Compare rational numbers using a number line

What we're going to 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 negative seven-fourths to negative three-fourths, 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 they're 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 seven-fourths less than zero. So let me think of each of these as a fourth. So one, two, three, four—that would be negative one. One, two, three, four—that would be negative two, and that's enough for us. But I could keep going if I liked. Now, where is negative seven-fourths on this number line? Well, I just said each of these is a fourth.

So negative one-fourth, two-fourths, three-fourths, four-fourths, five-fourths, six-fourths, seven-fourths. So this right over here is negative seven-fourths. And where is negative three-fourths on the number line? Negative one-fourth, negative two-fourths, negative three-fourths. So which one is greater? Well, we can see that negative three-fourths is to the right of negative seven-fourths.

So negative three-fourths is greater, or that negative seven-fourths is less than negative three-fourths. So I'll put a less than right over here. Let's do this next example. We're going to compare 0.6 to negative 1.8. If you haven't already given it a shot, or if this previous example helped inspire something in you, give it another shot, and then we'll do it together.

So let's draw a number line again, and let me put 0 right over here. That's 1, and that's 2. This is negative 1; this is negative 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 tenths—it's a little bit more than 5 tenths, a little bit more than a half. So 0.6 is going to be roughly right around here on our number line, 0.6. And where is negative 1.8? Well, it's negative, so it's going to be to the left of 0, and we're going to go 1.8 to the left.

So this is negative 1. This is negative 2; that's too far. This is negative 1.5. Negative 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, negative 1.8. And so you can see that it is left of 0.6 on our number line.

And so negative 1.8 is less than 0.6, or 0.6 is greater than negative 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 want to 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 one, this is two, this is negative one, this is negative two. Now where is 2 and 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 negative one and one-tenth? Well, we're not going to go below zero, so negative one, and we're going to go another one-tenth beyond that below zero. So it's going to be roughly around there, so that is negative one and one-tenth. And so we can see that negative one and one-tenth is less than positive two and one-fifth, or positive two and one-fifth is greater than negative one and one-tenth.

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 negative three right over here. So where would negative 1.5 sit? Well, we're going below zero.

So that's negative one. Negative 1.5 would be another half; it’d be right in between negative 1 and negative 2. So negative 1.5 is right over there. And where would negative 2.5 be? Well, we go negative 1, negative 2, and then another half. So this right over here is negative 2.5. And we could see very clearly that negative 1.5 is higher than negative 2.5, so it is also greater. And we're done.