Comparing fractions: number line

- Let's see if we can compare the fraction 5/3 to 10/7 or 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, this is 10/7. So which of these is going to be larger? And 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. Alright, so I have a number line, here. We have zero, one, two and, first, I divide the number line into thirds. You see right over here, this is 1/3, this is 2/3, the thirds are being marked off in blue right over here. You see that each from the space from zero to one is split into three equal sections, one, two, three. And then the space from one to two is split into three equal sections, one, two, and three, you see that right over here. So 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 one. This is 4/3, and then this right over here is going to be 5/3. And if we were to go over here, two would be the same thing as 6/3. But what we care about is 5/3, so that's that. Right over there, I don't want to fill it in so much. So 5/3 is that right over there. Now let's think about sevenths. Now to do sevenths I have to split the part of the number line between zero and one or between each whole number into seven equal spaces. So you see that here. One, two, three, four, five, six, seven. You have seven 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, one is the same thing as 7/7, 8/7, 9/7, 10/7 right over here. This, right over here is ten over seven. So we see that both 10/7 and 5/3 are between one and two, but which one of these is actually larger? Well we see 5/3 is further to the right on the number line than 10/7. I'm gonna make this a little bit easier to see. So 10/7 and that is right over there. So 5/3 is to the right of 10/7, so 5/3 is greater than 10/7. So how do we write the symbol? Well we always want to open it up to the larger number. 5/3 is the larger number so we want the larger side or the opening on the larger number. Or the smaller side, or the point, pointing to the smaller number. So we have 5/3 is greater than 10/7.