today we're going to be working on scales and scale factors often times you have used a scale if you've read a map before they give you a scale or a key at the bottom of a map like each inch is worth 50 miles and then you actually measure something on your map and you get how many inches it was and then convert that to find out how many miles it's going to be in real life okay we're going to do something simil today except we're also going to be looking at what's called scale factors and they're somewhat related okay let's take a look at the first example a graphic artist is creating an ad for new iPod if she uses a scale of 4 in equals 1 in in other words the advertisement is going to be bigger than the actual what is the length of the iPod on the advertisement okay to solve these we are going to set up proportions we are given a ratio what is the ratio 4 in equals 1 in okay now I'm going to put something else other than just inches 4 in this is in the ad or the advertisement compared to one inch and this is in the real world this is like the actual okay then over here this is like the real thing okay in reality your iPod's going to be about how How tall or how long 3 in so will that go on the top or on the bottom on the bottom because it's in real life or the actual thing we're going to put 3 inches so we do not know how many inches the ad's going to be and that's what we're going to find out because that's what it says the question is what is the length of the iPod on the advertisement okay so now we're going to use what to solve cross products let's start with 4 * 3 equal 12 and then 1 * X is 1 X okay write that down now what am I going to do to both sides to solve divide by one good so I get 12 is equal to x 12 what what will my label be 12 in equals X or 12 in will be how tall the ad will be okay are there any questions so basically if you're given a scale you can use that scale to help you solve problems okay and you set up a proportion in order to do so all right so let's take a look at another example this time they give us a picture okay this is not the real thing okay this is the picture they're telling us though that one unit on this grid is going to represent actually two feet in reality or they tell us that four units on the grid will be equal to 8T in reality is that pretty much the same thing if I have one unit that's going to be two if I have four that's going to be eight so that makes sense now we're going to convert all of our measurements to units here and we're going to answer these questions how long are the actual bleachers now we're just going to look at one set how long are these bleachers well again find your key or your rate or ratio that they give you what is the comparison that they give you I can either use four units to eight feet or somebody else said you could use one unit to two feet so I'm going to work it both ways so I need to have units on top feet on the bottom units on top feet on the bottom okay so how many units are my bleachers here okay you count seven 1 2 3 4 five six seven okay so what go on the top or bottom top top or bottom over here top okay so then this is your unknown all right let's work this one the first one we'll go ahead and do it first 8 * 7 is 56 = 4X so what do I need to do to both sides divide by 4 everybody got that what's 56 divided by 4 got it 14 what look at your labels and you can tell by where your variable is 14t let's see if we get the same thing if we do it this way what's 2 * 7 = 1 * x / 1 and you get 14 ft again so did it matter which one of the ratios you used not if they're representing the same thing it doesn't matter okay it says how long are the actual bleachers I'm thinking they're asking me just one set of bleachers is how long okay yes that would be a good thing they're 14t long each that might be a good thing to add and if you have that on a test or a quiz I think that's something that you might ask clarify and say is this just referring to one set of bleachers how long are the sets of bleachers or do they want both of them combined all right now let's look at the actual dimensions of the door let's start with the one to2 ratio this time one unit to two feet will be equivalent to units Over Feet okay find the doors what are the dimensions of the door okay two units they're two so we have two units here x down here use cross products okay 2 * 2 is 4 1 * x 1 x divide by 1 and you get 4 feet is the width of the door if we had each one it just wants to know what's the actual dimension of a door of the door okay now we've been working on scales and using the scale to help you establish your new length let's take a look at what is a scale factor a scale factor is something that you take times an amount in order to get your amount like say for instance that I have a little Cricket sitting here on the floor okay here's a little Cricket you know he's got his little head no there's just little legs or something my little Cricket's sitting here and I'm going to draw a picture of it but I'm going to fill up an 8 by1 sheet paper would I be making an enlargement or a reduction I'd be making an enlargement so the number or the scale factor I would take my measurement on my real Cricut byy would be a whole number a big number like it'd be 10 times maybe as big as what was originally but let's say for instance I have a real car sitting out here in the parking lot and I'm want to make a picture of it on my 8 by 11 sheet of paper I would have a reduction so I would be taking everything times a fraction like it might be6 do you need me collect those little toy tractors or implements okay they're they're they're sold by like 164 of the size or one 12th of the size and that's why because that's the scale factor that those tractors or those little implements are made from okay so let's take a look at this it says if the distance on a map 2 cm represents 50 m we're wanting to find the scale factor not the scale because this could be considered a scale although usually have 1 cm for 25 M would be the scale okay the scale factor is what would I take my Dimension times to get my new one so when I do that I have to make sure that my units are the same okay there can't be one cers and one meters they both have to be and in this case I'm going to make them both centimeters now you might ask why didn't I make them both meters I usually go with a smaller unit okay so whichever one's smaller which I know centimeters are smaller than meters I'm going to make them both centimeters right so 50 m is how many cenm 2 cm compared to 5,000 CM everybody remember King Henry Died Monday drinking chocolate milk okay so you do two hops right you get 5,000 and then we try to simplify this how can I simplify this divide them both by two and I get 1 cm to 2,500 CM so what I would be doing is if I have a length on something I would be taking it times 1 over 2500 and I would be shrinking it okay because this is a fraction I know that whatever I'm doing I would be shrinking what I'm I'm doing making it smaller it' be a reduction I guess this is just what we've kind of gone over so far then we're going to do some more examples scale drawings we've looked at two things we looked at Scales which the scales like the little key that you have on a map or a drawing where the scale factor is what is a fraction or whole number that you take your Dimensions times to get your new numbers now on the scale on a scale you don't necessarily have to have the same units okay in often case you you don't for instance on a map one inch is equal to 500 Miles okay so you don't have to compare you're comparing inches to miles and they don't have to be the same usually it refers to a key in which he like 1 in equals 50 miles sometimes we call the scale the same thing as a key and always one's on top so even if I started with 2 cm um is equal to 5 m you want it to be represented as 1 cimeter is equal to how many meters and sometimes in the scale problems you set up a proportion to solve most often you you will set up a proportion to solve it 1 in represents 50 miles well then how many inches on my drawing equals tell me how many miles that'll be now the scale factor is a fraction it could be impr proper but you always say the new over the original other words if it's a reduction then my new is going to be smaller than my original therefore it'll look like a fraction if it's an enlargement then my top number is going to be bigger than my bottom number and any number that does that going to be greater than one or as I stated earlier if it's a reduction then this is going to look like a fraction or it's a number less than one and this last note is really huge you have to have the same units when you're figuring the scale factor that's the key right here you'll have same units and for your purposes that's what you're going to to do just conver them to make sure that they have the same units and simplify so you may have to just do convert and then simplify okay so let's take a look at an example now this is using your scale and how you use it on maps they give you a key at the bottom do you notice that what is that key 1 cm represents 24 miles okay that's our first ratio that we know they want to know the actual distance between Hagerstown and Annapolis so with your rulers right now in your book I need you to measure in centimeters how far it is from Hagerstown to Annapolis go to there as half centimeter if you need to what'd you get four okay everybody saying four centimeters thumbs up if you agree with that okay do I know how many miles nope so let's put X miles or you can put n any kind of variable and what do I do to solve cross products 24 * 4 96 96 = 1X IDE by 1 remember we talked about showing your steps and you get 96 miles so in real life it's going to be 96 miles from hey Town Annapolis approximately okay so basically when you have a scale on a map or a drawing you're basically setting up a proportion and solving okay this one is from a drawing it says on the blueprint of the deck okay this is a deck here each square has a side length of half an inch okay so this represents a half an inch what is the actual width of the deck well here's the scale that they gave you so let's write write that down 1/ 12 of an inch compared to 4T will be equal to so many inches over so many feet now which piece of information can I get from the picture how many how many units is yes how many inches is this okay each one is 1/2 1/2 1/2 1/2 so a half in represents 4T this is 2 in okay and then this would be X feet now what I do cross products 4 * 2 is and then I have 12 time x ooh what do I do now I am multiply by half so I have to divide both sides by a half o we have to review fractions what do I do 8 times 2 over one multiply by its reciprocal so go to KFC flip it and you get 16 so would be actually 16 ft now let's see if that makes sense because it said each half inch here represents four so that's four 4 4T 4T is that right be 16 okay great all right let's take a look at a scale factor problem it says find the scale factor I notice it doesn't say just scale of a model sailboat if the scale is 1 inch to 6 feet now if you look at your notes what do we say had to happen if you're finding the scale factor same unit so what do we have to change feet to inches how do I do that right 6 * 12 is 72 therefore my scale factor is 1 to 72 now this is not setting up cross products or set as of proportion this is just like an equivalent ratio making it so that it's simplifying fractions just make because the one's already at the top I'm done when the scale factor you need to make sure your labels are the same one in to 72 in or we kind of just throw your labels out then they say the scale factor is 1 to 72 too other words this is a reduction I'm not going to put the real sailboat in there in order to get my picture I'm going to have to reduce it okay that concludes our lesson on scale drawings and scale factors