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Math 7 - Lesson 21 Day 2 and Problem Set Worked out

Added Feb 03, 2021 •

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doing with this formula this equation the scale factor equation alright much better so we have pretty much the Writ the OG number times the scale factor equals the new so let's do a nice example of that and that's the thing about formulas I always connect are English to arm our English class to this math class for you to understand what you're reading that's why I reading that Lexile stuff is super important so you connect the ideas what does that's short for original original what original measurement the thing about what makes math complicated is that we we don't always use all the words we shorten things up so your original measurement conjure scale factor equals your new measurement and the whole thing is the scale factor tells us something so the scale factor remember if it is a fraction less than 1 we shrink it down think about it I have 10 in x 1/2 it's going to be 5 measurement is 5 cuz I shrink it down if the scale factor was bigger than one let's say two times my my length of my rope is 10 ft long I'm going to double it times to that means 20 feet long so the scale factor tells you if your new number is going to be bigger or smaller a reduction or an enlargement and that's what's important what you guys do realize we use this we have used this formula since lesson number three remember Old Times k equals new or that's not much change that to a that symbol for multiplication x x k equals y this is another way of writing k x equals y this was in lesson starting with less than three it's the same thing this is the same thing K is a constant proportion so I'm going to review run it all the way back so if you look at it like this we started after we started with ratios ratios of just turn two numbers what does compare two numbers do 524 you know they're 524 of that so proportionality what did proportionality mean it means that all these numbers were either enlarged or reduced by the same number yeah pretty much running back here so if you think about I made up some that I'm going to make a bunch of numbers so here are like a set of old numbers for personality means the group numbers are multiplied by the same number so we had a group of numbers 3 * the same number it changes proportionally cuz everything grows or shrinks at the same rate I'm just going to make an example I'm going to go 5/8 and 12 go whisks 1/4 so here's a set of numbers sorry let's move it if there's a set of numbers 5/8 and 12 we're going to multiply each one of these by 1/4 and this equals and that's one thing you needed to know in order to succeed in all of these lessons how to multiply fractions you need to know how to multiply fraction 5 * 1/4 8 * 1/4 + 12 * 1/4 and what did these eat cuz we got to set these as a fraction put it over 1 that equals 5/4 this equals 8/4 with simplifies to to this equals to 12 number for which equals 3 but I'll write 5/4 again so if we compare if we cover all this inside up we only look at the edge is 5/4 2/3 the V Force 2 and 3 proportional to 5/8 and 12 yes cuz we both applied it by the same number proportionality is multiplying by the same number but if you look at it let me zoom out in terms of what we've been turn right here that's fine go ahead used by then look at this right here are pretty much what we've been working on the original measurement times a scale factor equals the new measurement understanding that the sky all factors are they going to shrink or enlarge your measurements that's right but we can't we could not have use this not this help a lot of people understand what we've been doing proportionality solar now that's great if you didn't learn then we took our original number original is 5/8 and 12 understanding that the scale factor if it is less than 1 fraction less than 1 1/4 is smaller than what we know that it's going to be over action in our measurement it's going to shrink look at it 5:00 traffic to 4548 Frank to 212 track23 reduce a reduction so many guys use the word reducement that's not a word but I get what you're saying is the is the action of reducing I'm not going to get what you're saying yes love you guys use that word it's your made up for this fine I the root word as that reduce but understanding that's what the scale factor if I made this as a fraction or a number and a number bigger one these numbers would be and if we multiply all of them by the same number they did Dee and large they grow the same amount it shrinks the same amount it grows the same amount that's what it means to be a proportion a reed horn enlargement we've done this all before so I'm going to chew something but I'm going to do a I'm going to do a meta version of what I'm going to talk about first so we have this right here we have the formula the original number times the scale factor equals the new number that means we have the original number and the scale factor we look for the new number but if we have the new number and the scale factor how do you find the original number that's what this last lesson in a lesson before talked about so what if we had what if we're looking for the original number you can say plug it in the formula OG X original X the scale factor equals the new what if we have the scale factor in the new how do you go back to the original do the opposite you are totally correct but why do people get freaked out and they don't understand so yeah thank you you're totally correct we divide but let me explain it to them, use an example of numbers will you do something simple first we do something simple that will do a complicated things what is the same thing 5 times 4 equals 20 so we that's a true statement the original number is 5 and we enlarged it by 4 we get 20 but what if we didn't have the five some number enlarged 4 times equals 20 how do you go backwards so the whole thing is we no going this way it's five times for gets us 20 but you got to understand how to go back this is why you we need you guys to do more of the Newsela of the eye radiator so you understand the concept in math this is what you guys been doing blank * 4 equals 20 we go this way but now you got to think how do I go in reverse how do I turn 20 I don't know because I'm going to buy for think about this 20 * 4 is 80 there's no way 80 x 4 is 20 you got to think it's going backwards understanding a logic this we took some number times for got us 20 but how do we go back some number that grew 4 * 1 to 20 if we go back to Bruce Banner angry turns in the credible Hulk grows 4 times but when Hulk comes down when the whole comes down he shrinks four times and turns back deposit but notice right here Bruce Banner grows into the Hulk the Hulk has to shrink back to Banner so you go do the opposite instead of times for to go back the other way around yes show me your correct you / for so if we go one way we multiply but if we go the other way we have to divide we / this number right here so if we're looking for the original number the new divided by the scale factor equals dog the original number notice it's not multiply its divide look at this let's use our example right here creeper staring some wasted time we got to finish this let's plug in it mostly of this our new number back there was 20 or scale factor was 4 / 4 20 divided by 4 is 5 and look at this our original number five times 4 equals 20 we get what's in the box and it works the other way around 2 if we want the scale factor it's the same thing if you want the scale factor oh someone said it wrote it another way I wrote okay so it right here by scale factor other person does a fraction good good look at this so they're saying I did this new over scale factor equals OG is what I wrote last time okay you remember this part you recognize a park excellent you saw the connection or remember this this is the part you forgot the fraction line is another way of writing what division what's it this 20/4 we read it as 20/4 but the math that we do is the vision 20 / 4 is 5 Division and fractions of the same thing just written differently now is go back to the scale factor I'm looking for the scale factor it's new / the OG it's the same thing we got her number. Her phone number the scale factor what's our scale factor scale factor for we know that it's for what's the for the new number is 20 the original number is 520 / 5 for you need to know all these you don't need to lift Circle these it's great if you remember this if you're looking for the original you need to remember new / scale factor if you're looking for the scalp new / the original but all you actually need to remember is this one right here the original kind of scale factor equals the new when we get to actually percent we're going to do prom percent like sale price discount price or if you're a salesperson how to raise the price and get people to buy your stuff and still make money off of them and stuck in the nut knowing how much you're ripping them off I it's a fine line for profit but this formula right here is the same thing for you and percents like like Let it wait let's go with that you're buying a what's coming up what's the next game MLB Manny Machado on the cover MLB the Show MLB the Show 21 you know it's when you when it comes out that you see 20% off what's 20% off the price of the MLB the Show so that's the type of problems we're going to go so MLB the Show retail price x 20% off that's your new price so we're always going to use the same formula over and over and over again so you guys don't realize but don't want to talk about the show stop not going to happen this year anyways the Ronis pushing it back again so it's about using the same formula over and over again one more before I finish listen 21 on so let's do one with the reduction all right so here's your original number let's look at the scale factor equals the new number so the x is what messes people up so the original number times a scale factor equals a new number all right that I like this example does the one I use last time so so for your Keen say you were supposed to get a piece of cake not a piece of cake a cake that's 54-in long that's pretty long 54 inch cake but because of the rotavirus you had to shrink it down cuz not know becoming year old parties ruin only your mom and dad are going to show up and then the scale factor tell you how many times it's Frank down 54 Frank to 9 what did you multiply 254 to get 9 some people you have done the opposite your answers good I like it so much do some people typing in numbers or tell me what a multiplying okay I'll take that list wait a second what do I multiply to 54 to get 9 what do I multiply to 54 to get 9 that's your scale factor all right you told me but is that multiplying how do you write what you just typed in as a multiplying what do you multiply think about it I'm going to tie it together you actually have a correct answer that's just another way of saying it okay thirdlove said the same exact thing I want * the three of these three people gave me / 6 3 / 6 truth 54 / 6 gets me 9 54 * what that's why I want you to think about what we're doing remember the scale factor we see this a bigger number becomes a smaller number so it's a reduction if / 6 is another way of writing supplied by what think about fractions so good so good good good good with set it up with set it up I'm going to do it another way some you guys gave me the formula scale factor equals the new number divided by the original number all right you are true yes a reduction is less than 1 so if we divided by six six is a bigger than one how do we represent that number six is less than 1 are scale factor just plug in the numbers so a lot of people got stuck what is r scale factor that's why we change it right here the original tons of scale factor equals the new alright 54 times some number equals 9 but how about go backwards instead of times and it by 54 weeks new number / 54 to go backwards simplify this 9 + 54 we can simplify divide top and bottom by 992 9 is 154 / 9 61 6th s less than 1 so look at this is plug it back in 54 times the scale factor of 1/6 equals 9 let's check that we put this over one that becomes 54 / 654 / 6 9 this is what we're expecting you guys to be able to do to find all three of these parts no one really in a mess up but you know 54 * 160 scale factor in this case know how to find the other two numbers know how to break it up use your Lexile to see what you have and so for everyone that said x x / 6 look at this divided by 6 is the same thing as X 1/6 treated like a fraction I'm going to go off to the side right here I'm going to have some number / 1/6 if we're dividing by a fraction we do not like dividing by a fraction so we changed division in a multiplication and we take the reciprocal of that number so divided by 1/6 the same thing as x 6 but let's go this way right what if we started with a whole number some number divided by a just make up a number let's go 9 let's say we don't like division can we like multiplication it follow the same rule so this is the same as some number divided by 9/1 let's change it to a fraction so we could see it like dividing we love publication some number we change division into multiplication and what's the reciprocal of 9/1 1 / 9 and before that we're going to try and be done done before that so this is the main idea right here know how to get what's missing so let me go get our lesson 221 stuff and we'll work on it from there can you want and we'll try and do some of the homework first so during academic support I don't have to keep on doing so let me go print out the homework will do the first two problems so everyone will have half the homework so give me a second let me print that out we're just going to walk through our notes I'm less than 21 you should have had it already with you if not you can look at the first video and you know it in all right one more let's get out of this the screen and let's go back to this right here yes I am so let's go back and do a quick quick run through and then we'll do stuff of the homework problems and call it a day unless you guys are showing up to academic support remember if you are I've been assigned academic support you have to go to p.m. if you are not assigned academic support you're more than welcome to join us for the heat of it and do your work we're going to do our homework together hopefully you understand what your minds me next class is less than 22 we're finished with module 1 be a week from now next class this day next week we're going to do you practice problems on your test and then a week and another class so next not this coming Wednesday but next Wednesday next Thursday we will have a test I do not know how many questions it is right now I'm making a test so right now I'm narrowing it down I'm stuck at about 35 question no you're not doing that we're not I want to try and give you guys six to eight questions tenant most 10 if I think they're stupid fix if I think there's a little bit of challenge 8 summary so you know you will know if your sign academic support if you go on your Aries and it lists and. Ate academic support if you do not have that in Aries you are how to sign it but anyone can join it with the zoom link that mr. Garza sense it sends out every Tuesday and Thursday okay we're done talking about that let's get back to this lesson 20 here's what we worked on so far so remember we measured what's up my original class your measurement someone figured out what I guessed that my portable classroom is that really portable cuz you need a truck to drag it was 24 and a half feet wide by 44 ft long and we we shrink it down 10 times and converted that into inches so if we shrink it down 10 time it would have been 2.45 ft by 4.4 ft that's still too big to fit on a piece of paper so we change feet into inches so this picture right here in the red represents the diagram the scale drawing scale measure of the classroom at 2.45 in bye 4.4 in and then the story for this problem says let's say we have school newspaper I like your drawing of my classroom a lot they wanted to reprint it but they said it's still too big we can't fit it on the newspaper cuz it takes up too much space we need you to shrink that picture down even more so we shrank it down even more by four times that right there are 1.1 in 2.6 125 in so this blue rectangle is proportional to this red rectangle which will a scale for 4 drawing of the original classroom that's alright your back that's all that matters keep coming back even if you get that it's all good so a scale of a scale is still the scale and thing that thing is we wanted to compare all right 5 things down what is the ratio of this drawing to this drawing so we put a scale factor over a scale factor Define measurements alright and using this we can find the original you can always find the original measurements all of these Define original measurements so I'm going to the last page before I do that other page trapezoid on it let's do a quick reading on this so what zone am I in and there's a couple of more summery things will go to that to produce a scale drawing different scale so to produce you're going to make a drawing but this time you're going to do it on a different scale so you know we shrink my classroom down 10 times but let's say let's drink it down another 50 * instead so reduce a scale drawing at a different scale you must determine the new scale factor so we got to find a news go bad we can't use the old one how do you find the new one the new scale factor where is found by dividing the different new drawing scale factor by the original scale factor so new drawing scale factor over the original scale factor get you a new skip this will using the homework example the homework is actually the better one to do then the trapezoid when I do that one first so we got to find a scale factor first but do you have after I'm going to tell you no statue weighs maybe more but finding the new measurements but this right here though this bullet point read this to find each new life we're going to find a new life equals new measure in New Lenox you can multiply each length in the original scale drawing what original length OG thanks multiply that by the new scale factor what times of scale factor if we're going to be taking you make a new scale drawing we take a length x the scale factor get that's the same we're just redoing it over and over again this right here is called a recursive formula means we're using it again just to do it again it's like a care let's say on your favorite pair of pants or the expensive pair of jeans that you you cry to Mom and Dad to go buy you over ever again over at the Levi's Outlet it's not what I don't know I only go there when it's on sale 50% off is 20% not worth it always know if you go shopping and the month never go in the beginning of the month unless it's a holiday at the end of every month the last the last weekend of every month the outlets everything's always 60% or more off if you go there's other days almost 25% off your saving nothing you go that last weekend and you probably get an extra two pairs close to set the clothes yeah people shaking their head that's right get yourself a new pair of kicks I hate going to the Vans Outlet enough is all you people are there I stick with puma in the Adidas store and I might be an old man to get me a pair of New Balances or I get the Asics the Asics Tiger shoes Futsal shoes come on but anyways you you you you are you you are goofy the sucky sucky your parents to buy you a pair of $89 pair of pants and then you decided to go straight to Sharpie without a cap and you put it in your pocket now you got a giant stain in your pants Target let me see some of you guys are laughing cuz I know you did it all you guys had put a penny in your pocket and got that one tiny what do I do so the whole thing is you have to wash your pants over and over and over again you do the same thing you wash your pants and dry it wash your pants and dry that's called recursive until you're finally said okay that's good enough you can keep on taking the scale drawing and keep on shrinking it and shrinking it and drinking it you just got to do the same thing over and over and over again that's called recursive you take whatever measurement you have you * about the scale factor you get a new one if you want to shrink it down again you take your measurement that you had now we original number times by the scale factor you get an even newer number now he becomes are old enough to keep on doing it till your satisfied you guys are annoying me how do you how do you how do I take out ink stains all right I use dish soap so here's how it without messing up because someone said if you keep on washing your pants that one spot just gets faded now instead of a Black Ink Spot you got this faded spot all right I'm going to teach you how I'm going to teach you how to save your pants never ever use hot water do not use hot water and do not put your pants in the dryer until you get the stain out anything that includes your eye that includes the Dogs Out... The greasy oil from your beauty itacos that spelled the same things just like ain't never ever wash it in hot water and put it in the dryer you got to let it air-dry here's what you do the stain just bring your bring your whatever staying the same put it under the sink and put cold water on it so it's wet don't use do not use your laundry detergent used the soap used to wash your dishes with dish soap liquid Dawn d a w n dawn is the best soap that's what they used to save all all those ducks and birds that are stuck in the ocean because of an oil spill do you watch the commercials that use Liquid on to wash off the grease cuz it bites all that stuff Inc grease whatever liquid on a good dollop of liquid on over your stain your gear Taco grease stain your your marker grease day and you rub it you rub it together so it creates a ladder in that little spot keep on rubbing it and you wash it and now look at it the ink stains kind of faded but it hasn't gone away then you put some more soap and repeat but after while you're like it's not fading anymore then you let it dry air-dry don't put it in the dryer just let it hang dry and then when it's dry enough again repeat over and put it under cold water liquid on rub it with your smash it together and keep on doing it and you'll notice that the stay goes away and if you're that little spot did not fade so now you have saved your pants and you can could show your parents cuz they won't smack you upside the head for wasting $90 and you messed up your $90 pair of pants already yeah yeah I got a bunch of yeah that's what happened okay we're wasting time song that's what we do we keep on using this formula it's called recursive when you keep on doing something till you get the result that you if you're happy with yeah no but this Superior could be a lot of people so how do you find all the saints find the scale factor the scalp comparing lengths so find the scale factor if you'd if they don't give you a scale factor find it first remember one way to do it is compare and I'm using a word we using a couple lessons compare corresponding sides what I'm talking about corresponding sides let's look at this rectangle so I'm just making up some numbers I got to see two sides on this one listed in and I got one side on this one listed what's the scale factor going from here to here you can see this is an enlargement it grew it got bigger you know what's up is the enlargement number what's the scale factor soap you want to go remember it yes you are correct it's scale factor is the new over the old and you want to have math notice I want to have corresponding corresponding means matching size what's the matching size 18 in the 9 it does not match with the four cuz the four is this side right here there's nothing there long size match up so it's 18/9 which is two that means my scale factor is just double so this site is double O is it to the scale factor is too good correct so the scale factor is 2 and what do you do with a scale factor you take the old measurements X or scale factor to get your new measurement all kinds of scale factor gets you in there so we're we don't have this side but we have it on this one so let's look at that we got four times 2 equals 8 original 10 the scale factor equals a new so look at this yes it is 2 times bigger now let's go backwards I'm going to do an example similar to this I don't know I'm just making something up yes I know this side is longer than that when the numbers but that's the thing believe the picture believe we're their place than what they match up with so going from here to there here she's going from here to there you could see that it shrinks we have a reduction again this right here doesn't match with that because this is a side of match of corresponds with so if I don't care to hear this is my new number my scale factor is 3 overnight it's smaller three times but what do you multiply with Sonu over the old one third so it shrank three times a look at this one now I don't have the original number myogi so let's go this part my OG I'm looking for that one my OG X my scale factor of 1/3 equals 5 1/3 of what number gets me five so I got to go backwards OG X on 3rd gets me 5 how do I get back my original number yes excellent you guys are doing good good good good I got two correct answers even without asking nice why do guys respect here I'ma take a second out the original number the bigger side that's why you need to let it can't be smaller I took this is the bigger rectangle the bigger side x 1/3 means that shrank three times he comes five think about it the whole track to become Banner going backwards what you have to do one person you are correct so what is the number I only got two people gave me that number good what is the number then what number goes here if this site is 5 and here's dr. Banner Bruce Banner the Hulk shrank 1/3 of the time to get me Bruce Banner now Bruce yes going in reverse instead of instead of multiplying by 1/3 you / 1/3 / 1/3 is the same thing as multiplying by 3 15 excellent oh I confuse people I confuse all right nice nice nice I like this person what do you mean divided by 3 and the opposite all right I like it all right so this right here is the original x 1/3 equals 5 the opposite you are correct this person said how is it 3:00 is in 1/3 again their correct going this way we x 1/3 going backwards you have to divide by 1/3 5 / 1/3 we don't like to mess with ugly things like that that's that's that's complex fraction that's an ugly beauty is in the eye of the beholder some people think it's okay but that's why I want you to write complex fractions like this 5 / 1/3 5 / 1/3 rewrite it as division you see this you recommend I do not like to divide with a fraction change that to multiply by the reciprocal reciprocal of 1/3 this is where people forget a lot of guys remember to change the multiplication but you get lost a reciprocal is you take a fraction and flip it upside down 3/1 is another way of just writing 5 * 3 wishes 15 / 1/3 is the same thing as multiplying by 3 if you want me to write things out instead of just say it thank you just let me know this person did and that's what we see right here this is the stuff I'm going to ask you guys you know well I have pictures and all these know you're gonna have to know how to set up a picture on your own that's another thing you need to know all right let's go do a couple of problems and we'll get through this. Let's finish that say yeah by the original scale factor hey right there so you find that and then divide the given lengths that's what we did right here house this last line divide the given lengths by the new scale factor closer to the prior step what this last step is saying hey let's say I have this number how do I find one of the original numbers that's what this is saying that last bullet point let's go do something get out of piece of paper and take this down so you can actually have half of your homework done and ask if you witnessed these two will call it a day so let's read this first this a lesson summary on all the problem sets you guys should read this cuz this actually summarizes everything in all those pages into a bullet point or two Barry missions meaning different versions variations of scale drawings with different scale factors are scale drawings of an original drawing so if I take a scale drawing of a scale drawing where's my scale 9 this right here this red is a scale drawing of the original this blue is a scale drawing of the red but because this is connected to this this is also a scale drawing of the original that's what that saying from a scale drawing at a different scale the scale factor for the original scale drawing can be computed without information of the actual object like my blue my blue rectangle by Clash of I can't find the actual measurements of the actual classroom here's what you do for example if a scale drawing has a scale factor of 1/24 meaning I had no item and I shrink it down 24 times and then I decided to do another scale drawing and I shrink it down 72 times then the scale factor relating scale drawing number to to scale drawing 1 scale drawing one scale drawing number one scale drawing number to cuz that's where they change a lot of people got confused where they got this SD from a scale drawing was down 24 times scale drawing to a strength of 72 time but what are they to each other and that's all you got to do then the scale drawing from still trying to descale drying one is this 1/72 to 124 and they set it up as a fraction over a fraction a complex ratio so let me do this right here 1/72 / 1 / 24 can be re-written as 1/72 divided by 1/24 but we do not like writing division for fraction so it's 1 / 72 times the reciprocal that's 24 mifold reciprocal of 1 / 2424 / 1 that's why they rewrote it as this room here so how did this change this they did an extra step and that's why we're back to here 1/72 * 24/1 is that equal 1/3 multiplying fractions all you do is multiply across 1 * 24 2472 * 1 72 and you need to know how to simplify your fractions so we have this fraction 24 over 72 how is that 1/3 well first 24 and 72 both of these can be divided by 820 / 8 is 372 / 8 is 9 but I can simplify both of these again by dividing by 3 the end up with 1/3 scale factor between these two objects is 1/3 that means this want this 124 front is bigger than the 172nd that means it's three times as big or the other was three times as small so we can't reduce 3 time scale drawing so let's use number one right here to understand all of this is this synthesized all our work zoom out all right so if you don't get it now come back just yes if you're going to come to academic support just pay attention right now we're going to redo this first couple so you can copy it down then so pay attention to try and understand it if you don't want to copy it down now Jake read the following problem if the originals El factor for a scale drawing of square swimming pool is 190 so we got a square swimming pool we got a scale drawing that we know is 90 times smaller did the actual swimming pool so we got a scale factor of 1/90 square swimming pool and the length of the original drawing measured 8 in the other side 8 inch so I can track down my swimming pool and I got a tin what is the length on a new scale drawing so we met the new drawing if the scale factor of the new drawing is to the actual length is 1 over 102 week instead of shrinking it down 90 x we're going to shrink it down a hundred and forty four times all right hard to read that's why I shrinking time limit so the question is they're going to ask the question they're going to ask is what's that measurement right there what is the length of that side so using this idea right here I'm going to ignore this is working due to problems in one Ikon original drawing that shrink a 90 x I don't know what the original length is you know what I don't care cuz I can still find the measure of this because I know they're connected look at this right here I got to find my new scale factor first new that's not new new that's a double used factor to find the new scale factor I set up the right here cuz I'm looking for this one 1 / 144 / 190th that looks pretty, can I see some faces let me zoom in EIC eyes and like you're freaked out don't me remember this one right here this division rewrite it as the vision is going to become super easy 1 / 144 / 1 / 90 again we don't like division of fractions so what do you keep the first fraction the same and then we change division into multiplication and then we flip we take the reciprocal of the second fraction instead of 1 over 90 90 year old one and then you just multiply across we get we get this fracture I hear we'd 90 / 144 you know what I do not like to do that I don't multiply with a 9 if you have a fraction you should always check to see if you can simplify 90 and 144 what can we divide that the same number top and bottom ghilotti has accomplished trying to find a big number keep it simple Yes person right here this person is what you just used to why can I divide both numbers by 2 how do you know I can divide 90 and 144 both by 2 it should not be a question this person answered even even with the? Even yes they're both even that's what he / 2 1/2 of 90 is 45 half of 144 is 72 and I realize that I could divide both of these by 9 what is what is a 45 / 9 5 72 / 9 8 so my scale factor I'm going to use is 5/8 look at this I have my old number I have my scale factor I can find this new number OG time scale factor equals new and I'm screwed it up my OG that this right here is Lexile so you have your equation the hard part is what do I plug-in that's what reading and working and understanding what each part means I realized that I have this number I realize I have my scale factor and I'm looking for this new number cuz this came first that must be the old number I have this side times the scale factor gets me this and you side so 8 scale factor of 5/8 my new number but this / 1/8 * 5 is 41 * 840 / 8 I get five this side equals 5 inches done this work I just showed every little step man I could have skipped all that and went straight to here and simplify that so I showed extra work just the show All the Little Steps but this lot of mental math but let's look at it that's one way to do it let me zoom out and let's look at the look at his way here's what Jake reads so he decided to do this all right let me find the original swimming pool first so he decides that okay if it's 80 in and I shrink it down 90 where to go find my original so 80 / 191 90th remember cuz I got to figure out how big the original go back so he had a tin and that's a scale factor he wants to find the actual OG swimming pool so he had OG time scale factor equals new and he did this right here so this right here is OG X scale factor 1/90 equals the new which is 8 but going backwards to find the OG number 8 + 7 * 1/90 / 1 9 get the fines that the OG is 720 in what is that 60ft that's a huge swimming pool so19 growing 90 * 720 720 Vista Ridge Road swimming pool now that I take my swimming pool because it says I need to do make a new scale factor dry and what did they do original time scale factor equals new we can just wait a bit we're almost done 3 minutes or less but thanks for asking so he took he found what he found original length found actual lynx swimming pool then he took the actual length and shrink it down instead of 9 * 144 * used formula to shrink 100 three four times to find new life is he correct yes he is how do we know where correct look at this number two yeah she did it what is a scale factor of the new drawing skill new scale drawing to the original what is the scale factor of this to this day we found that out by doing the work like this scale drawing to scale drawing 1 scale drawing to 2 scale drawing 1 this trying to this drawing is 5/8 the size that ranked shrinks down 8 * * by 5 1 + 2 is done foam take a break let's take a 15 latte so yes we are done for the class. Freddy if you have mods yes what's up support so right now we got more than 15 minutes I did one and two I'm asking you what you again for people who don't understand during I can do some pork butt before you leave do your I ready so let's continue on finish the homework number 3 and number for Billet start with three so it says use the scale using the scale if the length of the pool measures 10 cm in the knee to scale drawing alright so we got the swimming pool again it's a square swimming pool and it is 10 cm long so using that sew a using the scale factor from problem number one 1 / 144 find the actual length of the swimming pool in meters so they tell if so let's write down so we got its tents the swimming pool is 10 centimeters on our drawing we have the scale factor at 1/144 Tessa and it was the actual length actual pool length ? So that is our problem right there how do we find and solve it raising their anytime you are stuck and you got this diagram and information and you know you got a formula to use you use the formula so let's plug it in the formula right here so let's go read read it quickly and then we'll go back through so using the scale if the length of the pool measures 10 cm on the news gold run do we have a scale drawing and it says start over that's pretty much what it's saying start over your swimpure Square swimming pool you have a diagram or scale drawing is 10 cm long in length but we have the scale factor 144 what's natural pool length use the formula R formula is the original length the OG length time the scale factor equals the new length the thing where you guys get messed up I'll send it in a bit let me finish this right here so this is the original length and in this case end story this is the actual length the scale factor actual x a scale factor equals the new scale length what's the actual length right here so we're looking for the actual pool length if you pug all the information in Watch What Happens so we have 10 centimeters that is the scale you are not zooming in a 10-centimeter swimming pool Eden Barbie swimming pools didn't that so does your scale length you got it that's the Lexile right that you have to know that it's 10 centimeters right here scale factor is 1 hundred 44th and we're looking for the actual length the extra point we're looking for this right here what number fits in this box what times 1 / 144 equals 10 centimeters so that is what we are looking for so I'm going to give you a second to try this out on your own and that was the hard part this is always the hard part in any word problem in any math problem if I give you a word problem information how do you translate into an equation we're going to make you yes you can make another equation if you know how set it up differently but right here what number * 1 / 144 equals 10 cm I'm going to give you a little bit of time to work that out not too much I was back we go check this and I get your number to second yes that is the number not typing sorry all right so let's play this is number 3 on lesson 21 the homework problem set number three money one can get ahold of double check that I wrote all over this one wanting to but let's assume what's the summary back in a second alright so now let's go back so we have the scales and we got the square swimming pool and now they say the square swimming pool is 10 cm long and we got the scale factor at 1 1 / 144 1 1 40/4 find the actual length here's the thing this is not book to a this is the lesson 21 math 7 find the actual length in meters meters so you got to think let's go back and finish this you got the 1440 that is a correct number what does that represent so let's look at this right here so some number times some number * 1/144 equals 10 going backwards to find this number the actual number cuz with the shrink let's try this number is a huge number it shrank by 144 times to get you 10 going in reverse going in reverse instead of multiplying by 1 / 144 it's going to be 10 / 1 / 144 that equals this number right here so we divided both sides by we end up with this but this can be re-written as a division problem 10 / 1 / 140 4 but we don't like dividing fractions let's multiply by the reciprocal sawbuck 10 change division in the multiplication change the second fraction into the reciprocal which is 144 over one technically that's just 10 * 144 and this number right here this box this unknown number which we've been playing with is bring it down 10 times 141400 but look at this that's the centimeters I'm going to look for questions that aren't going to really mess with units will we got to convert it was a trick the question said how many meters is the actual swimming pool length so this is 1440 CM but it wants the answer in just meters how many meters is the actual swimming pool length so you had this you have to know what is the can you had a convert I almost almost so there is a hundred centimeters in 1 m 8 / 100 so to convert centimeters to meters cuz that's a whole thing so. I'm do this extra you want a * 1 in 1 meter there is 100 centimeters centimeters over CM goes away so then you got this right here 1000 140 / 100 what is that move the decimal place over twice 14.40 or 14.4 meters long that's still a pretty long swimming pool 14.4 M around about a yardstick oh my gosh look at hey Siri how many feet is in 1 m what's bigger than a yard so yeah SOB X 1000 GMC you have a 1440 meter long swimming pool that's huge cuz he's messed it up one meter is longer than a yard little bit longer you know so we got to move the desk so we had to convert centimeters where's my ruler I had it a second ago cuz he got to think what's a center a centimeter is this much right here on a ruler I got 1440 of though so this right here is only 30 that's a foot let's about a foot so we got to go that's one of the that's why I messed up in that chemistry I'll be honest with you cuz unit conversion I messed up on my unit conversions a lot I didn't pay attention that when I was your age is a little bit older around your age so it's one thing that you guys are mr. C know when you guys have for chemistry he'll make sure you guys always keep on top of your measurements so we had to convert I'm not going to trip too much I might choose problems that won't focus too much on changing units so 14.4 M long let's go to the next question be if the surface area if the surface area of the floor what is the surface area of the floor of the actual swimming pool round to the nearest tenth so we're going to do a sketch of our swimming pool the swimming pool was 14.4 meters long so let's do that so we know the swimming pool is in the shape of a square and we know the actual length is 14.4 M long put each side on here but we don't need because we know it's Square I'm just putting it on so we can see it so this Square swimming pool is 14.4 M long Alside huge Square swimming pool now we have to see what the surface area is so you got to take a swimming pool though isn't just a square a swimming pool has a little death I'm going to try and draw a 3d figure our swimming pool hey there's our swimming pool because the swim pool has was called debts how deep it is you know most women pools are at a slope so yeah people can't drown in the shallow end like me 3 ft then it's a slope but let's assume it's not it's like the magic like a cake box or shoe box there is edges on it the swimming pool but surface area surface area says ignore how high it is ignore the walls if we just look at the area if you look straight down what is the area of the square forget the cube that you fill in water so what is the area of this Cube how many little squares can we fit in here how many unit squares so the area of a square good is length times width and since the length and the width of the same the area find what is a surface area of the floor of the actual swimming pool and went round to the nearest tenth we'll deal with that later area equals 14.4 * 14.4 let's go lynx wit in the Square it's the same so all we do is multiply that out I'm going to give you a second to multiply that out and then I'll do it check your answer but then it wants this round to the nearest and that's how many decimal places you want so we'll do that in a second also make sure you do that try that on your own I'm going to start in 30 seconds and catch up to you unless you're using a calculator cuz you're cheating all right so let's go. 14.4 * 414.4 * 14.44 * 4 is 16 tarot 116:17 Cheerio one 45760 placeholder and that's pretty much the same thing 675 put two placeholder zeros one so it's for 4 and 1/2 add that 61301 what is this 1 * 566 + 4 is 1010 + 7 is 17 carrier one that's 10 carrier one to 20736 I said don't worry I'm multiplying a my fault you don't see it let's go see so I multiply 14.4 cousin wants the surface area right here so I'm multiplying to get the area so I got 20736 but don't forget there two decimal places so I got to put two decimal places right there so 207 36 now the whole thing is the instructions also said round to the nearest tenth the 10th is right here but in order to round to the tenth spot you always got to look back one space anytime it says bounce whatever space it is you need to go one decimal place back rounding 207.36 I need a dime look at it like this think about in terms of money 200 $7.36 I need to run to the nearest dime the nearest Ten Cent since I was going to be $0.30 or $0.40 that's why the penny comes into play if it's 5 or more Chinese you round up to the nearest dime one up if it's less than 5 pennies 4 or 0 you just cut it off so 6 is greater than 5 so that means the three needs to raise up by 1 so it's 207.4 nearest tenth so that is the area the area is not equal because we had the roundoff is about that's the samba what about if you remember 207 point for all right so that's the flat area of the swimming pool I drew my nicer 3D diagram of a swimming pool not that we need to drown in it but cuz it's go to the next question right here so running herself already got it see if the swimming pool has a constant depth of 1.5 m is the volume of the swimming pool round to the nearest tenth. Let's do that again so 14.4 14.4 and this right here is one .5 1.5 that's how high or How deep the swimming pool is that's Lexa understanding the debts Now volume I'm going to do something there to formula volume volume means how much water you can fill in right here if the Constable was the cause of death of 1.5 what is the volume of the pool volume is how much water you can fill in let me see if I got a bottle of water I don't have a fluid at but I have myself knock off Lacroix I got the Safeway brand list soda notice right here though it's measured in fluid ounces fluid ounces is pretty much how much space it fills up in terms of ounces so if I got a can opener and cut this out that's how much water 12 fluid ounces fit inside inside my can so how much water the volume how much water can fit in it so it's not a flat little square when you're talking about volume is that little Cube how many cubes of water fit in there am I driving it right looks like I'm driving it right now and I messed up on the second one but how many little cubes can you stack next to each other to you completely fill it in so that's the volume volume has the original formula of length times width x height but what's length times width length times width is area area times height that's the volume so that's why we did this problem before we did this one we already know the area let's save I'm so the volume is the area times the height and the height is 1.5 meters high so volume is 207 point 4 times are height of 1.5 how it is multiplication then where did the work I'm going to show you though this is only an approximation 2 7.4 * 1.5 that's volume area times height of 4 * 5 is 20 carrier to 3537 carrier 3 peanuts at 3 attend is there a placeholder for 702 that's added 11 carry a 11011 carrier one 3 and we got two decimal places 311.1 cubic meters meters to cubic meters cuz this was in meters so 311.11 decimal place boom but here's the thing where did this 274 it came from here area should have been this let's see though I'm just going to do something different and show you it should be the same thing even when we round up let's go 200 7.36 * 1.5 6 * 5 is 30 carrier 3 15-18 carrier 135-36. 30263 and then we get 10 right here we got a tattoo place 63702 84 Des 14219 10K and 11113 we got three decimal places look at this right here hello which is correct and it says round to the nearest tenth if I round to the nearest tenth it's just 311 is that 311 + 473 + 311 + $0.10 sorry dog barking now I'm going to tell you this 3 111 should be the answer even though it said round to the nearest test 3.11 because right here this add this prom asks us to round the air round off the air to the nearest tenth around 8 to the nearest tenth we use 2.0 - 207.42 * 1.5 and we got our way down here there's our answer but if we did not round the area and we use length times width times height we would have did 207 point 36 * 1.5 little difference right there. Just look at that little bit of difference 207 and thirty-six cents 207 and 40 cents * 1.5 that $0.04 makes a huge difference we multiply it out 311 and 4 * 311 and 10 cents if we round to the nearest tenth 4 is less than 5 so we cut it off no. 311 vs 311.1 I would not knock this off cuz I see both pre-algebra and a 7 so they both count knowing how to round off so it's both example of both so this is a better answer than this one but I would not take away points for this one because the previous question ask you to do that rounding off is an important thing it's a thing that hurts a lot of it hurt me cuz I messed up in chemistry hey I know the difference is when I can fix things but all right so that's that let's go on to the next question look at this practice stuff if one cubic meter of water equals 264.2 gallon so in one little meter so just imagine you make a cube that's a meter by meter by a meter hair let's draw a picture that so one keep so here's my swimming pool how many cubes can I fit in there about 311 but depending on this one 311.1 but let's ignore for now but one Cube just imagine I have forget one cute think of this is a can of soda in a basic can of soda this is not soda this is Apple sparkling beverage water knock-off Hayes to Safeway knockoff LaCroix this can fit 12 fluid ounces you can you got to talk to the counselor you can you can just I have your parents that's not call the school talk to counselor so you know the school so this here you have the cube this too bizarre can is in this cubiscan it says it could fit in let's see where did I have it when it is 264.2 gallons water the volume equals 264.2 gallons of water high quality H2O you fit in not much all right how much water will the swimming pool how much water will the pool contain went completely filled round to the nearest unit nearest unit mean no decimal hold on let me just being without you so how many of these has how many gallons of water will fit in so since we have the volume that's how many cubes that can fit in each Cube has this much water so we actually got to multiply this right here and round to the nearest I'll do both and show you it's pretty much similar so well round to the nearest gallon of waters what it wants so will do 26 4.2 * 311 and will do to 64.2 * 301.11 the decimal see what the difference is going to be so you know what you got a lot to do and let me just use the calculator 264 .2 * 311 82166.2 gallons let's do this 126 4.2 * 311.1 8080 2190 2.6 to look at that one other one extra decimal point raise the amount raise the amount of water look at that difference even one decimal place changes it route to the nearest whole unit though 82166 gallons of water if you go to this one 82100 here's our we want whole units we don't care about that 6 May set of 3 8080 2193 we've been tricked there pretty much a 30 almost 30 and pretty much 27-gallon differ 27 gallon 17 gallon difference my fault 17 17 gallon difference so that is I would have to take both answers cuz I didn't say which volume to use both answers would be correct so one of the other and this last one complete a new scale drawing of your dream Zoom from problem set in 20 by either reducing by 1/4 or enlarging it by 4 I'm going to use my classroom measurements in a second so I'm going to shrink my classroom down by 4th what you kind of already did and I'm going to barge my classroom by force by 4 so you can see the difference will find her new measurements in a second so try and do yours first the Cy your room attract I'm use my classroom measurements you should use your room measurements from your problem set yes let me finish this last problem and I will do that 3.2 and the decimal thing so for this last problem right here for the homework Cletus complete a new scale drawing of your dream room from the problem set lesson 20 either bruised by reducing it by 1/4 or buy large it by 4 and I'm going to show you that the reduction would be better let's do a quick sketch of my original classroom remember the classroom is a rectangle it's supposed to be 24 and 1/2 ft wide 44 ft long I don't have a big enough piece of paper again to Jamaica actual picture that big so we can reduce it so what do we do remember you your original measurement times the scale factor that equals your new measurement so original measurement we're going to do it twice that's what it means to be proportional so we're going to actually I'm used to different colors do you like that with Asko Inc and we'll use a scale factor and so we're going to take the original now 24.5 and we're going to multiply it by the scale factor which is 1/4 cuz we got to reduce it shrink it down and then I'm going to multiply the other side 44 feet x the same scale factor and we're going to get a reduction I reduce them both by 1/4 so it keeps the same shape and that's what we're do right here so let's go Eagles equals so 44 x 1/4 that is 44 / 144 / 490 11 11 feet shrinks it down to 11:50 and then this one right here by stroke it down by four man I can't do it on top what I'm going to do is convert it to multiply across I'm going to get 24 and 1/2 / 4 that becomes what is that at 4847 / 247 / 2 / or which is the same thing at so what I did is I change this mixed number to a improper fraction and then I change this into a / 4 but I don't want to divide I want a x my reciprocal which is 1/4 40 7 overate what is that now 47 / 847 / 8/8 * 5 5 7/8 of a foot and I could convert this I could convert this to a piece of paper hair let's see so my actual drawing so here let's go take even though it's not actual the actual classroom is 24.5 ft long Why by 44 ft in height but if I reduce them both if I reduce the whole thing by a force I end up with a 5 and 7/8 footlong by 11 feet long is a piece of paper which is still huge but I can convert this I can convert this to a pretty much a piece of copy paper piece of copy is 11 in Long by 8 1/8 and 1/2 in wide so I just cut off a little bit hey I got a scale drawing if I decided to increase it though if I decided to enlarge it so this is the read action I shrink it down but if I decided to enlarge it instead of multiplying by 1/4 I would * 5 so let's look the enlarged measurements 24.544 instead of the scale factor being 1/4 the scale factor would be for if I was going to do the opposite and enlarge it instead of shrink it down four times I'm going to multiply 4 times that make it bigger so I end up with 24 / 9 h 176 South this would equal 98 feet by 176 ft I would still have the same shape but instead of a shrunken down to a piece of size of a piece of paper type of a thing this would be 98 ft long Disturbia 176 if I decide to make it bigger 4 times the difference between an enlargement and a reduction is one the reserve in a reduction my scale factor is a fraction less than one If I multiply it out look at the numbers I get 5 and 5 and 7/8 inches vs 24.5 11 feet feet inches versus 44 that's a reduction and enlargement X number bigger than one notice it grows four times a Grue for tie shape stays the same but it gets bigger

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