sandbox

mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye

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mic and we'll be good to go it's switching over it's about it's 0:06 almost halfway it's 0:13 done we're good okay so now let me come back to zoom alrighty there we go so um a couple 0:22 of people asked me about um I think it 0:28 was question number 18 on um 10.5 and it was talking about 0:34 something that was in the shape of a cylinder and that's kind of what I did with that banana when I brought it into 0:40 class and I cut out a crosssection so when you cut out a piece of it and pull 0:46 it out and see what shape it is that's called a cross-section well I remembered 0:51 that I had um a case that some sunglasses came in that was in this in the shape of the cylinder and one of the 0:58 questions it was part B it said if you cut through this C cylinder shape 1:05 straight down right through the Middle where it's perpendicular or to the you know to the base so just cut straight 1:12 down if you could take a slice out what it would what would it look like well when you oh gosh it's hard to see on the 1:19 black let me see if I can bring it in closer there you go so see this half 1:24 right here where my fingers are sticking in can you guys see how it makes a a rectangle so so that's what happens when 1:31 you cut straight down into the cylinder if I could cover up half of it 1:38 let me try like that it looks like a rectangle so I know 1:44 that problem was kind of tricky and I think um you guys have some of these yeah you 1:52 guys are going to do some uh crosssections down here where it shows you that they're taking a slice and you 1:58 have to try to identify what the slice looks like they're actually called conic 2:05 sections in Algebra 2 um and and they're pretty cool so um I just want to 2:12 introduce you to that as we continue on with these um 2:19 threedimensional shapes what we're going to do first is 2:25 we're going to take a look at a couple more problems that are come going to come up in your homework from that same 2:33 lesson from 10-5 and so I'm keeping you there and 2:39 letting you work a couple more problems and let's take a look at this one and you know what I'm going to grab a 2:49 calculator okay I'm getting it right 2:55 now and then if you have a calculator make sure that you do the calculations 3:00 with me so we have a cylinder right here and 3:08 it says that what we're going to do is we're going to find the surface area 3:13 again and remember the formula for surface 3:20 area now surface area of a prison is 2 V 3:26 plus p h and we work on that last week 3:31 well a cylinder has the same formula but just a tiny bit of a 3:37 change it's two bases plus c 3:43 h since a cylinder doesn't have a base that has straight lines it's got a 3:49 circular base they change the C to the C to stand for 3:55 circumference so the 2B is this part right here this is the two bases and p r 4:06 s is the area of the circle and you've got two circles you have a circle on top and a circle on bottom in a cylinder and 4:14 then the circumference formula is 2 pi r so it's F part is the C and then times 4:22 the H so that's where they get the 2b + CH but in MTH 4:30 we like to use this one now you'll also I saw that micaa was using a different 4:37 formula so she must have looked it up on something because I don't teach that one but I teach um these two formulas right 4:45 here this is the going formula so I would stay with this and then I would I 4:50 would use this one for the cylinders and try to stay with those two if you go off 4:55 and use a different formula that's fine but really ideally what trying to do is memorize them and these two are so close 5:03 together and so when you take an act um and an SAT you're not going to get the 5:10 formulas and so it's just easier to use these good formulas um that are really 5:17 closely matched so you don't have to memorize so 5:23 much I think I I'm might forgotten one other thing no I'm not 5:28 good okay let me rest 5:37 this and I'm going to grab a can out of my pantry which is right next to me and 5:45 let me see which one I want to get um I don't have I don't have a here we'll use 5:53 this one this is a can of um chicken broth 5:59 and you can see that the bases are circular and so this is the diagram 6:06 that's similar to my can right here now remember the surface area is the entire 6:12 can it's the top the bottom and the part that goes around if you could slice this 6:19 with a knife and peel it off the can it would be in the shape of a rectangle and 6:25 remember in your homework a lot of times the directions are going to ask you to draw the Nets and so if we had to draw 6:33 the net and make sure that you don't skip that if we had to draw the 6:40 net for a 6:45 cylinder it would look like that I'm not great at drawing but so be 6:51 sure and draw those Nets be sure to read your 6:58 directions all right so got my calculator if you have one 7:03 please do the calculations with me as well and if I mess up on anything be 7:10 sure that you jump in and tell me okay I hate not seeing you guys I mean I I like 7:16 seeing all your names up there but I like seeing your faces better all right usually in my high school classes 7:22 everybody just leaves their camera on most of the time so that I can see them 7:30 so I'm going to write two Pi because we're going to find the surface area of 7:36 this cylinder so one of the things that you want to do first is you want to identify what you got well right here 7:44 from the center out to the edge of the circle I have the radius so I know that 7:50 my radius is two and 7:55 then the line that attaches the two bases here is my height line and so my 8:03 height line is 4.4 and I'm in yards so obviously I mean 8:09 yards are really long so this diagram is not to scale okay so now we're ready 8:15 we're going to keep our two we're going to keep the pi here and then R is 8:23 two and it says to square it hang on let me make my squar a little bit bigger for 8:28 you guys that looks good and then now on the formula it says write two write Pi again 8:36 and now we're going to put R again which is two and then my height was 8:43 4.4 and then you're just going to run this through on the calculator you don't 8:48 have to use um parentheses all right so here we go two 8:55 where're in the world is p hang on a second let me find p oh I found it 2 9:02 pi and then 2 squared and then plus don't foret your 9:09 plus sign two where Pi go there it is 9:15 pi * 2 * 9:21 4.4 I hope I get the right answer I don't have any answers so I got 9:34 8042 and when I rounded I got [Music] 9:40 80425 so let's see how the directions are going to ask you guys to round on this one so I saw 9:48 some that said round to the nearest unit or round to the nearest whole number which means you don't have any 9:55 [Music] decimals and that one says round to the nearest 10:00 whole number let's see what this one says round to the nearest square inch 10:05 okay so we could say round to the nearest square yard so if I was going to round this so that I didn't have any 10:13 decimals it would just round to 80 and then it would be 10:20 yards squ 10:25 okay so that was just some review from from um from the homework that you had 10:32 last week so on Tuesday when I woke up my uh I heard this terrible noise coming 10:40 outside my bedroom and it was it was my furnace and it was 10:46 going so it died and it was like so cold on Tuesday and my husband was driving 10:53 over with the babies and um so anyway we had to um turn on the fireplace and 11:00 space heaters and all of that stuff and and um it was it was a it was it finally 11:08 the house finally warmed up and so that was really nice there's your breakfast 11:13 thank you I didn't know you're going to do that close and then I um walked into the 11:20 living room and looked at toward my couch and this is what I saw um I didn't 11:27 do anything to her hair it's just the fireplace and all the space heaters going um our hair was like 11:35 flying around so anyway I'm very glad that um we have heat CU that was 11:44 cold so I bet the heat and air people are really busy this 11:49 week so what we're going to do now is we're going to take a look at something 11:54 that's called a composite shape and a composite shape is when you have two or 12:01 more shapes that are stacked on top of each other um let's see oh my gosh 12:08 there's so many like kids toys that are like that or if you even think about like a house is kind of like a boxy 12:16 shape and then the roof is like triangular and so those are composite 12:21 shapes so we we see composite shapes like all over the place um especially 12:27 when you're out driving around and so when you stack things on top of each other um those are called composite 12:34 shapes and so what we're going to do now is we're going to take a look at this fabulous picture that I drew this 12:41 morning and we're going to try to find the surface area of this composite shape 12:47 and I've got composite shape written here so what does this look like to me 12:53 it kind of looks like um we used to have some old like bread boxes a long time 12:59 ago that were kind of round on top and that look similar to this some in some 13:06 ways it kind of looks like a maybe a mailbox to me and so if you're going to 13:12 find the surface area you're just going to find everything that you would have to use to 13:19 make the shape just the outside all the outside all the way around we're going 13:24 to try to find each piece of this so first of all you want to identify the 13:30 two pieces that got stacked and let me just say that this 13:36 drawing is no way it isn't even close to scale because this line right here is 8 13:43 in well this one is 180 I tried to make it pretty long but the drawing is not to 13:50 scale so first of all we have something 14:00 that that looks like this let me see if I got that 14:10 around um hang on a second you guys know that I can't 14:17 draw let me see how that looks oh that looks terrible let me look at the video and 14:24 see if I can do it from licky looks like it needs to go 14:29 like that oh that's even worse it looks like it needs to go like 14:36 that okay it's getting better now you have a half of a cylinder on top 14:46 so it's like you've got a cylinder but you got to cut it in half so you got half of the cylinder on top so you have 14:52 this boxy thing here but with a half cylinder on top now I just want to just 14:58 want to draw some little Stripes right here should have probably done them in a 15:04 different color but this part is open there's it's like 15:13 the lid is open and this is set on top so this stripe part right here that 15:20 shaded where it's not included in the surface area because the cylinder 15:27 sitting on top of it the part that we can see and touch that's all that we have to find so first of 15:34 all this rectangular box has six faces 15:39 remember you kind of talked about that in class I think I got my marker Expo marker box and we're talking about the 15:46 six faces and so let me grab this really quick I see something perfect we had a 15:54 gigantic party for my mom on Sunday for her night birthday and my sister had 16:02 Panera delivered and they sent a box that has um chips in it so anyway with 16:08 this box it's like this piece right here this top piece is open so this piece 16:14 isn't here it's just the box kind of without the um the top 16:21 face so what do I need to do well I need to find this little front piece right here 16:29 and of course there's a matching back piece and then I need to find um this 16:38 piece right here the long bottom piece and then the other side so I need to find the bottom 16:45 piece so I'll put the bottom and then I need to 16:52 find um the two side panels okay I'll call this a side one 16:59 and side two so this is the 17:05 front this is the back it's sitting on the bottom and then 17:11 I've got this side panel right here and then I have a side panel in the back that we can't see so now we've just got 17:18 to transfer these numbers so this part this pretty easy it makes sense so right 17:23 here I've got an eight so I need this value right here but I also need that 17:31 one right there what what's the value that goes right there does anybody 17:41 know I can tell some of you 17:46 now are you trying to show me with your hands okay it's an eight isn't it so 17:53 this eight right here on this uh height line is is going 17:59 to transfer we're going to slide it over here so I've got 8 by 8 so 8 * 8 is 18:09 64 and of course this is the same exact size so I've got two that are 64 so I'm 18:17 going to keep those now on the bottom this bottom piece right 18:23 here uh let's see we need let me do this in a different 18:29 color we need this length right here this measurement okay and then we 18:37 need this one or this one well that no that's not 18:45 right that's the side panel okay we 18:53 need this one 19:00 because that's what makes up oh here you know I can do this and this might help a little bit we 19:08 can um I feel like it needs to go did that help at all yeah that looks a 19:14 little bit better so on the bottom piece I have 19:20 180 and then I've got eight over there in blue and so remember to find the area 19:27 of a rectangle you just do length time wet so I'm going to multiply 180 * 8 19:33 with my calculator please use your calculator on any shapes and I get 19:43 1,440 and now I'm going to take a pink and I need the side panel right 19:51 here so I need this I need to find the area 19:58 and this side panel well what's nice it's still 180 and eight isn't 20:07 it so this long part is 180 and this is eight so that's going to 20:13 be 1440 again and there's two of them that are identical so if I add up the 20:21 surface area of all of these panels these faces let's see what we get here 20:27 and then we'll finish up with our cend okay so I've got 64 * 2 20:37 plus, 1440 and I've got three of those times three okay and that gives me 4 20:48 448 so all of these give me 44 20:54 48 so I'm going to keep that number now I'm going to come over and I'm just going to find the surface area of the 21:00 cylinder and remember this is our formula for the 21:07 cylinders okay be slide this ever so I'm not in the 21:14 way so let's take a look at this cylinder so if I bring the cylinder out 21:30 like I said this is half of it boy that looks pretty good did you see that this eight right 21:38 here on the bottom would would actually move up here because these two lengths 21:45 are the same because they're they're on one of the rectangular prisms so all the 21:52 way across here from here to here is eight so my d diameter is a well in the 22:01 formula I don't need the diameter I need the radius and so if you cut that in two 22:08 and half you find the radius is four okay now I'm ready to plug into my 22:13 formula there so it says the surface area is 2 22:19 pi r 2 + 2 pi RH so make sure you write 22:26 the formula down and then I'm going to right 2 pi now I'm plugging in my 22:31 numbers I have to put four there four squar plus 2 pi and there's my four 22:38 again for the radius and now what's my height well if you hold your hands on 22:44 the two circular bases the height is the line that that joins those two bases and 22:52 my height is down here but I can also transfer it up here so it's 180 so I'm 22:59 going to write 180 here and now I'm ready to plug all this in on the 23:05 calculator so if you have a calculator do it with me so I've got two and then 23:13 Pi there it is and then 4 23:20 SAR + 2 * 23:26 piun * 4 times 180 so write the formula plug in all the 23:34 numbers and then give me your 23:49 answer I didn't get the right 23:56 answer what did I do wrong okay so first of all I got the right 24:02 answer for my formula but I need to stop and just take a minute and just think about this I've only got half the 24:10 cylinder this is only half of it so I got to take this number and I've 24:17 got to divide it by two so that I get half the cylinder and so we're going to take that and divide it by 24:26 two and now we get [Music] 24:31 2,312 and I'm going to go in ahead and round it to the nearest hole 24:37 number and so this is the surface area of that half of the cylinder and this is 24:44 the surface area of the rectangular box that it's sitting on and if I add those 24:50 two numbers together that gives me my total 25:01 and I get 25:06 6,760 that was kind of a lot of work wasn't it so you're going to see um a 25:11 composite shap in your homework so just be sure that you look at it because you 25:18 might have the half a cylinder on there and just don't forget to divide it by two so that you get half of the cylinder 25:26 okay let's go on ahead and um move off the geometric shapes and we're going to 25:32 take a look at some more sections of chapter five and 25:40 then if we have time I'll um go over another geometric shape and Rie from 25:47 last week okay so let me just you a little faster for me to spray 25:53 any R it's still snowing 26:02 here same over here it's BN down snow got some this snack flakes are 26:09 still kind of 26:15 small but yeah last night when I was looking at the Weather Underground app 26:21 that's pretty good um I think it said we have like a 60% chance the snow right 26:29 now and then this morning when I looked at it at 6: a.m. it said we had 100% 26:37 so when it's cold it's nice to get night might as well get some snow if we're 26:42 going to have to stay stay home and have the snow day 26:49 right very good let me get a drink 27:02 last week we worked on um multiplying fractions and those were pretty fun and 27:08 you also did some addition and subtraction so now we're going to move into section 5.5 does anybody have any 27:18 questions from the fraction work that we did any questions from the 27:24 fractions last week everybody do okay with it or if you 27:30 missed one were you able to fix it Henry are you feeling any better yes I am can you hear me yeah I 27:39 have yeah okay I have a couple of students that um have the flu so that's 27:46 not good yeah all right so we're gonna continue 27:52 to work with fractions today and what's neat is what you learned last week is 27:58 just going to come right back into play here in just a minute so the first thing that we're 28:04 going to do is we're going to kind of go back into Elementary School and look at 28:11 this vocabulary word let me write a couple of numbers up 28:25 here so reciprocal means that you're going to have a number or a 28:31 fraction and you're going to have to turn it upside down flip it so if we saw 28:37 if we saw the number five and you had to flip it upside down it's really five 28:44 over one and so if you had to write the reciprocal here we'll just do it in a 28:49 different color since I got all the Mark here the reciprocal would be 1 over five 28:57 okay if we look at this fraction 29:02 27s put a little mustache on it so it doesn't look like one there 27 if we had 29:09 to write the reciprocal of this we would just flip it upside down 29:17 inverted and then of course on this one we would do the same thing we would just 29:22 flip it upside down and it doesn't really matter where 29:29 the negative is it can be on the eight it can be on the five it can be even with the fraction bar as long as there's 29:36 one negative in front of it it continues to stay 29:43 negative let's do one more let's say you had two and A3 and that you needed to 29:51 write the reciprocal of this mixed number so the first thing that you would do to write the reciprocal correctly is 29:58 you would change this into an improper fraction so You' multiply 3 * 2 is 6 + 1 30:04 is [Music] 7 so you'd write it as an improper 30:09 fraction and then you would invert it or flip it and that would be the 30:15 reciprocal so you're going to uh see maybe a couple of problems where it asks 30:21 you to write the reciprocal of a number usually this one is a little bit tricky in elementary school but hopefully um 30:29 you guys are kind of past that part this one might be a little chy but it's not too 30:39 bad almost time for me to get a new 30:46 board a new dry rice board my last one lasted about 12 years 30:54 and it was only um about $15 so the expensive one 31:00 it seems like the Finish is starting to come off of it a little bit or it's because my markers are are um 31:09 new and that stuff that's inside of them is nice and 31:14 bold okay let's do this we are going to 31:20 divide fractions and this is so easy 31:29 last week we added subtracted and multiplied with 31:34 fractions and today we're g to just go back to kind of elementary school on 31:41 just this one problem and we're going to divide with fractions all right so 31:46 what's the rule in math you can never ever um divide fractions unless you kind 31:54 of fix some things so first of all find the division sign and the the number 32:02 that is on the right hand side of the division sign must be flipped you must 32:07 write the reciprocal so I kind of like to Circle this one because sometimes 32:13 when I teach this in elementary school students and even Junior High math students will flip this one the first 32:20 one stays the same it's the one to the right of the division sign that uh you 32:25 write the reciprocal so you're going to flip it the first fraction stays the same and 32:33 now you're going to change the division sign to multiplication so you can never 32:39 ever divide when there's a fraction in the problem I'm sorry yeah that's 32:46 right you have to change it to multiplication and do the flipping the 32:51 reciprocal so in public school um I've heard him say Keep 33:03 change and flip that's one of the few say that I that I've gotten that I've 33:09 actually you know I'm like okay that works I'm I'm okay with that then keep this one change division to 33:16 multiplication and then flep write the reciprocal there and then now we're going to do the 33:24 same thing that we did last week we're going to look for cross cancellation so on this diagonal I've 33:31 got a seven on top and a two on bottom I can't knock those numbers down at all 33:37 because they don't have anything in common they don't go into each other but when I look on this diagonal the three 33:43 goes into the 12 four times and that's it that's all I can do let me darken 33:49 that one right there and now I'm just going to multiply the numerator 7 * 1 is 33:54 7 and then 4 * 2 is 8 and there we go and then just make sure 34:02 that your fraction answer is simplified and that one is so we're okay 34:08 with that oh it's so nice to have heat in the 34:17 house it is really cold out there 34:41 when we take a look at this one of the things that we want to notice is why are the parentheses there well it's because 34:49 this fraction is negative you're not supposed to have two math operation signs next to each other so they enclose 34:57 this one in parentheses so again we have a fraction involved in the problem you 35:02 can never divide with fractions and so we have to follow that math rule where 35:08 you find the division sign and then you must WR the reciprocal to of the number 35:13 whatever whatever it is fraction or number you have to write the reciprocal of the one on the right so this one is 35:20 going to I'm going to keep it right where it is now I'm going to change this to multiplication and then I'm going to 35:26 flip this one at side down and I don't care if you write the parentheses first 35:33 of all I notice right off the bat that my answer is going to be positive and so 35:38 then I don't have to worry so much about the signs because we're using the even and odd Rule and when I count the number 35:45 of negative signs I get two which is an even amount so I know this is going to be positive so then I don't have to 35:52 worry about the negative sign so I could actually go like this if I wanted to I kind of like that better I'm going to 35:58 look across for cross cancellation on this diagonal from left to right and four does go into eight evenly now I 36:07 look on this diagonal I've got nine on the bottom and 11 on top there's nothing they don't go into each other that have 36:13 anything in common so I'm done and I'm just going to multiply so 1 * 11 is 11 36:19 and 9 * 2 is 18 and that fraction is simplified and I'm done so what did they 36:25 do well first they started as out on a really simple problem then they took us to a step up where they added the 36:33 negatives in so that you would have to pay attention to that but it was still relatively 36:41 simple and of course cross cancellation is fabulous so please please make 36:48 yourself look for it it it definitely speeds things up um and makes problems a 36:56 little bit easier 37:11 get a little bit bigger so we've got -38 / 9 37:19 and6 so remember you can't divide when there's a fraction in the 37:24 problem see the division sign look at the term term on the right and remember we've got to flip this we have to write 37:31 the reciprocal well we don't flip the six remember on that problem a couple of 37:37 minutes ago I showed you a mixed number and I told you that if you had to flip 37:43 this you would need to change it to improper first so 6 * 9 is 54 I think + 37:50 1 is 55 over six so I just changed this to 37:58 improper and now I have to flip 38:03 it I'm going to keep this one I'm going to multiply and then now I have to write 38:09 the reciprocal let's see how would I do this 38:16 if if I was going to do this one I'd probably do it like 38:22 this so I'm just going to be super detailed to show you how I would do it 38:30 then I would go like this but either way I'm okay either 38:37 way so I'll let you go from here to here for me I would go from here to here to 38:43 here because I'm just more detailed so either way you want to doce 38:48 fine now three doesn't go into 55 evenly does it so when I look across here 38:54 there's nothing I can do now when I look across here the eight and the six they 39:00 don't go into each other but they do have a greatest common factor of two and 39:05 so I'm going to go on ahead and divide them both by two and knock those numbers down so 6 / two is three and 8 / two is 39:13 four and now I'm ready to just multiply across so I've got 3 * 3 which is 39:20 9 and then I have four * 55 which I have no idea what that is 39:29 is it like two 10 or something I don't 39:34 know 5 * 4 is 20 I'm barely away 4 * 5 is 20 and 2 is 22 I got 2 39:46 20 am I done I'm not done because I have to look 39:52 at the negative sign there was a negative up there in the original problem and so just make sure that at 39:59 the end you go back and check that so how many negatives did you count there's one and one is an odd amount of 40:06 negatives and so that's our rule that we use for multiplication and division and 40:11 so that's going to make my answer negative let's do 40:26 another e 41:05 again we have a parentheses there but it's just separating that negative sign 41:12 from the division sign if I look at this I already know that my answer is going 41:17 to be positive because I'm using the even and AAL there's two negatives and 41:23 it's going to make this a positive the second thing that I notic is I have quite a mess here don't I I've got two 41:29 mixed numbers remember you can never divide mixed numbers you always have to 41:34 change into improper fractions and then remember you can't divide fractions so you have to do the reciprocal thing the 41:42 reciprocal rule um so let's change these mixed numbers to improper fractions and 41:50 then we'll move on from there so go on ahead and see if you can work ahead of me and get to the 41:55 answer so 4 * 5 is 20 + 1 is 42:03 21 and then 5 * 2 is 10 + 2 is 42:09 12 and I really don't need the negative signs because I know my answer is going to be positive so I'm going to go ahead 42:15 and erase them now I'm going to follow the rule you can't divide when there's a 42:23 fraction so you have to write the reciprocal and then now I'm definitely 42:28 going to try my best to apply my cross cancellation skills when I look at 21 42:36 and 12 they don't go into each other evenly but they are divisible by three 42:41 so I'm going to knock them down and divide both of them by three and that's all I can do because on 42:48 this diagonal there is no cross [Music] cancellation 7 * 5 is 35 42:57 and 4 * 4 is 16 now when you get 43:02 here you are going to have to go ahead and simplify it and change it back to a 43:09 mixed number so 16 * 2 is 32 so this 43:14 goes in two times and if I take 35 minus 32 that leaves me three as a remainder 43:23 and then I'm just going to keep my 16 43:33 very good on that one so does that one seem to make sense 43:40 is that pretty [Music] good all 43:51 right basically this is kind of an elementary math skill but just with the 43:57 positives and the negatives mixed in 44:46 all right so in this particular problem I'm going to let you try this one on your 44:53 own what we have to do is we have to follow the order of operations both of 44:58 these problems that are given follow we have to think about the order of operations the order of operations Pim 45:05 says I must work the parentheses first I must get this answer I got to add these 45:11 two fractions get this answer and then set up my division so give that one a 45:16 try and I'll uh be right 45:25 back 45:55 e e 46:55 okay so we had to find a denominator first with the 25 and 15 so you always 47:01 have to find a common denominator when you add your fractions so what was the common 47:15 denominator the common denominator for number eight was 47:20 50 50 47:27 it's mad it's got board spray come 47:34 on all right so if you count by 25s you get 25 50 75 100 if you count by 15 you 47:42 get 15 30 45 60 75 so the common 47:49 denominator would be 75 so 25 * what that would be times 47:57 three so that's going to give me a 21 when I multiply the numerator by three 48:03 and then 15 was times 5 so I have to multiply the numerator times 48:09 five and so I get 45 and now I've got to add these two 48:14 together and I get 66 over 75 I'm a little 48:22 close yeah 66 over 75 is that what you got I 48:32 got boy I sure hope so I've got 81 15 divided by 48:42 66 over 75 I know that these are divisible by 48:50 three 48:58 how do I know that if you take 49:04 66 and 75 this works for threes and nines this is the divisibility rule if 49:11 you add these two numbers together see how you get 12 and you can add them together again since there's two digits 49:17 and see how you get three um 66 is divisible by 3 but you 49:24 could have stopped right here at the 12 and said does three go into 12 yes it 49:29 does so you know that 66 is divisible by three again if you take 7 + 5 from the 49:37 denominator and you add it up you get 12 so three goes into both of these so if I 49:44 divide this one by three I get 22 and if I divide this one by three I we get 49:52 25 and now I'm G to change and write the reciprocal so the 25 is on 50:01 top and the 22 is on bottom so the numbers are a little bit 50:09 smaller which might help you and then eight and 22 don't go into each other 50:15 evenly but they are both divisible by two so I'm going to knock them down by dividing them by two so that gives me 50:21 four on the top and 11 on the bottom again on the other diagonal for 15 to 25 50:28 they don't go into each other evenly but they are both divisible by five so I'm going to knock the numbers down and 50:34 divide both by five 15 IDE 5 is 3 and 25id 5 is five and now I'm going to 50:41 multiply straight across 4 * 5 is 20 and then 3 * 11 is 33 and so I came 50:50 out with an answer that I don't have to simplify and so that was kind of nice did you guys do okay with that 50:57 going can't see anybody you can also use your thumbs up if you know where that button 51:07 is it's at the bottom of your screen yeah are you could show me your 51:13 thumbs up sometimes if I'm sitting over here on the side the light kind of um 51:20 blocks but if you guys show me a thumbs up I can usually see that super 51:29 so remember that three divisibility rule if you haven't seen it before pretty 51:36 cool it helps when those numbers get a little bit bigger now over here on this 51:42 one they don't have any parentheses so according to the order of oper order of 51:47 operations please excuse my dear Aunt Sally I would have to do the division 51:53 first so I'm just going to take it over here 67 and then I'm going to 52:00 flip the one to the right and I'm just going to solve this 52:05 first I'm going to come out with my answer and then I'm going to subtract so we're doing please excuse my dear Aunt 52:14 Sally these are in a tie these are in a tie parentheses exponent multiplication 52:20 and division from left to right and addition and subtraction from left to right 52:27 oh we do have cross cancellation yay two goes into six three times okay and then 52:33 we get nine Sev I would go in ahead and leave it just like that because look so 52:41 I did this and I got 97 minus 52:47 37 see how that people that wrote this problem made have come out with the same 52:52 denominator so when the denominator is the same from last week you learned that you just keep it slide it over and then 53:01 subtract the numerators 9 minus 3 is six so that wasn't too bad sometimes those 53:08 problems like uh a little bit daunting but then once you get into it's like oh 53:14 that wasn't so 53:24 bad all right and now we're going to work a problem with a cutting board so I got my cutting 53:32 board because it um definitely applies with this with this problem that we're 53:37 going to do so it says that you want to 53:43 make some cutting boards and this long piece right here is 53:48 going to be 15 in and you want this top piece right here to be at least 12 in 53:57 but you want this part to be longer so this is my cutting board and it definitely goes along with this problem 54:04 so it says that you are going to go and you're going to buy these strips and if 54:10 you look at this closely you can see this is a strip and then I've got another strip can you can you see the 54:17 little grooves right here where they've like glued them together so you're going 54:22 to buy these strips and you're going to glue them together and you're going to assemble a a a wood cutting 54:37 board okay so here's my cutting 54:47 board but up at the top you want this to be at least 12 in but you want the 54:53 length to be longer and you want it to be 15 in all right now you're going to 55:00 have to glue these strips 55:18 together and the strips p in 1 and 58 in section 55:27 okay so the width of this strip is 1 and 5/8 now the lengths are all 15 so we 55:34 don't have to worry about the lengths but we need to know how many of these we're going to get how many do we need 55:42 to put together to glue it now are you going to do this in your 55:47 head are you going to guess some of you might let's see if we 55:54 can work out a method where we don't have and gas okay and this is 1 and 58 56:00 in so we're going to glue all these strips together see I love it when you're in my house because I have all 56:06 this stuff that I can get and show you all right so how many strips do we need 56:11 well we want it to be um at least 12 in 56:18 Long across the top so we're going to take that 12 and now we're going to 56:24 divide it by the width of the strips so if I want 56:31 this to be 12 in Long on the top that's the width of The Cutting Board well I need to divide it by the width of the 56:39 strip now remember we've got to change our mixed number into an improper 56:44 fraction so 8 * 1 is 8 + 56:52 5 so 8 * 1 is 8 + 5 is 138 and now remember we're going to write the 56:59 12 but then we're going to write the reciprocal so we're going to have 8 over 13 and this isn't looking really really 57:07 uh like nice for cross cancellation there is none and remember the 12 is 57:13 like over a one so what do I have to do I've just got to multiply straight across isn't 8 * 57:21 12.96 yep if you know your 12 family and and then now here's my 13 well I don't 57:29 know what 96 / 13 is I'm going to have to um I'm going to have to make some 57:36 attempts here okay so 13 times 57:42 5 six 7even I think 13 * 7 is like 91 let 57:49 me check um I was thinking about my you know that green sheet with the prime 57:55 number on it 91 is green and I think I remember 13 * 7 is 91 7 * 3 is 1 carry 58:03 your 2 7 * 1 is 7 + 2 is 9 oh that got me 58:09 close so 13 goes in seven times and then we have five left 58:19 over so I got seven and 5 58:24 133 so how how many strips do I need because you you aren't going to get 58:30 to cut one of the strips um you know you're not going to cut anything so how 58:36 many strips do I need well it has to be at least 12 in well that means I need 58:42 seven and 513 of a strip well I can't take part of the strip I I've got to add 58:48 another strip on to catch the 513 so I need seven plus one more strip which 58:55 covers the five 13 so I would actually need eight 59:01 strips to make the cutting board and it would be a little bit longer than 12 in 59:08 but the length of it would still be um bigger or the number would be greater 59:13 than the width okay so that was a good 59:19 problem gosh I miss you guys everybody's so quiet 59:34 this remember don't use the chat 59:42 function be very respectful because I can look at all your 59:47 chats all right and I I think I have them disabled [Music] 1:00:02 okay it all looks good now we're going to move to the next 1:00:09 little lesson which is 5-6 and again we're going to stay on 1:00:16 fractions so this this lesson is one that I really like um I like fractions 1:00:23 and let me just mention something on the assignment sheet right here when you get 1:00:28 to Tuesday that's well let's see it actually starts on Monday so I'm going to have you start working out of 5.6 on 1:00:35 Monday and then Tuesday you're going to continue to work out of section 1:00:40 5.6 and on Tuesday it says watch my YouTube video and it's called solving 1:00:47 equations with fractions and clearing fractions I am not going to teach you 1:00:53 clearing fractions today but that's part of the video it starts out and it shows 1:00:59 you how to work equations with fractions and it shows you how to clear them next week I'm going to show you how to clear 1:01:04 fractions and we use that a lot um especially in Algebra 2 and so it's a 1:01:10 good skill to learn at this level or at least get introduced to it and it just 1:01:16 makes things a whole lot easier and so just remember I have a YouTube channel 1:01:21 with short video clips most of the clips are like six minutes seven minutes eight 1:01:28 minutes and the problems get harder as you go through the clip so if you guys will be sure to watch that little um 1:01:35 YouTube video that would be fantastic 1:01:40 okay so here we go we've added and subtracted fractions 1:01:49 we've multip fractions we just finished division with fractions which was pretty 1:01:54 easy because it's a lot like multiplication we used a little bit of order of operations with it and then now 1:02:00 what we're going to do is now that we understand the rules and how to work with those fractions we're going to now 1:02:07 apply that the skills that we've got but now we're going to move it to equations 1:02:13 which I 1:02:18 love so if you were in one of my math classes last year then you've already 1:02:25 seen this let me write this vocabulary word on the 1:02:32 board it's called multiplicative in 1:02:47 inverse oh getting some nice snow here here I'll let you guys look real quick 1:02:53 let's see if a camera f it up it's coming down good I love to look out 1:02:59 the window all right so we're going to work with the multiplicative inverse and let 1:03:06 me show you what it does it's so so cool let's say that you had the fraction 3 1:03:14 fths well if you flip that upside down okay it just clear that if you flip that 1:03:20 upside down to 5 over three and you multiply them do you see how everything 1:03:27 cross cancels out and you get one one one and one and so when you use the 1:03:34 multiplicative inverse you flip the fraction upside down and when you multiply them it gives you 1:03:41 one and this comes in really handy in math especially in equations so I love 1:03:47 it when there is a fraction in front of a variable in an equation because I know 1:03:53 how to get rid of it so on the left hand side of the equation I have one term on 1:03:58 the right hand side of the equal sign I have one term so I can use the multiplicative inverse and so let me 1:04:05 show you how it work you take the fraction and you just flip it upside 1:04:10 down you write the reciprocal and you do that on the other 1:04:16 side as well and now you 1:04:23 multiply what happens on the left hand side just like over 1:04:29 here we saw that when we multiply we get one because remember everything cross 1:04:35 cancels out you don't have to do this you don't have to mark these out you just go straight to the X isn't that 1:04:41 pool so you write 74s and just go straight to the X because 1 * X is X and 1:04:48 then on this side you definitely want to look for cross cancellation so four 1:04:54 cross cancels into 12 three times and now I just get 3 * 7 is 1:05:00 21 and what what am I missing in my answer 1:05:06 here anybody see it the 1:05:12 negative sure that's it all right so I 1:05:20 love multiplicative inverse CU it's so easy let's try another one 1:05:31 hang on a 1:05:41 second and I'll get out of the way in just a second so you guys can 1:05:47 write this down I believe on your next test you're 1:05:55 just is going to have one or two questions that involve um you know kind 1:06:00 of the skills from today so make sure to let me know if you need any like 1:06:05 additional help on 1:06:18 these so pretty snowl I don't know if you guys are aware 1:06:25 but there are some major major fires in um 1:06:31 Los Angeles right now and this is day number three from what I understand and 1:06:38 they know the the um where the fire originated but they don't 1:06:45 know how it started they don't know if it was arson but um I guess it's it's like 1:06:52 burned up some like really really beautiful areas and they um don't have 1:06:58 the fire contained last night that it was 0% contained in all the all the 1:07:04 areas that were on fire so it's really it's really sad to see so if you get a 1:07:10 chance you might uh go on to YouTube or something and maybe watch a couple of 1:07:17 Fox News clips about it because it's it's definitely a a historic fire for 1:07:24 that area when I cut my equation through the equal 1:07:31 sign do you see I have two different terms on the left this is called a 1:07:36 two-step equation but it's a little souped up here because we're in 1:07:43 fractions so sometimes like um let's say for an ACT test sometimes if I was 1:07:50 taking a test and I didn't know what to do I might just write all the numerators 1:07:55 down and leave the denominators out kind of like this I know this is weird but this might help 1:08:03 me figure out how to start this so this looks a little bit better doesn't it 1:08:09 when I leave all the denominators off then I go oh yeah I need to subtract four on both sides so this is a two-step 1:08:17 equation and we're going to subtract first on both sides because we can't do 1:08:22 anything with the term with the X because it's attached through multiplication so step one is always do 1:08:30 the addition and subtraction first so I'm going to take the for Fist and move it to the other 1:08:47 side now I'm going to bring down my 11 over 15x and I'm just going to let it sit 1:08:54 there for a minute and I'm just going to wait on that I'm going to look at the 1:09:00 right hand side you can see that over here on this 1:09:05 side of the equation we don't have common denominators so I'm going to go on ahead and count by threes and count 1:09:12 by fives and the first number that I run into is 15 and so 15 is called the least 1:09:21 common denominator or the least common multiple 1:09:27 and so 5 * 3 is 15 so I have to multiply the numerator by the same thing by three 1:09:36 and remember it's negative and 3 * 5 is 15 so I have to multiply the numerator 1:09:42 by five as well so that I can stay and keep my equivalent fractions so now look 1:09:49 how messy that is so what do I get well I've got the same denominator so I just 1:09:54 bring the 15 down and then I have 5 - 12 well 5 - 12 is 1:10:02 -7 and then I'm going to keep the 15 now over on the leftand side I can 1:10:13 use this skill called the multiplicative inverse and I can flip this upside 1:10:22 down even if it's negative I can flip it upside down so when I multiply get one 1:10:29 and the two negatives are even so it's positive one and so 1 * X is 1:10:41 X like I said don't worry about where the negative goes I mean put the 1:10:46 negative in front but don't worry if it's on the numerator or the denominator just stick it out in front so on the 1:10:53 left I've got X and then on the right hand side usually the people that author 1:11:00 um these problems for you are going to make it where you're going to be able to use some cross cancellation so I can see 1:11:07 the two negatives over here are going to make my answer positive so I'm going to come back and look at that again at the 1:11:13 end but I can see that I have a 15 in the denominator and a 15 in the 1:11:18 numerator so on that diagonal those cancel out and I'm just left with 7 over 1:11:24 11 and again I would check the signs two negatives through multiplication and you 1:11:31 can use the multiplication dot right here that would probably be a good 1:11:37 idea and I really like that you could also use parentheses I'm not going to do 1:11:44 that but just make sure that you indicate multiplication there so that 1:11:49 there's no confusion at all and then go back and check your negatives so that 1:11:54 you can make make sure that you are putting the right sign on your final answer and of course seven and 1:12:02 11 they're both prime numbers so they're called relatively prime because they 1:12:07 don't go into each other it's simplified might remember relatively prime back 1:12:14 from seemed like that was chapter [Music] 1:12:20 four I think that was from September that was a while back 1:12:35 so make sure that you're breathing take some nice deep breaths hopefully you 1:12:40 guys aren asleep so take some nice deep breaths 1:12:46 this is a really good day for like um you know what kind of one of those like 1:12:52 hot chocolate or hot chocolate with coffee in it chocolate chip cookies I 1:12:58 mean fireplace this is just one of those really nice days so um make sure that 1:13:04 you do something uh something special since it's snowing or maybe take some 1:13:09 pictures outside because it is it is really beautiful snow is very beautiful 1:13:31 Canon you want to try this 1:13:36 one sure um well it's a one step so we would 1:13:44 start by um using the mul multiplicative inverse 1:13:50 yeah that thing so tell me what to write Okay so 1:13:55 would be 6 over 5 to the left and then * 1:14:00 6 over 5 * 20 uh you said 1:14:06 that and then you put uh one under the 20 then add 1:14:15 it um that would be you can cross cancel the 20 and five and you get uh four 1:14:26 yeah so 24 over 1:14:31 one or just 24 yeah and if you have a one in the denominator then you won't 1:14:38 have to write it very good see it's pretty easy isn't it I love that somebody figured out this multiplicative 1:14:46 inverse thing it's amazing because you could whatever you do to one side as 1:14:51 long as you do it to the other side it still keep keeps your equation you know 1:14:57 balanced and so you're still balancing that equation so it is so so 1:15:15 cool I can't see who all is is with me 1:15:21 um I mean I see James Josh Riley Jimmy micaa Liam and Canon and that's 1:15:28 all I see is is there anybody else can you guys see anybody 1:15:37 else so I don't see Jack I don't see 1:15:43 Preston so not everybody I don't see Winnie I know Preston was here earlier I 1:15:49 haven't seen uh Wy or Jack okay because usually it'll have a 1:15:56 little arrow on the top of my screen you know that I can I can slide 1:16:02 over so let's take a look at this one now again don't let this fraction scare 1:16:08 you okay so if you weren't sure what to do you could kind of look at it like that do you see how we need to add 20 1:16:16 first on both sides because this is a two step so I'm just going to add 20 on both sides 1:16:31 both cancel out and I get three fours in and then now -6 and positive 20 just 1:16:39 gives me a four there okay Jimmy what would I do 1:16:50 next I was trying to figure this out and I couldn't 1:16:56 okay but do you see how to add the 20 on both sides does that make sense 1:17:01 yeah okay so remember what I what I told you guys if you don't know what to do 1:17:08 write the equation but take the denominator off and see how it's like oh I see a two step so I'm gonna add 20 on 1:17:16 both sides okay so and then so would you so would you times 34 times four 1:17:27 kind of so what you want to do is you really want to focus on on that just the 1:17:34 three fours when you see a fraction in front 1:17:42 of a variable it's so easy all you have to do is flip it upside down so when I 1:17:47 flip it upside down Jimmy what does it turn into 1:17:55 so it' be four3 now this is kind of weird because 1:18:02 I'm going to put it right here okay I mean you could put it right 1:18:08 here but I'm going to put it over on the right hand side it's going to look weird because see how that n is there so try 1:18:16 to ignore the N okay that n is going to be in the middle but just try to pretend that you 1:18:22 don't see it okay and then see how the fours cancel out and the threes cancel out so it just 1:18:31 leaves and then you're going to take the same four3 to the other 1:18:37 side it it's probably good you use the multiplication 1:18:42 dot so when we when we multiplied with fractions last week we did stuff like 1:18:48 this it's just it looks really weird when it comes into an equation now remember there's a one under 1:18:56 here and so I took 34 and I flipped it upside down to 4/3 and now I don't have 1:19:04 any cross cancellation do I no * 4 is 16 1:19:10 and 3 * 1 is three and so from here 16/3 1:19:15 is the answer but most likely they're going to have you go ahead and simplify it and change it to a mixed number so 1:19:23 you're going to think three goes into 16 five times that' be 15 and 16 - 15 is 1 and then just keep 1:19:32 that same denominator and there you 1:19:39 go let's do another one 1:20:06 all right James what would you do 1:20:16 first what do you think I should do first 1:20:27 any ideas sorry I didn't realize I was still 1:20:34 muted you subtract one half from both sides absolutely assignment is subtract one 1:20:41 half because these two are attached through multiplication I can't do anything to this one but I can move this 1:20:48 one over and then that way I might be able to use the multiplicative inverse here 1:20:54 in a minute so I'm going to drop my 2/3 P down because that's what my goal was to 1:20:59 isolate the variable so I'm getting closer and now I've got two fractions that don't have the same denominator so 1:21:06 I'm going to change 12 to a six in the 1:21:13 denominator because that's the least common multiple is 2 4 six so six is the 1:21:19 smallest number that they have in common so what did I do to make two change to a 1:21:25 six I multiply times three so I multiply the numerator time three and again it's 1:21:31 negative and so 5 - 3 is 2 and I've got my six there now you could change it to 1:21:39 1/3 or you could just leave it I'm just going to go on ahead and leave 1:21:45 it all right so James what would I do next all right so we're going to use the 1:21:52 multiplicative inverse on negative 23 flip it and then subtract it from 1:21:59 both 1:22:07 sides use the multiplicative inverse I now I've got to put a negative here when I use the multiplicative inverse I like 1:22:14 it to be furthest on the outside on the left and on the right so that's why you see me sticking with them you know in 1:22:22 those one spots okay okay so I'm going to put my negative here these two are going to cancel out 1:22:29 and just give me one because that's what the multiplicative inverse skill does it just lets you come up with a one 1:22:37 and one time p is p there were two negatives here so now my P is positive and then over here I can use cross 1:22:44 cancellation two and two cross cancel out and then three goes into six two 1:22:49 times and when I look closely at that I've got 1/2 and I can see it it's 1:22:56 negative so multiplicative inverse I mean we can't do it without it it's 1:23:02 great I mean you could do it step you know in separate steps but you really 1:23:08 need to apply this skill so like I said that video that I mentioned that I have down for I think 1:23:15 it was Tuesday make sure that you watch that and watch the problem over you know 1:23:21 like sometimes I might watch one problem eight or 10 times I'm serious you guys 1:23:26 just one little section so I I can get what they're saying CU sometimes it's so 1:23:32 hard and it seems like they don't everything so make sure that you go through and watch those so that you 1:23:38 understand how to use that multiplicative inverse it's a good skill to know and 1:23:45 it'll come back up again if any of you need to leave to get 1:23:51 to a another class you can just sign off you don't have to tell me cuz I know 1:23:56 it's 9:56 but I've got one more problem to do so I'm going to go on ahead and finish 1:24:02 with this last one 1:24:24 now this skill that I'm going to show you next week which is called clearing fractions I would most definitely uh use 1:24:32 it on this problem but right now I'm going to do it the long slow way but next week I'll show you how to do it a 1:24:39 little bit of then what I think is an easier way so again I'm going to look at this 1:24:45 if I cut it into two I can see that I've got two terms on the left and one of them has a variable the other one 1:24:51 doesn't so now I'm at a twostep but with fractions and like I said this other 1:24:57 video that I've got listed as part of your assignment that you're required to watch it it's going to go through these 1:25:04 problems too in fact I'm working the problems out of your textbook so I might be working the same problems as your 1:25:09 homework so what am I going to do first I want to um get the X term the variable 1:25:16 term isolated so I got to get rid of this so I'm going to do the opposite so I'm just going to subtract 1:25:23 both sides by 3 A's now you can see I got yucky stuff over there on the 1:25:29 right so I'm just going to drop my 34 x down now8 goes into 32 so the common 1:25:37 denominator is going to just be 32 so I'm going to go ahead and slide this one 1:25:43 over I'm going to write my 32 here I'm going to create equivalent fraction by 1:25:49 multiplying 8 times something to get 32 and that's times 4 so of course like 1:25:54 this multiply my numerator times 4 and that gives me a result of -12 so I'm 1:26:01 watching my negative sign there and now I've got common denominators of 1:26:07 32 and so I can just simply subtract my numerators 27 - 12 is 15 I 1:26:17 think okay and then now what do we get to do we get to use the multip plative 1:26:24 inverse don't we so we're going to take this skill and apply it right here and we're just going to flip this horrible 1:26:31 looking fraction upside down it's so easy so put your multiplication dot flip 1:26:38 your fraction upside down do you see that negative on it I'm just going to stick it there now I'm going to write 1:26:44 the exact same thing on the other side and I'm not going to use 1:26:49 parentheses CU this is how I do it and I just like it like this this giv gives me 1:26:54 one and it actually gives me positive one and 1 * X is X so all I have to do is write down 1:27:01 X and then now when I look at this like oh nice you guys three goes into 15 five 1:27:08 times and four goes into 32 eight times and I'm just left with 1:27:15 58 and of course I'm going to iall it again and go there this was multiplication I counted one negative so 1:27:23 this is going to give me a -58 in my 1:27:33 answer all right um ODD will post uh something on band as 1:27:41 well this is my recommendation in your homework hang on a second the doorbell 1:27:48 ring I can't believe the doorbell's ringing with the snow he just that 1:28:20 Mama's back okay um so now let me talk to you about your 1:28:27 homework really 1:28:32 quick if I need to look at your homework I would upload it on iig grade I'll 1:28:39 probably shoot a video of how to um upload on irra and post it on band here 1:28:46 uh today it's going to be easier for me if you I mean I hate it but it's going to 1:28:52 be easier if you up load your homework and post it on IG if you absolutely 1:28:58 cannot figure out how to do it we really should have practiced earlier in the 1:29:03 year you can turn it in next week but you guys are going to have a test 1:29:10 assigned so if you turn in your homework next week and I can't look at it before 1:29:15 you take the test I'm not going to be able to help you so it's better if you 1:29:21 get me your homework today so try to upload your homework to ig grade I know 1:29:26 that micaa knows how to do it I know Riley knows how I'm sure James knows how 1:29:32 and I definitely know Jimmy does and I'm sure most of the rest of the students do 1:29:38 as well so it's just always great to practice uploading so if we do get into 1:29:43 you know kind of a situation like this um that we're good to go now one last 1:29:48 thing that I want to mention to you guys it really is good to upload 1:29:54 because we might have another snow I mean I haven't looked at the 10day forecast but we could have another snow 1:30:01 day next week and we could have another one the next week we've never had three in a row but we have had two in a row 1:30:07 and we have had coach have to close multiple weeks because the majority of 1:30:13 the teachers and the staff had the flu so um I'm I'm just saying that because 1:30:19 be really careful you know that you don't come you know to class six 1:30:24 and spread it to your teachers because it has caused us to have to close down for multiple weeks to kind of let 1:30:31 everybody have a chance to recover so I'm super thankful that we have um you 1:30:37 know this opportunity to meet on zoom and we can continue on with our studies 1:30:43 and like I said be sure to watch this reference video right here and if you're 1:30:48 still having trouble with it after you watch this watch it again and then make sure that you give me a heads up but 1:30:54 give it to me you know like this weekend or something so that I can help you watch the directions make sure that you 1:31:02 draw Nets when you're working in chapter 10 and um this week is 1:31:08 probably with the fractions and the geometry stuff I mean it is going to require a little bit more um you know 1:31:15 kind of taking your time thinking skills the problems may not go super fast do you guys have any questions for me at 1:31:21 all anything I have one question about uh 1:31:29 last week's homework okay it was Wednesday page 236 1:31:35 problem number seven me and my father were looking at that and neither of us could figure out 1:31:41 how to use it we looked at the answer sheet and we couldn't figure out from there so we went back to the solutions 1:31:48 manual yeah number seven number seven I believe it 1:31:54 number was it okay did you say 1:32:00 236 uh I believe so hold on let me check that it says point8 1:32:09 repeating I believe that was it okay it takes a split second whenever 1:32:16 you have a repeating digit all you do is count how many digits repeat there's 1:32:22 this one or how many digits there are that repeat there's this one so I'm 1:32:27 having you do this to see if you can catch the shortcut all you do is write a nine under it and you wrote it as a 1:32:34 fraction do you remember it yes I do 1:32:40 now me and my dad were looking at like the solutions manual and there was so many weird steps we were super confused 1:32:48 yeah and make sure that you text me when you see something like that that's what happens sometimes I show you guys a 1:32:55 little trick a little shortcut and it's so easy that we forget it so anytime you 1:33:00 see that repeating you always take it and write a nine under it sometimes you 1:33:06 can simplify it but in this case this is your final answer I don't want you going through all those steps not when you can 1:33:13 do this I mean it's like use your time for you know something else besides 1:33:18 going through all those crazy steps they have I mean I I can understand that this 1:33:24 way is so much better I mean you're going to get this answer anyway so any anybody else have another 1:33:33 one that's kind of one of those uh good little you know shortcuts to put on a 1:33:39 like a flash card and stick it inside your three- ring binder because it's so simple like I said it just takes a split 1:33:46 second okay thank well here let me show you how the creek is I don't know if you can see the creek but it's a 1:33:54 the snow's come still coming down and things are getting a good good little snow covered there all right thank you 1:34:01 guys and you guys have a great day and like I said if you can at all get your homework uploaded for me and I'll grade 1:34:08 it thanks so much all right byebye