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Compare rational numbers using a number line

Sal compares pairs of rational numbers using number lines. Created by Sal Khan.

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Video transcript

- [Sal] What we're gonna do in this video is get some practice comparing numbers, especially positive and negative numbers. So for each of these pairs of numbers, I want you to either write a less than sign or a greater than sign, or just think about which of these two is greater than the other. Pause this video and see if you can work through these four pairs. All right, now let's do it together. So let's first compare -7/4 to -3/4. And I'm going to try to do that by visualizing them on a number line. So let me draw a straighter line. There we go. Let's see, they're both negative, which means both to the left of zero. So I'll focus on the left of zero. So that's zero. And let's see, they're both given in fourths and we need to go all the way to 7/4, less than zero. So let me think of each of these as a fourth. So one, two, three, four. That would be -1. One, two, three, four. That would be -2 and that's enough for us, but I could keep going if I liked. Now, where is -7/4 on this number line? Well, I just said each of these is a fourth, so negative 1/4, 2/4, 3/4, 4/4, 5/4, 6/4, 7/4. So this right over here is -7/4. And where is negative -3/4 on the number line? - 1/4, -2/4, -3/4. So which one is greater? Well, we can see that -3/4 is to the right of -7/4. So -3/4 is greater or that -7/4 is less than -3/4. So I'll put a less than right over here. Let's do this next example. We're going to compare 0.6 to -1.8. If you haven't already given it a shot or if this previous example helped inspire something and you give it another shot, and then we'll do it together. So let's draw a number line again. And let me put zero right over here. That's 1. That's 2. This is -1. This is -2. And actually let me make half marks here, so we can get a little bit closer to thinking about where these two numbers sit on the number line. I'll start with 0.6. 0.6 is you could view that as 6/10. It's a little bit more than 5/10. It's a little bit more than 1/2. So 0.6 is gonna be roughly right around here on our number line, 0.6. And where is -1.8? Well, it's negative. So it's going to be to the left of zero, and we're gonna go 1.8 to the left. So this is -1. This is -2, that's too far. This is -1.5. - 1.8 is going to be roughly, let me do this in this color, right over here. It's going to be roughly right over there, -1.8. And so you can see that it is left of 0.6 on our number line. And so -1.8 is less than 0.6, or 0.6 is greater than -1.8. Let's do more examples here. Let's compare these two numbers. Well, once again, let me put them on a number line. And I wanna show you that the number line does not have to go left-right. It could go up-down. So let's try that. And I'll do it in a different color. So I'll make a line like this. And I am going to have, let's call this zero right over here. And so this is 1. This is 2. This is -1. This is -2. Now, where is 2 1/5 on the number line? So that is positive 1, positive 2. And then we're going to go about a fifth. So that'll get us roughly right over there. And then where is -1 1/10? Well, we're not gonna go below zero, so -1. And we're gonna go another 1/10 beyond that below zero. So it's gonna be roughly around there. So that is -1 1/10. And so we can see that -1 1/10 is less than positive 2 1/5, or positive 2 1/5 is greater than -1 1/10. Let's do one last example, comparing these two numbers here. And actually, I can extend this number line right over here, and I should be able to fit both of these numbers. So let me try to do that. So I'm going to extend it. This is -3 right over here. So where would -1.5 sit? Well, we're going below zero so that's a -1. - 1.5 would be another half, it'd be right in between -1 and -2. So -1.5 is right over there. And where would -2.5 be? Well, we go -1, -2, and then another half. So this right over here is -2.5. And we could see very clearly that -1.5 is higher than -2.5, so it is also greater. And we're done.