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Math 7 - Module 1D - Lesson 18 Problems Worked Out

Added Jan 14, 2021 •

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this is the exercise this is the last example from the note that you were supposed to join your own and we're going to go over this before we start the homework so after this will be the first homework problem so use this this is a good one right here to have for your notes for let's say a test sometime down the line someone else was a test I think two to three weeks from now students why is it crooked that's better that's better students from the high school are going to the perform one of the acts from their upcoming musical at the atrium at the mall students want to bring some of the set with them so the artist can get her better feel the whole production the backdrop the scene the background but they want to bring has panels that measures 10 feet by 10 ft the students are not sure if they will be able to fit the panels through the mall entrance since they need to be transported and transported and each panel was 10 x 10 they get a copy of the mall map and they want to see if this diagram is able to fit so the first example I showed was that you do not even need to use the formula stuff you could do it just might logic so we want to make sure that the 10-foot by 10-foot wall panel can fit through this 3/8 of an inch muldaur and look at this scale right here 1/8 of an inch on drawing represents four and a half feet in real life that's 1/8 but the mall door is 3/8 so it's three times as big as this I change 4 1/2 to 4.5 cuz it's easier to multiply 3/8 is 3 times bigger than 1/8 so 4.5 * 305 * 3 is 15 Korean Won the mall Doris 13.5 my feet why and if the panels are 10 ft of course you can fit it through so I'm going to do a drawing I'm going to do two ways so find the actual distance of the mall entrance I'm going to do this way again but Picture Show this is 1/8 of an inch I'm going to say that's one eighth of an inch in real life that is 4 and 1/2 feet long so now I'm not going to make a bigger one 1/8 I'm using number line 1/8 2/8 this is 3/8 cuz remember the mall doors 3/8 which is why 1828 3/8 so each one of these is four and a half feet long floor 1/2 for 1/2 for 1/2 so together that makes 13 1/2 Connell equal 10 ft so enough room yes enough space you have enough space to fit it through now here's another way to actually do it remember we want to figure out what 3/8 is in real life so we have that formula so we need the scale factor what is the scale factor we always look at this scale factor is real life measurements over the diagram measurement and the scale tells us whether scale factor is in real life we have four and a half feet in the diagram you have 1/8 of an mixed number over a fraction you got to change that to simplify so let's do that's not too hard change the mixed number into a fraction 2 4 is 8/8 + 1 is 9 so that is equal to 9/2 over-18s and we got this complex fraction this weird keep on doing you need to understand that a fraction is another way of writing division so instead of writing it as a fraction we're going to write this complex fraction as a division of fractions 9/2 / 1/8 this little step right here was the heart with S easy as it looks right now so many guys forgot this these were the last 2 questions on your final last semester what are simple it is and all you got to remember is that dividing fractions is the same thing as multiplying by the reciprocal so we got to change a division or multiplication and this the reciprocal is 8 / 1 and so what does this become 9 * 8 is 72 72/2 another way of writing that is 72 / 2 which is 36 that is our scale factor what does that mean it means in Real Life 1 inch equals 36 feet 36 ft matches corresponds 2 1 inch is 36 over 136 ft course that's word corresponds to one in what does italic so if 1 in is that much what's half an inch half an inch is 18 ft look at this right here 3/8 is a little less than 1/2 the west and 1/2 is 13.5 you can easily guess that you can fit at 3 so how do you say there's another so we this right here is just using logic look at the amount of writing look how quick it is to find the measurement in real life if you just had your scale factor scale factor x is the most work and you got to remember how do you find the real life measurements it is diagram diagram measurements timescale fact equals real life measurement so what's our diagram measurements are diagram measurement was what 3/8 of an inch what was our scale factor we found our scale factors 36, draw an arrow to it 3/8 x 36 that is what are real life measurements going to be and this is where people met kind of mess up and they're like oh I don't know what to do when you have a fraction X number change the other number into a fraction whatever this answer is that your real life regiment so 3 x 36 I'm going to do it off to the side 18 Carol 1108 so it's 108 / 8 I don't know what that is that's the top of my head but what I do know is I can divide again / 2 / 2 I get 54 if I / 2 I get four like a / 2 again / 2 I get to / 2 2727 / 250 real life what is 27 / 2 in real life well let's just do that 27 divided by 2 goes into 1 time Northern Tool X look at that 13.5 ft 13 and 1/2 ft which one's better they're both the how does 4 and 1/2 it my fault I didn't see it as a lot of people are looking changing a mixed number into an improper fraction or an improper fraction to a mixed number knowing how to go back and forth the right here we always we never want to play with the mixed number when we're doing work as an answer cool but as work you always want to change it to a fraction so to change any mixed number when you have an integer in a fraction just a fraction you take the bottom number times the whole numbers are 2 * 4 is 8 that number you add it to the top number line has let's do a quick example before I move on to the Walmart so I'm going to make some messed up looking mixed mixed numbers go into 8 and 5 sevenths so how you do this right here you always keep your denominator you know the mom's going to be 7 cuz it needs to match up what you do to find the top number you take this bottom number and you multiply so you go this way it's like a half circle 7 * 8 that's 56 and then you add it to 56 + 561 so that's how you change a mixed number to an improper fraction all right so let's go to the homework and you should be able to turn it in today or at least most of it or get most of it done and finish the rest alright let's do this together thank you those that are here and understand that we can do the homework together your grade up a toy company is redesigning its packaging for model cars graphic design team needs to take the old image shown below Andre sizes so that half an inch on the old packaging represents 1/3 of an inch on the new packaging find the length of the image on the new packaging because no longer is it real life it's what you want is the new over the old car image length in the old packaging measure so they give you measurements so find the length of the image so they measure the right here so let's first create our scale factor member here how to find a new measurements so I wrote down one formula that was like diagram measurement times the scale factor equals real life but this isn't real life really let's Translate we want the old packaging today new packaging another way is to say this old time's the scale factor equals the new and so if we're doing this if we're doing this the scale factor is also this to the scale factor is equal to new over old who is bothering me I do not know who you are so let's look at this the graphic design team needs to take the oil damage there's the old damage and we're going to have our new image so scale factor let's put it on this side scale factor is 1/2 and 1/3 those are the two numbers were going to play with remember it's a new over old the new is 1/3 the oldest 1/2 one-third to one-half that's our scale factor kind of funky looking but you can always change it to something simpler looking you just need to remember what this is right here and good a lot of guys got that it needs division so when you have a fraction over a fraction or a fraction in side of a fraction rewrite it as a division problem division problem 1/3 / 1/2 dividing fractions we still don't like that we still dividing fractions we need to change it to multiplying fractions and a lot of guys can do that take a second out and you'll see what the scale factor is in a second I'm going to wait a little bit so you get a chance to look at it and do it one one third divided by one half trying to do that on your own I'm going to give you a second well I take a sip of water if you got the answer put it in the chat box let me eat so you can check your answer with what I'm going to put in a second good you are correct that is the scale factor the job so the hardest thing is one the hardest thing first two parts first set it up as a fraction number and if you have a fraction over a fraction need to change it to division the first we're trying to find the new length and if you're always trying to find the new like you using a formula old or the diagram x a scale factor gets us the real life new number that we want so it says we have is packaging that's 2 in long I want to find the new length but they give us a scale 1/2 in Vizio old one and it wants to scale to be one-third on the new one so that's why the scale factor is new over old so new is 1/3 / 1/2 so first always find the scale for us to use this equation we need to scale factor and once we have that all we got to do is multiply the old measurement that it gives us to find the new one so 1/3 / 1/2 fraction over a fraction we don't like having a complex fraction next thing after you write this I'm going to change it to a division if you have a complex fraction but again who likes dividing fractions multiplying the reciprocal the reciprocal multiplying the reciprocal 1/2 which is 2/1 and all you got to do is straight across so the scale factor is 2/3 I'll put that right here so in this equation that's our scale factor x 2/3 old-time the scale factor equals the new number that we want and look at this right here this is what we're playing with the car image is the from the old packaging measures to what's the old the old is to 2 * 2/3 equals our new measurement this is a fraction this is not change this into a fraction 2 inch ecom's 2 x 2 1 x 3/4 / 3 in so now we have an improper fraction now we need to go backwards how do you make an improper fraction into a mixed number you just divide and keep the remainder don't change it to a decimal this is our new measurements but that's a mixed number let's change it to a improper fraction let's change the mixed number 4 / 3 three goals in a 4-1 time and we have a remainder of 1 so 1 and you take this fine and you put it here and over that like they're 1 1/3 inches so on the old packaging this car is 2 inches long but on the new packaging watch out watch out how is it to jerseyman No One the Run Okay so we're not okay so 1 divided by 1 gets us one true but what's 3 / 2 she got a skill 3 / 2 but he had a flip it 2/3 they're so yes one / one gets you one but you got to go across you could do the other way but what's 3 / 2 so then you have to deal with that are you doing on separate piece of paper do it that way so a lot of people confused on that part so let's do it this way 1/3 / 1 / 2 1 / 1 to go across and 3 / 2 you can do it this way also but people get stuck right here so 1 / 1 is 1/3 / 2 you don't really get anything yet something messed up so let's rewrite this as a fraction 3/2 but this right here is still a complex fraction so we can rewrite this as one / 3/2 but we don't like dividing a fraction we always want a mole fly by the reciprocal witches 2/3 1 * 2/3 2/3 dividing fractions that's why I lock people just say magistrate up by the reciprocal cuz you end up with the same work anyways so remember these are the formulas you want to find if you want to find the new number or the real life number it's the diagram old times scale factor you don't have to but it helps to understand what's a good number two the city of St Louis is creating a welcome sign on a billboard for visitors to see as they enter the city the fall picture needs to be enlarged so that 1/2 inch represent 7 ft and the actual billboard will it fit on a billboard that measures 14 ft High so this right here they say is half an inch 7 ft the following picture needs to be in Marshall that 1/2 inch 7 ft hot so let's measure this so you need a ruler this line from the top to the bottom is one inch long from here to here how high is 1 in and we need to make sure that it fits let's use some logic let's use some logic here's what I'm going to put it off to the side here I'm going to go that's what that's about the same this is one in which if I cut one inch in half would you like a number line 0 is 1/2 here's 2/2 which is one in the whole thing is 1 inch so if it's a half an inch that represent 7 ft and if I have another seven feet does it have to have how tall is it total if half an inch look at this right here half an inch represent 7 ft in real life here is half an inch 7 feet in real life and if I stack up do midgets standing on top of each other if what if one midget what happens midget is it is in large There's 7 feet also no longer are there midget there it's like a it's like the guy that made Thor's hammer Stormbreaker Stormbreaker Hammer Stormbreaker in real life is it is a short person in Thor in Thor it was end game will go over a 16 in a bit she was a giant so if your giant is 7 foot high and you stand another giant that's the same height on top how tall is that Social Security ears 7 here to here is 777 makes how tall good 14 so I will do that will fit on a billboard that measures 14 feet high yes it will yes it will so this is just using a bar graph so you don't need to do all that complicated stuff like up here because you figure this stuff out just by drawing lines and these are lying grass line pictures bar graphs tape grass just by using like I call it the Lego method just connecting pieces together you can actually figure this stuff out without doing anything and that's that right there number two just told you that 1/2 equals 7 in 1/2 and 1/2 makes one hole that's the only thing that logic part deal with all right let's go get number 3 your mom is home okay we got to answer will it fit on a billboard that make yes it will fit your mama is repainting your younger brother's room that's messed up your room is still messed up cuz you as a child she didn't want your younger brother is the child she wanted that's why she's rude and then she looks at you can see the side eye she's going to she's going to project the image shown below onto his wall so that she can paint an enlarged version as a mural so some he hasn't seen they get like a little overhead projector and the getting my soul train see that little train small little train and she puts it on overhead projector on the wall so your baby brother gets a train on his wall use a ruler to determine the length of the image of the train alright so you need a ruler I'm going to do it for you cuz most guys break your rulers and you don't have one select a measure this so how long is the train the train from end-to-end is 2 in SO2 in long so let's write this down to in can use a ruler to determine the length of the image of the train then determine go buy a new ruler use a real determine the length of the image of train so we figure out it was 2 in then determine how long the mural will be if the projector uses a scale or 1 in the image represents two and a half feet of the wall even easier I'm going to stop and give you a second let's read this lessons together some of you guys thank you some you guys already got the car answer put it up thank you for letting me know yes it's easy 1 inch of this image this is the image one inch of this image is 2 and 1/2 ft on the wall when it's projected so how long the Wall how long on the wall is the train going to be if 1 inch is two and a half feet on the wall you have two in here Lego pieces 1 in 2 and 1/2 in the wall what is the train in real-life correct answer all right I got four people who put up the correct answer for me already ciresi ice think about it don't, get a stop looking out the window Derek's not out there all right what is this with I'm not even going to use I'm not even to use the calculation stuff I'm just going to ask you do you diagram drawings so this is very important skill you want to match this so this is true in right here with ruler if I measure 2 inches that means half of this if I cut it in half that means here to hear is 1 in here to here is one inch and if they play one in two and a half feet let's use another color where we can easily see in Real Life 1 in 2 and 1/2 ft 1 in 2 and 1/2 ft I ran out of space but in real life cuz I'm going to transport this Violet up top so if this here to hear cuz it's halfway 1 inch and 1 inch that makes two in two and a half with 2 and 1/2 ft if you combine these Lego pieces together in real life how long is it thank you for people I'm waiting for more people to type in how long is it in real life here's one in one in two and is also one in two and a half feet think about combining them together correct five people have got it right so in real life 6 7 guitar I just put it in so for those guys those that don't see all you got to do is add these together 1 in 2 and 1/2 ft $2.50 and another in 215 250 that makes think about this if one in two and a half feet what's 2 in double that what's double 2 and 1/2 5 that's another way to look at it 2 and 1/2 x 2 all we did was double this 2102 / 22 * 2. Solve for 4 plus 1 equals five that's another way of thinking about it good jobs with those you guys outside I listen to this one right here this one's harder for one reason there's no picture here's the thing so I doubled 1/2 that gets me 2 / 2 1/2 and 1/2 so that's two has and then two times two is four I already doubled it so I got four and one for Monday 5 so yeah so you got it this next one is harder on because there's no picture a model of a skyscraper is made so that 1 inch represents 75 ft what is the height of the virtual building if the height of the model is 8 3/5 in 18 in equals 75 ft and I got 18 right there you can do the whole number and then you can do the fraction so you got to think what one in is 1 in 1 inch on your model represent in real life 75 ft you have a model that's a whole thing this is like what it be I don't have a 18 3/5 in to draw a line so you need to know right here that this is supposed to be my skyscraper this is my building right here. My TransAmerica building I'm making it up my pyramid how tall is this my model my model is 18 3/5 in how tall is it in real life what is it in IR what is it in the Earl so this is your model of us like that model in your model 1in matches 7 in real life your model is 18 3/5 in so if its 18 3/5 inches what is it in real life so first we want to find our scale factor remember scale factor let's use dark color scale factor is real life over diagram real life is 75 model is 1 so our scale factor is just 75 yes you multiply good job to job that's all you do I'm going to give you a second to multiply it out to see if you got the right answer I'm going to give you a second to multiply before I set it up so I'm going to write down the farm the rest of you that didn't get it so for us now we got the scale factor we want to find the real life new measurement in order to do that alright we're I'm going to stop I'm going to write the formula first I want you to set it up first so the setup remember is the diagram model thanks times the scale factor equals the real life measurements real life that's measurements I want you to plug in a even if you don't know how to do it I want you to plug it in to set up this equation I want you to at least write down and for you if you multiply it it check your answer in a second after I give these people some time to write down this equation show what is the diagram modeling in tainted what is a scale factor we're looking for that that still unknown so write it down I want you to write it down first that's the thing about math even if you don't know right down as far as you can go don't quit even before he could get more points get as many points if this was a test question and you gave me these measurements I'll give you a half a point at least you understood that it needs to match up if you wrote down the scale I'll give you a point and a half cuz you realize I got to find my scale factor if you're able to write down and get as far as the equation you're halfway there I would give you two out of four points so diagram model is 18 3/5 in enter scale factor is 75 we don't have a real life measurement cuz that's what we're looking for in real life so we got a multiply these two real life that are L stands for real life measurements measurements real life measurements measurements so we can't do mixed number while we can but it's not worth it change it to an improper fraction 18 * 5 + 3 * what is 18 * 5 8 + 8 what is 45 * 1018 * 5 is 9090 + 393 / 5 so I'm running out of color but let's 93 5 * 75/1 that's our real life so you can't see it let me read it while you're copying it down I know we're all running out of room 93 / 5 how did I get 93 / 5 + 5 * 18 is 9090 + 3 is 93 so the improper fraction of this mixed numbers 93 / that's five and then multiplying it by 75% this is a fraction I'm going to put it at 75 / 1 we got time we got time plenty of time so this is let me write it up in this space so cuz we ran out let's put it over here I'm going to rewrite it 93 / 5 * 75 / 1 equals the real life measurements oh man this is all jacked up 93 * 75 and then divided by 5 that's that's a lot to deal with but I'm going to do something else I'm going to show you why you can do this is called the commutative property something to write it like this unless I'm going to write it on a sudden don't copy this down look at it stop copying look up so when you multiply fractions you multiply the numerator X the numerator and the denominator X adinon so we made two fractions into one now I want you to look at it as another concept when you multiply numbers it doesn't matter what order you multiply them and look at what I'm saying is 4 * 5 equals 25 times 4 equals 20 so I'm not going to multiply yet my fault 4 * 5 is 25 * 420 it doesn't matter what or we multiply it's going to be the same number so instead of 93 * 75/5 * 1 I'm going to switch it around going to go One X 5 why did I do this what happens if I break it up into two fractions now 93 / one that's 9375 / 5 that is 15 I'm going to rewrite it like this just so you could see 93 * 15 + 93 * 15 is so much of an expression that 93/5 * 75/1 which is 93 * 75 I don't know what that number is and I don't want to know what that number is and then I divide by 5 so it's called the commutative property so let's just multiply 93 * 15 5 * 3 is 15 carrier 145 46 465 0 placeholder than you got 93 and let's add 5 9 1395 there it is Loop sorry ran out of space so let's put this back over here so let's do it over here 93/1 * 75/593 * 15 equals 1895 through 1395 ft real life so if you had a model that was 18 3/5 in Long in real life it is 1395 feet high you were right and I'm going to show you another way to do this right now before I move on so that's using that the calculations and whatnot let's use a model let's use a bar model again so let's look at this right here we know the models 18 3/5 inch high so let's go teen and 3/5 we know that 1 inch equals 75 so let's do the 18 first suppose 75 * 18 75 * 18 so that's going to be 40 carry or a T56 600 075 so that is 1350 so 18 inches is 1350 ft what about the 3/5 so let's go give this so 1 inch equals 75 ft but V is 5 pieces let's cut it into five pieces one so that would be fine equal pieces let's say these are all 5 equal pieces out of Assisi they're not I got one piece two-piece three piece for piece five pieces right here five sections 3/5 is right here this is three 7 inch in real life how high is that let's look at this I have one in I know it's 75 ft if I divide 1 in the five pieces let's divide 75 in into five pieces 75 / 5 that means each one of these little pieces is correct 15 15 15 15 15 * 5 is 75 but if this is 15 right here this is 15 right here 15 + 15 + 30 30 plus another 15 for V that means 3/5 is 45 ft high that is 3/5 of an inch 45 plus the eight BHM which is 1350 1395 the same answer without using a formula and just using logic and that's why you should play with Legos if you understand Legos and how they connect side-by-side to find the lengths this is Lego logic that's not a correct term play that up Lego logic can actually help you find it let's look at this gibberish like you just said it's complicated for you but if used Lego Logix and building blocks if the same thing except you're thinking it through with pieces you can do that I'm not saying don't do it all right let's look at this right here for more problems as far as we get all of these we have no space to do it so I'm going to get scratch paper it's a favor I would suggest you do it on a separate piece of paper to cuz look at this that's why I hate this when they give you the problem set they give you no room give you a note Room be like that use up her whole notebook except she's not writing any of this down cuz it's just one name over and over again that's not true though every single thing that you've been saying okay along with the one word the portrait company that takes little league baseball team photos is offering option where a portrait of your baseball post can be enlarged to be used as a wall decal sticker that's like those fat faces those fat face stickers that you can order I see some of your backgrounds Wenatchee has a fat face BTS of one of the BTS guys not any of you guys here obviously anyways your height in the portrait measures 3 1/2 in sew in they're able to photoshop you out of your team picture take you out and your 3 and 1/2 in your the size of a GI Joe action figure if you guys know what GI Joe is is the company a scale where one inch on the portrait represents 20in on the wall decal so old vs new find the height of the wall decal your actual height 55in if you stand next to the wall decal so it's two proms in one will it be larger or smaller than you that's a second question right there is it time to go no and the 330i 30 minutes play the time it's all good so let's look at this let's first let's go steps steps fine scale some of these two ways first I'm always going to do the formula way and we're going to check or way using the logic Lego logic way so find the scale factor if you want to find a new man I meant to use scale factor to find new measurement now what's the formula so since we don't have all these different things we don't need to teach art but you do need the formula the formula so 1 Formula was diagram length diagram measurements times of scale factor equals real life measurement RL real life the other one which matches this let's say we're not talking about something in real life we're not we're not even doing the diagram old your old measurement * your scale factor equals your new measurements that you want so let's go through this store and first let's set up a scale factor say blah blah blah blah blah all right so your height in the portrait measures 3 1/2 in if the company uses a scale factor for 1in on the portrait that's the old one represents 20 in urine cuz you're going to make a new wall decal so there's a scale factor new overall here's the thing there's two new and old this is new and old I'm put this the scale from the scale that's a new note I haven't played in yet so from the skeleton of the scale work for that scale 1 inch represents 20 in so news 28th August the 1 and it's just 20 scale factor is 20 let's go through and plug it in your height in the portrait is 3 and 1/2 inches so you take the oil a three and a half and you're * 20 that's how high the decals going to be fine so 3 and 1/2 that's your old height from the picture from the picture cuz we're going to change this picture into your fat face sticker decal that you're going to throw on the wall so 3 and 1/2 x scale factor which is us is this going to be a fraction that's right the scale factor is 20/1 this will equal or fat face decal let's write new new decal that's what we want to look at how tall is it going to be mixed numbers we don't like mixed numbers change to improper fraction so if you're stuck again you like I don't know what to do with the mixed number take a second outlook here's how you change a mixed number into an improper fraction rewrite your denominator which is to you take your denominator X the whole number 3 x 2 which is 6 and then you add 6 + 1 7/2 that's how 3 and 1/2 become 7/2 and we're going and then multiply it by our scale factor 20 / 1/7 * 20 / 2 so that is equal to 140 / to 140 / 2 that equals 7 inches 70 that's how tall the decal is 70 in 70 let me zoom out so we can read the problem again now it's too small you can't see so your decal height of your decal is 70 in let's go look at this right here so find the height of the wall decal so your fat face decal of yourself cuz you're that are to have your own face on your own wall it's like having a poster of yourself from here since from scale from scale all right so we now know or decal is 77 in 770 in tall your actual height is 55 in if you stand next to the wall decal will the decal be larger or smaller than you looking at this the decal is 70 your 55 which ones bigger the details you are 55 which ones bigger yeah just comparison of numbers good the decal is bigger but let's look at this if you stand next to the wall decal will it the decal be bigger or smaller than you is larger than you larger than you 70 is greater than 55 since I'm getting a couple of the same comments a lot of people think I'm just having problem doing the calculations stuff I guess this is the calculations. Let's say you do not know how to do the calculation stuff but you can draw a line drawings Guess store with that let's do this with line drawings a lot of guys are freaked out we will practice this stuff right here this is always practice but you can still get the right answer even if it's safe you keep the word I get from you guys it's complicated but you say you understand the idea all right let's go with this our scale drawing it says 1 in so that's why you have yourself sketches here's one this is 0 to 1 in that's one inch and I told you that one inch on a diagram will represent 20 in in real life so you just have a mall right here so this is supposed to be 20 now the picture of you and you know they don't need to be accurate 20 to 120 over one came from this sentence right here if the company uses a scale where one in on the portrait one in the picture represents 20in on the wall decal it's Lexile So reading is very key to this so 1 in equals 20 in in real life for the wall decal and then even though it's not match up here's a picture of you they say they got that that they were able to photoshop you out yes you're a stick figure and you your height is going supposed to be 3 and 1/2 in turn on the picture 3 and 1/2 inches but the decal the decal you know is going to be 20 times bigger than this will it rain here the decal is so this right here is the decal of you this is going to be on the wall creepy stick figure is 20 times bigger so this right here is the decal and you know what the scale factor is 20 times bigger so he got three and a so if you got one of these you got to take your stacking 20 of these high 20 more of these is what it's going to be bigger she got 3 and 1/2 3 1/2 + keep on doing 3 and 1/2 more you get 20 times 20 times more 20 more times and that helps you get a clue so that's just three and a half * 20 so you just add three have to run a 3 and 1/2 3 and 1/2 you do a 20 time and look at that swear this comes from this Lego Lodge help you understand that right there 7/2 again remember we don't like messing with mixed numbers change it to an improper fraction it's always going to be over the same number 2 * 3 6/6 + 1 7 3 and 1/2 equals 7/2 think about this I got 23 and a half of you to get the same height as the decal 20 * 3 20 * 320 * 3 60 and that means I still got to have to do it one half X 20 20 of those 20 1/2 23 option 23 in 1/2 what's 20 x 1/2 or what's half of 20 1060 + 1070 so using logic using Lego logic you can still figure out no 7 so the 727 / 2 is not random we're changing mixed numbers into improper fractions again here let's flip it over on at the skyscraper what I'm saying is this if I have something that looks like that and 3/7 when we do work we don't like to play with mixed numbers you need to convert it to an improper fraction it's not random Randy would be totally something different there's a cyst we want to make this into one fraction without the whole number in front so we know it's going to be over 7 to change a mixed number to an improper fraction you take the denominator which is 7 x helmet does he have a thing this right I got five whole units five whole units made out of seven pieces 35 / 7 and then I got three 35 / 7 that's 5 I got I took things cut up in the seven pieces and I got 35 I got these I got five whole 7.5 hole 7 and 3/7 that's 30 at least 7 times 535 that tells me how many whole units I have so I got five whole units that's 35 / 7:35 plus the leftover amount of units which is 3/7 35 + 3 38 units that are cut up in the seven 38/7 4 + 2/5 I got four whole units and I got one that's not a whole unit I got to 250 unit my whole units are made up of five so if I got four whole units of five that's 20 I-25 that's for whole units and I have this remainder 20/5 and 2/5 gets me 22/5 for 5 * 42020 + 2 this is just a shortcut of doing that right there all right next one most of it done let's look at number six let's zoom in we got just enough time for this one right here wakala today with this one so you got two to really do on your own let's try and do this see if you could get into the other one at least start it up the sponsor of a 5K run walk for charity wishes to create a stamp of its billboard to commemorate the event if the sponsor uses a scale where 1 inch represents 4 feet and the billboard is a rectangle with the width of 14 ft and a length of 48 ft what will the shape and size of what will be the shape and size of the stamp the shape stays the same the shape stays the same it's just the size of a stamp so we got to shrink it down what's a shrinking thing we're shrinking it down so let's look at this right here so let's first find the scale factor so we don't care that it's a 5K run we just care that we have the scale so one from the scale write the scale factor and remember scale factor yeah we're shrinking it down the scale factor is equal to real life over the diagram and let's look at this and that's from the scale so we have all these words and numbers but look at this right here if if the sponsor uses a scale that's where you identify it from the scale a scale where one inch represents 4 feet in real life we have four feet and in the diagram that's one inch so the scale factor is equal to 4/1 we're just for Depends depends right the scale factor Step 2 make a t chart measurements no T chart diagram times your skin Factor equals real life resume at slightly so he still read this I don't care about the Top If the sponsor uses a scale factor of a blah blah blah blah and a billboard is a rectangle so let's draw yourself a sketch you don't need to do this but it do we know we got a rectangle of the billboard right billboard and it tells us what the measurements are it's how wide it is it's 14 and how long is it the length is 48 ft 14 to 48 all right what will be the shape and size of the stamp all right I'm going to tell you this if it's a proportional figure it's going to be a rectangle the shape isn't going to change what's going to change because we're shrinking it down as a reduction here's the thing but we'll figure this out and I'll show you how to figure it out in the second so we actually have the real life numbers instead okay we'll finish this when we're almost done so we have the real life measurements we have 14 and we have 48 we have the scale factor which is 4 this freaks out a lot of people so you got to think backwards look at it we don't have the. We don't have the diagram we don't have the diagram but I'll show you another way of setting it up where you understand if if you the real life one sometimes and you're looking for this right here what does a t chart T chart some people get stuck right here I'm Anna has this side but I don't have this side some * 4 equals 14 something * 4 equals 48 if you're stuck and it's like this this I haven't talked yet I want you to flip it around we're going to go real life I'm dying cuz now like Diana said we're making a reduction so anytime you're stuck it helps to do this 1448 and this is the diagram which we want this is your stamp but notice the scale factor I didn't write that down if I flip things around that means everything is now the opposite side instead of x 4 going the other way is what so if I went this way blank * 4 equals 14 if I go backwards what does this become yes one person good job think about this some number times 4 equals 48 how would you find that number how'd you do it how'd you do it how did you do that how did you get that number yes what somebody else good good divide yes so instead of mold play my for let's / 4 and it's not the scale factor and I'll show you what that is in a second 48 / 4 well so your stamp is going that's huge that's a huge stamp it's going to be 12 12in for your stamp but how how is it going to be so 14 / 4 that's going to be divided by 2 he gets 7/2 7/2 that's 3 and 1/2 three and a half inch that's a huge stamp 3 and 1/2 in here's my ruler you can kind of see that's a foot long and then how tall is your standard of a bumper sticker that's a bumper sticker right there so anytime you have it you flip it around but the scale factor look at the scale factor if I'm dividing by 4 remember what do you supposed to do with the scale factor you're times scale factors was the times with it how does division become multiplication by multiplying the reciprocal so divided by 4 is the same thing as divided by 4/1 the scale factor is 1/4 so from the original let me zoom out so you can see all this 48 feet by 14 feet billboard shrinks down to the giant stamp which is a bumper sticker 12 ft by 3 and 1/2 12in by 3 and 1/2 in we reduced it 1/4 times scale factor is 1/4 that one was a little bit more complicated more thinking involved that's all right so is right here SCI record pretty much said we're going to end it right here cuz it's 24 what are you fine fine fine let me let people copy let's start the setup of the next one then as far as we can until they kick us out then alright everyone got this one right thank you all right Danielle is create a scale drawing of her room so that means Daniels creating a scale drawing of her the rectangular room measures 20 1/2 feet by 25 ft if her drawing uses the scale where one inch represents two feet of actual room will Hurd Running Fit eight and a half by 11 piece of paper I don't know let's go figure it out so when we're doing a reduction things get flipped around let's look at this so let's look at our scale factor first scale scale factor if her drawing uses a scale of 1 inch represents 2ft in actual so two feet two feet to 1 in that's real life over the diagram so these are kind of funky and hard only in the sea discuss the scale factors real life over diagram but what if we're looking for the what if we have the real life and we're actually looking for the diagram so most of the time I always said Ali this is what you want over what you have but in this case we don't want the real life we want diagram so this gets flipped in this case we want the diagram over the real life so will it flip it so this is Lexa right here Lexa watch out the number 6 and 7 so if we want to follow it what we want over what we have the diagram is what we want one inch over to feet so the scale factor in this case is 1/2 so it's a reduction where is shrinking everything down by 1/2 and changing the units from inches from feet to inches so 1/2 so if you look at this right here let's me T chart we have a real life we have diagram now and what do we do with the scale factor we multiply in a scale factor is 1/2 real life we got 20 and 1/2 25 so we're taking half of everything and changing into inches 20 and a half feet 5ft what is it as inches x 1/2 is dividing by 2 what's half of 25 what's half of 25 Eva 25 dual half of 30 is 15 what's half of 25 we got $25 and you were going to amongst germ baby siblings $13 15 you got $1 too much $12 + 12.5 + 12.5 salt off of 25 is 2 2.5 half of 20 and 1/2 half of 20 is 10 half of 1/2 House of fifty cents is two 5 so the diagram of her blueprint of a room is going to be 10 and 10 and 2/5 by 12 and a half a piece of paper is eight and a half by 11 in so her diagram of a roux will not fit 8 1/2 no will not fit on paper seven seconds you guys finish up the road best on your own planet and good job everyone for participating

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