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Math 7 - Module 1D - Lesson 17 Problem Set Worked out

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An explanation and working out of the steps for the problem set. Check and compare your work. Still unsure or lost, ask questions during class or Academic Support.

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Bonnie I'm going to do it on a separate piece of paper cuz we don't have enough space Giovanni went to Los Angeles California for the summer to visit his cousins he used a map a bus routes to get from the airport to his cousin's house the distance from the airport to his cousin's house is 56 km NE on the map the distance is 4 cm what is the scale factor so it's one this is the whole thing there's two parts so we got to now all you're doing is making a fraction what's the scale factor and the thing that  it doesn't tell you what are you comparing to do you want the actual real distance or do you want the map distance so we're going to both if we're talking about an enlargement so let's look at this what is a Sol went from lav cousin to use the map bus route to get from the airport to his cousin's house the distance from the airport who is cousin's house is 56 km on his map the distance is 4 cm well let's look there's two ways to think about it and literally depends on what you're doing with it what is the scale factor so could go 56 km equals 4 cm is 2 4 cm that's one way or we can go the other way 4 centimeters is 256 km which one is which that's the whole thing it depends on what the problem is this questions kind of sucky cuz it doesn't tell you what does it want doesn't want the map does it want a reduction or does it want an enlargement so this right here let's go look at it let's simplify first what's 56 / 4 goes into at 1:14 14 if I divided by 4 what's divided by 4 one centimeter is 14 km in real life that's your scale factor one centimeter equals 4 km I remember it wants unit rate this is the easiest one to make a unit rate look 14/1 we have a unit rate and then 4 cm to 56 + / 4 again and I / 4 1 cm is equal to 14 kilometers just got to match up the units which ones which it depends on the problem all right let's go to the next one Nicole is running for school president what Diana stop laughing at your reflection we know you look funny detention I'm not laughing at my reflection Nicole is running for school president her best design her campaign poster which measures 3 ft by 2 ft Nicole like the picture so much she reproduce the artwork on a rectangular buttons that measure to in by 1 1/3 in what is the scale factor so it's a reduction so it's a reduction so let me get a separate piece of paper so we know we got a reduction so let's look at this we have the OG and we have the new we're trying to find the scale factor remember OG X scale factor which is also known as the letter K or propped on several personality equals a new we're looking for what that is how do we find that lets you put all the information now 3 feet by 2 feet so we know it's 3ft by and she did it and made it as button so it won't hear let's go feet feet and cheese shrink it down to 2 inch by 1 and 1/3 inches I don't like that one and one-third but let's go look at this so she went from 3 feet to to in let's go what do I multiply to 3 ft to get to inches that's hard right there so that's my let's make our remember our scale factor is the new over the old once we find this to check this one so the news who is 2 in the old is 3 feet when your units don't match up it's smart to change it to units that are the same so I asked this last. If you were last raid hopefully you saw it how many inches are in 1 foot by 1 foot equals how many inches 1 foot think about a ruler one foot one 1 foot how many inches is 1 ft I've been in I'm not moving until I get that answer you have a ruler where's my ruler which is my my my little a clipboard as a ruler on the side look at it this route this clipboard is a foot long and tinted how many inches is 1 ft 12 thank you if 1 foot equals 12 in I have 3 ft 3 ft equals how many inches one foot is 12 and I got three of those yes use your calculator I see you doing it 3 ft equals how many inches we have to convert 3 feet 1 foot is 12 in 3 feet would then be how many times bigger is 3 ft to 1 ft so it's 36 thank you sub for those few that didn't see it look at it so we know that one foot is 12 in and one foot is three times as small as three feet so three feet is 3 times bigger so that means 12 inches three times bigger 36in so we convert that let's rewrite this right here so we have this 2 inches is 2 36in that's our scale factor new over the old so we have the 2 in over the 3ft but inches and feet different measurement let's make them the same inches / inches it's the same now 2 / 36 how many times did we shrink it down I think they all do 2 and 36 we should always simplify a fraction 2 and 36 what do we divide by to make an equivalent simplified fraction simplified ratio 6 what do we divide by so look at this we're going to make this 2/36 into a simpler looking fraction that's the same value we want to look simpler so look for two numbers that both of them share look for one number that both of them shared by both of them by 1:36 okay / thank you divided by 2 2 / 2 is 136 / 2 is 18 that means our scale factor we went from here to here 3 ft * 1/8 converted to 2 inches to Ft hopefully we're going to check that in a second to feet x blank into 1 1/3 in let's check that in a second so our scale factor equals 1/8 1/18 my fault we shrank everything down 1/18 let's check to see if that's the true scale factor cuz I got to check this one right here so 3 ft * 1/18 Plies the 2in but what we had to do with change this in the inches so one thing we should do first let's change to feet into inches so we have inches to inches for comparing the same thing if one foot is 12 in 3 feet is 36 in to Ft Diana equals how many inches thank you Jesse Kofi stupid yes correct * 2 is 24 24in so instead of writing that let's rewrite this whole thing so we got two feet becomes 24in and let's multiply that by 118th and see if we got this right here one and one get that in a second let's double-check so less than 180 so that looks all messed up lips give it more space 24 * 1/18 to multiply fractions or multiply with a fraction everything should be a fraction so with that how do I change 4 into a fraction thank you for 24/1 and then you multiply across thank you Laura we get 24 / 18 does that equal 1 1/3 let's check simplify this 24 and 18 both of them what can I divide both of these by thank you all right let's see that / 2 / 2 I get 24 / 2 is 1218 / 289 can I divided by something else 12 + 9 12 + 9 what can I / for excellent Sasha / 4 again 12 / am I doing I listen to you see iMessages in this divided by 3 is 49 / 3 is 3 look at this one in 1/3 4/3 are they the same let's convert no no they're the same yes so that's what you got to watch out for you get 1 1/3 vs 4/3 zloty has free this is a mixed number this is an improper fraction change this to an improper fraction 3 * 133 + 144 thirds 4/3 / 4/3 so the question was what is the scale factor yes so Nicole friend her best friend who doesn't she doesn't want to give credit for a look at that Nicole is running for school president her best friend who she doesn't want a name and is using so if that was you Diana Diana is that mean Nick what's your middle name not even close to say that okay you're going to be a trombone Ian School presidents are going to use people you use your best friend and didn't even give didn't even name your best friend and took credit for it and you like a poster so much you shrank it down and what was the scale factor you track it down by 1:18 Shrek the poster down 18 x they can fit in a button next one I give credit when it's necessary all when is necessary you guys heard that don't be her best friend cuz she's only what she thinks it's right well it's always right so that's why I always give the scale factor find me the scale factor using the given scale drawing and measurements below scale factor we're feeling that in so here's the actual drawing on a scale drawing now lesonal since you weren't here getting your haircut this is a review of let the lesson before the 16th if we're going from the actual drawing to the scale drawing look at it Mana is this a reduction or an enlargement you know it you know it is this a type in anything now take her credit away is this an enlargement good you see we are enlarging this enlargement so because it's an enlargement the scale factor has to be greater than 1 so if you wrote something less than one you're wrong knowing that it's an enlargement has to be bigger than one so remember how do you make a scale factor the scale factor is made up of the new number over the original number actual is the original your scale drawing is the new someone give you a second to set that up yourself look at it or New Years are new look at its 5 cm here's our old it's 3cm this is like a double-double a lie show enlargement so look at the measurements you have write your fraction and I will go and set it up in a second I'll give you 15 seconds to write it down cuz it should take you five seconds to do this problem look are your measurements just set up new over original all you got to do to find the scale factor thank you yes it is easy so new versus original my new number is 5 my original number is 3 there's a scale factor gun super easy and is 5/3 bigger than one yeah I got five out of three pieces this is one one and two thirds that's bigger than one now let's go the other way around and let's say you messed up let's say you messed up and flip the numbers around don't copy this down do not just watch and pay attention you knew you had to make a fraction and you made these two numbers because this and you saw that it's an enlargement but so you flipped it around 3/5 there's my scale factor and you said it's an enlargement the scale factor has to be greater than 1 is 3/5 greater than 1 know so you know this is wrong so you flip it around 5:30 yes what's up do I have to do like fractions for that for the answer or do we just write the answer fraction all right Bayside what you have to know how to write it the next question was how did I get one and two thirds, right so that's let's do a quick mini lesson how to change an improper fraction to a mixed number so it's the same thing as changing a fraction to a decimal except you don't make the decimal you leave the remainder so this is 5 / 3 and you just do the division how many threes going to 51 so 3 * 1 is 3 and then we subtract we have a remainder of 2 this is our whole number this is how many Whole30 are there's a one and then the remainder is down here so that's our numerator that's how many pieces we have left left from what what did we cut it out of pieces of three so that's how 5/3 becomes 1 and 2/3 improper fraction to mixed number which which app is a which answer is better it doesn't matter I would prefer you leaving it as a myth number unless I unless the answer says to change it to a mixed number that's more work than you need to do so leave it as an improper fraction all right looking at this right here this right here is a trick question and I'll go over this in a second look at the drawing find the scale factor and I'm the type most people will get this one wrong it's a trick question this right here is actually an SAT I've seen it before this is an old SAT question and it's a trick question what is a scale factor first let's go give this here's the actual drawing and then we're going to scale it to hear actual to this so just looking at it is it an enlargement or reduction is it an enlargement or reduction answer that person I answer that question reduction good so that should give you a hint so we know it's a reduction so the scale factor should be less than 1 but I'mma tell you most people don't get it wrong so the question was PSAT so California supposedly got rid of it but other states have not there are two tests that all students need to take in high school to get into most universities one is the SAT the other is ACT SAT stands for Scholastic aptitude test it means pretty much what did you learn in school test Act you know what I only know the T stands for test what the f u c stands for but you take to take test and take a test to send the score in the college but you guys got a couple years see if I didn't tell you the trick question you wouldn't have got it but you're you're so yes yes so somebody said is 1/4 or for those of you guys are said that you're wrong and I'll show you where the trick is and yes you got to take a look at this right here it says from here to here is 24 cm that's what's called a diameter diameter goes from one side of the circle through the center of the circle to the other side of the circle so it cuts a circle in half but this right here all you have is from here to hear the trick of this trick question is you need to match it is this a six and that's from the center to the side you need to know that that's called a radius and that's half a diameter yeah 6 + 6 6 + 6 says that whole segment right there is 12 this is a common trick question that they give so you need to know you need to that's good that's good that's good so 6 + 6 is 12 so let's go from this remember scale factor is the new over the old so the new that's what you got to watch out for is 12 newest 12 and the old is 24 so you have the 12 American college test you look that up really American college test all right I didn't know that so I hope you looked it up and just made it up and anyways this is our song but do not forget if a fraction can be simplified you have to do that what's 12 / 24 simplified almost almost let's / 12 and I'll show you why your answer is off listen to buy top and bottom by 12 I know why you wrote it cuz you saw a 12 / 12 is a 1:24 divided by 12 is 2 but think where is the two not on the top 12 divided by 12 is 1 24 divided by 12 is to its 1/2 not to over one she got to watch out 2 / 1 equals 2 but 1 / 2 is just a half yeah so in lowest terms it's 1/2 so the scale factor is 1/2 look at the scalp where is less than 1 if you wrote to look at this that's why you need to do that extra step we know it's a reduction is 2 less than 1 prison thing is 2 less than 1 2 is greater than 1 because it's a reduction that's why you want to check first this is a reduction or an enlargement because it's less than one the scale factor cannot be to what you did you flipped you took the reciprocal around which is a common mistake don't worries common lot of people do that sometimes doing that so we divide the top and bottom by 12 to simplify to 1/2 the scale factor is 1/2 it is less than 1 where does the 110 go back here so let redo this right here 12/24 when you have a fraction you always want to simplify it that's where Salon people can get the here but they can't get to the cross the finish line you see where it is 12 + 24 fractions if you can simplify simplify and a lot of people mess up and they don't see it so 12 and 24 what can we bye-bye if you don't see 12 that's okay give me another number what's another number that both 12 and 24 can both be divided by to all right I used to 12 / 2 624 / 212 and you need to keep on doing it till you can't simplify anymore 6 and 12 what can they both / to yes I read your lips three all right I'll do three 6 / 3 is 212 / 3 is 4 + 2 + 42/4 what can I divide both of them by everything can be divided by 1 2 divided by 2 2 / 2 is 1/4 / 2 is too and I can't go anymore so you always when you simplify fractions done good job whenever you simplify project you need to keep on dividing until you can't go anymore when you can't divide anymore that's when it's done in simplified so 2012 / 24 simplifies to 1/2 that's where the one came from all simplifying until you can't anymore is it always one no it's not always one pretty much yeah yeah I would go with that all right the next one all we got three more problems than we are Dawn let's read this number 5 using the given scale factor create a scale drawing from the actual picture in inches I'll look at this so they gave us a scale factor if the scale factor is bigger than one sold our new picture is it going to be an enlargement or reduction is the new picture going to be an enlargement or reduction yeah large since 3 is greater than 1 that means we have any Sgt now we got this picture of a I don't know is it a is it a birthday card envelope it's in an envelope let's go with that all we have is that this is one I got a bust out my ruler now and measure the other parts so looking at this so it's off the thing I can't you can't even see it let's measure this way alright so now that I measuring it here to here that's the beginning of my inches 1 inch is right there so it's not quite one-inch but here is a half then it scoots over its 1 it's .75 in 3/4 of a is half is right there a half an inch charity here's one half and then we go over right there that's .25 a 3.25 so this is .75 in before we move all we know this is look at it we can I ball that's the middle that's the middle right here so we want to make a triangle that meets in the middle measure the length of those pieces of the triangle so do those pieces right here not quite .75 but it's almost there what is that 5678 cheap flights 6 1.7 inches that's .7 right there that's .7 so without a ruler this part you can't do all right so we got her measurements right there so now we have all the lengths we have and we're going to have to make a brand new picture that's three times as big accurately and you all can do that so remember the steps first we find our measurements which we did second thing put in a t chart always be this your original and your new an original siletz list all alarms are measurements 1 in we got .75 in and we got point seven add we need to list both of them we don't need it cuz we got our numbers but if you want to you can the other point seven also we don't need to write it down again cuz they're the same kind of redundant you know cuz you already know the number it's just like right here can someone tell me how long the stop edges how long stop Edge yeah it's 1 how do you know which one how do you know that this top Edge is one because of the picture how because of the picture how do you know the top Edge is one how come I didn't write that down yes because of the picture how a little bit bigger no I get what you're saying so look this is a rectangle the bottom edges one so the top and it has to be one just the same thing why do write down the number for the right Edge because I already have the left Edge which is .75 so these right here is plantar .7 so technically I need to do there so I actually have my three numbers I need to remember the formula if I give you the original number and a scale factor how do you find the new number the new number is equal to the original number time's the scale factor so new equals original time scale factor what's my original original is one and here scale factor is 3 let's write that down scale factor equals 3 so my original number brighten all my original numbers again and what am I supposed to do with them to find my new number I'm three three times bigger a little bit bigger 1 * 3 3 $0.75 * 3 will do that in a second 7 * 3 notice I read it as seven times 21 but it's 7 so we have one decimal place 2.1 2.1 and then right here I got points 7 * 2.75 * 3 let's do it up here $0.75 * 3 3 * 5 is 15 carrier 1:21 22 and then we got two decimal places 2.25 20 quarter where did I get the three the stealth that right up here look at it so where did I get the three from the three it tells us the scale factor is equal to 3 so I wrote it down right here instead that's why he's you to cease O scale factor equals 3 and so when I took my measurements are all my measurements original measurements from original picture one in .75 in .7 in anime I need to find if I'm going to redraw this three times as big I need to find my new numbers my new measurements how do you find your new numbers you take your original numbers times each of them by the scale factor so I rewrote all my original numbers one play 75.7 and all multiplying by 3 so now I have the new measurements of my brand new envelope and I'm going to make my drawing right now so it's going to be 3 in Long 2 and 1/4 inches high and my enveloped it's right here 2.1 in so let's draw that where's my room actual size 3 in so let's go do 3in and I don't have a corner Square so it's going to be close so there are three and how high was it supposed to be 2.25 so let's go 2.25 in there's two and a half of 2.2 let's hope I make it perfectly straight I hope thing on it when it's 2 that's close and then I finished making my rectangle I don't have a nice little corner Square to make it quite even so I'm eyeballing it hopefully it's good enough three and then just connect the dots and then I have this then I have the envelope folding labels so we know it's homework is the same for everyone over to that get is this the home work from home work from fifth v. V 7th and 1st so at 3 in the middle is 1.5 so that's about a year so that right here should be summer in here I'm going to go Loosely somewhere there and I need to have the Links at 2.1 in so needs to be 2.1 in from here to here so I need to have a better angle to that looks about right Are we almost done two more problems can't you see. You did not print out this sheet to recognize that this is the last page look at that perfect drawing excuses excuses I can't cuz I don't have a printer here or you can even do it on a piece of paper and turn it in so this is I already did my homework do that was for the other assignment Lesson 16 this is 17 all of a sudden not all but not my fault you take class to get a haircut I cut class to get a haircut what today yesterday I don't know no I never cut class to go get a haircut but you didn't show up to class that's why you missed the lesson to take this down so what this right here no. Wasted time we're almost done what was Don so look at my drawings yeah I know they always use all the sudden you are correct good observation but let's look at this so look this is this right here is three times as big that's why it's an large ship that look at all the measurements point72 Point 1.75 2.251 in * 3 in its right now this one right here look zoom in scale factor 3/4 that is less than 1 3/4 is less than 1 so my new drawing is it supposed to be an in-law judgment or reduction is it where's my thing I lost my paper I don't have my mice sheet remember smaller when your scale factor is less than 1 so let's do a quick review on this side scale factor if it's bigger than 1 it is an enlargement scale factor if it is less than 1 then it's a reduction one or the other so let's flip it over look look look look look look look like or scale factor is 3/4 3/4 three out of four I do not have a hole so it has to be less than one so because it's less than one this is going to be a reduction so we got a match all of these when we find our measurements just * 3/4 we're going to get that I'm not going to try this right now I will measure it and we'll do one of these what do you want to live so you can get the idea all right so let's measure this side right here from here to here it is two and a half inch is a 2 and 1/2 no it's not 2 and 1/2 in like it was let's say it is and how it is two and a half so this is 2.5 in Trufant the new measurement on our reduce little tag we got a x 3/4 got plenty of time I'm just going to do a couple of these let's measure this one right here this is us Two and a Half Men looks like 2 and 1/2 or is it too corner to corner this is three and then this is 1 + 1 + 2 + 1.25 + 1 to 5 and this side is .75 so these others sorry these other side's match up the mirror so I'm not going to bother writing that and this little circle thing is I don't have a compass to copy that will just deal with that so 3 2.0 530 and 1.2 5.75 how do you find the new measurements if it's a reduction let's just do the T chart and we'll go from there you could draw it later cuz that took so much time I want to just move on so let's do this easy one first if my original is 3in that's 3in what do I have to do to find the new one remember new equals the original kinds of scale factor what's my original Three what's my scale factor 3/4 what's put that in here scale factor equals 3/4 so I take my original Three find 3/4 so this is going to be 9/4 what's 9/4 though this is yes the top line is also three but you see that's three correct and then all right let's finals fill them all in so 9/4 of an inch how many fours are in 9 good to their two sets of 4 and 9 that's all right it's a good guess so they're there to two forces 8 if we take away 8 there's one left 2 and 1/4 so the new length of this is going to be 2 and 1/4 in and in terms of a decimal 2.2 5 inch so all for all these you X so this 2.5 2.5 Nita * 3/4 and you're going to get your new measurements right here .75 1.25 for both of these e x 3/4 in your fire new measurements and then you connected the drawings where did I get 2 this one right here so I use the ruler to my ruler I measured it and it's 2 and 1/2 in two and a half inches get the new remember original times your scale factor equals your new your original measurement X your scale factor equals your new measurements I mean this to right here so that's it 2 or this to right here black to her okay alright so for all these all you have to do is this * 3/4 and you'll get your new measurement alright let's get on with this cuz I don't want to drive that I would just move on lat fine you can finish this and you got some work to do on your own for the homework all right number 6 Hayden like building radio-controlled sailboats with her father one of the sails shaped like a right triangle gives you a hit we should always draw this will draw this in a second and I'll Define has side lengths measuring 6in 8in and 10in to log her activity Hayden creates and collects drawings of all boats she and her father built together using the scale factor of 1/4 create a scale drawing of the sale alright so first let's make a drawing of the triangle sheets on a right triangle so she made one of the sale she made was a right triangle has side lengths 6 8 10 a right triangle is called the right time because one of the angles is a perfect Corner 90° that means it's Square so that's a right triangle and a right triangle the side across from riding a look at it imagine this is an arrow tip the right angle symbol right here points to was called the hypotenuse the hypotenuse of a triangle is always the longest side so which size do you wear the number so you got 6 8 and 10 the longest side is always planted by this Arrow so this points to the longest side which is 10 and then the other sides are called legs and it's pretty much you have the long leg and the short leg so which one looks longer a little bit longer to stay this is eight and this has to be the six then so that's how you label a triangle hypotenuse long leg and short leg and so activity log sled to make drawings of everything so use the scale factor and create a scale drawing of the cell with the scale factor of 1/4 so our scale factor equals 1/4 what's the difference between this problem and these up here it's a word problem that's the only difference your Lexile skills guys that know how to read and take the information from here translated to a picture or pull it out and then set it up no different than what we did up here so let's finish and make a t chart are original and then we're going to go original time scale factor equals the new laurenzside made an extra column cuz let's get a little bit more organized so our original lengths just put it in this right here use these right here so 6 8 10 put in an order shortest medium longest and all you got to do is take your original time's the scale factor all right let's do the work off to the side up here to calculations is that my same dinner is that new dinner when did you get two dinners pay attention towards us a feast and this other one over here I don't want that one that was lazy that wasn't ugly let's get on with this is finish up we're almost done so 6 * 1/4 + 6 * 1/4 but again when multiplied by fraction let's change this control 6/1 now we have a fraction over a fraction 6 * 1 is 601 * 4 is 4 we can simplify this I'm doing Mental Math right here at / 2 3/2 inches 3/2 in 1 and 1/2 in so I'm going to write it as a mixed number 1 and 1/2 in it's easier to write the decimal that way I mean find the measurements so we got eight * 1/4 let's change this to a fraction 8 * 1 is 881 * 4 4/8 / 4 which is 8 / 4 too so we have 2 in 1 and 1/2 in 2 in and let's do this last one right here 10 and you guys look at the pattern muscles put her 1 * 1/4 10 * 1 is 10 + 10/4 look at this 10 / 4 I could / 2 I get 5 / 2 I got two sets of 2 so that's 2 and 1/2 inches so there is my new flag measurements there is there are those are my measurements so I'm running out of space but let's finish this so my longest side but short sides are going to 2 + 1 1/2 let's go to inches high I ran out of space so I got to have to go over my notes a little bit so 2 inches from here all the way down to hear that's 2 in and then that's my lost right there the next the shirts that's the medium sized the shortest side is 1 and 1/2 so let's try and make it as straight as I can 1 + 1/2 is right there and here's the thing I'm going to use red so it stands out I am going to just use my ruler and I'm going to show you this should be this should be closed if that looks pretty Raiders Corner that should be this from here this corner to this corner should be 2 and 1/2 let's go look at our ruler and put it right there connected I'm slightly off but it's right there I'm pretty close so that's good. So here's our begins that's good it up a little bit more should go right there to do that there and look right here there's my two here's three my half markers right there I was pretty close to and a half right triangles always fit like that so that's too and this is 1 and 1/2 in and this is too I did it right

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