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# Comparing fractions: number line

CCSS.Math:

## Video transcript

let's see if we can compare the fraction 5/3 to 10/7 soar which if we can figure out which one of these fractions is larger and you might notice both of these are larger than a whole a whole would be 3/3 this is 5/3 and a whole here would be 7 7 so this is 10 7s so which of these is going to be larger to help us with that I'm going to plot each of these on a number line and I encourage you to pause this video and try to do the same before I work it out all right so I have a number line here we have 0 1 2 and first I divide the number line in 2/3 you see it right over here this is 1/3 this is 2/3 the the thirds the thirds are being marked off in blue right over here you see that each from the space from 0 to 1 is split into three equal sections 1 2 3 and then the space from 1 to 2 is put into three equal sections 1 2 & 3 you see that right over here so I'm marking off I'm marking off all of the I'm marking off all of the thirds so this is 1/3 this is 2/3 this is 3/3 which is of course the same thing as 1 this is 4/3 and then this right over here is going to be 5/3 and if we were to go over here 2 would be the same thing as 6 thirds but we care about is 5/3 so that's that right over there we don't want to fill it in so much so 5/3 5/3 is that right over there now let's think about sevenths now to do sevenths I have to split this the the part of the number line between 0 & 1 or between each whole number into 7 equal spaces so you see that here 1 2 3 4 5 6 7 you have 7 equal sections so this is 1/7 this is 2/7 3/7 4/7 5/7 6 7 this is 7/7 I could write that down this is 1 is the same thing as 7 7 8 7 9 7 10 sevenths right over here this right over here is 10 over 7 so we see that both and seven and five thirds are between one and two but which of these is actually larger well we see 5/3 is further to the right on the number line than ten sevenths let me make this a little bit easier to see so ten sevenths and that is right over there five thirds is to the right of ten sevenths so 5/3 is greater than ten sevenths so how do we write the symbol well we always want to open it up to the larger number 5/3 is a larger number so we want the larger side or the opening on the larger number or the smaller side or this point pointing to the smaller number so we have 5/3 is greater than ten sevenths