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Current time:0:00Total duration:3:49

Identifying values in scale copies

CCSS.Math:

Video transcript

we're told that figure a is a scale image of Figure B so that's figure a this is figure B here the scale that map's figure a to figure B is 1 2 2 and 1/2 what is the value of X all right pause this video and see if you can figure it out all right so X is the length of this side right over here in figure a and the corresponding side on Figure B has length 5 and so one way to think about it is the ratio between X and 5 should be one to two and a half because that's the scale that goes from figure a to figure B figure a to figure B so the ratio let me write this out the ratio between X and 5 so the ratio of X to 5 this should be an equivalent ratio as 1 1 to 2 and 1/2 1 to 2 and 1/2 and that one is hard to read let me because deeper blue there you go all right so let's just think about how to do this to go from two and a half to five to go that way you would multiply by two so to go from 1 to X you would also multiply by 2 so the value of x is equal to 2 if these are scaled up you multiply this by 2 and 1/2 you get to 5 so the scale factor is 1 to 2 and 1/2 let's do another example we're told figure a is a scale image of a figure B and we see them both right over here and once again we need to figure out what X is going to be and they don't give us the scale factor but we can figure out the scale factor how do we do that well we can see when you go from course this is this side right over here corresponds to this side it's the shorter side that forms a right angle with the base this is the longer side that forms a right angle with the base and so you could set up some ratios you could say look the ratio of 3 to 4 you could say the ratio of 3 to or that blue color the ratio of three to four is going to be the same thing as the ratio of X to 7.2 the ratio of X to 7.2 X to 7.2 and so how do we figure out what X is going to be well how do you go from four to seven point two what do you have to multiply by you might want to get out a calculator or you might be able to do this in your head for 72 is 2 times 36 which is 2 times 18 so 4 times 18 would be 72 or 4 times 1 point 8 would be 7.2 and if you don't feel good about that mental arithmetic you could just do the division 4 goes into 7 one time one times four is four subtract you get a three you're gonna have your decimal right over there bring down the 2 32 4 goes into 32 eight times eight times four is thirty-two and we're done so to go from four to seven point two you have to multiply by one point eight and so to go from three to X you also have to multiply by one point eight and so X is three times one point eight what is that going to be well three times 18 is what 30 it's 54 so this is going to be five point four now let me verify that or show you that 18 or 1.8 times 3 3 times 8 is 24 three times one is three plus two is five one number behind the decimal point five point four and we're done