We’ve already seen that fractions could be used to represent parts of wholes. Now we’re going to extend that idea a little bit to think about them as actual numbers on the number line.

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## Plotting basic fractions on the number line

So let me draw a number line right over here. So that’s my number line. Let’s say that this is 0, this is 1, and let’s say that this is 2.

And let’s say I wanted to represent the fraction 3/4. So one way to think about it is let’s go between 0 and 1. So this fraction, the numerator here is less than the denominator.

So the value of this is going to be less than 1. So this is going to be someplace between 0 and 1. And one way we could think about it is divide this section into 4 equal spaces. So that would be dividing it into 2 equal spaces.

So if I divide those again, now I’ve divided the space. Let me draw that a little bit neater. Now I’m dividing the space between 0 and 1 into 4 equal spaces. Now, 3/4 means that I’ve gone 3 out of the 4 spaces towards 1.

So I’ve gone 1, 2, 3. So this point right over here on the number line, this is 3/4. This point right over here, what do you think this is going to be? Well, we’ve moved 1, 2 of the spaces towards 4, so this is 2/4.

And this space right over here, or this mark right over here on the number line, what is that going to be? Well, we’ve moved 1 of the 4 spaces towards 1. So this is 1/4. What about this one? Well, you could call this 0/4, which is the same thing as 0. So you normally wouldn’t call that just 0/4.

And now we have another interesting question. What could you also call this space? Well, we already know based on how we already marked the number line that this is 1. But using the 4’s in the denominator, we could say, hey, look. We’ve moved 1, 2, 3, 4 out of 4 spaces.

We could call that 4/4/ And that also makes sense. So let me make this clear. 4 parts out of 4 total parts equals 1 whole.

But this also makes sense from what we know of division. This little fraction symbol that we keep using, this is the same thing as divided by. This is 4 divided by 4. And we know that any number divided by itself– except for 0.

0 is a little bit strange. But any non-zero number divided by itself is going to be 1. So this could be viewed as 4/4. So let’s do a few exercises with our newfound knowledge of fractions on the number line.

So let me get a little exercise going. So here we have move the orange dot to 3/6 on the number line. So we already see that they’ve divided up the space between 0 and 1 into 6 equal sections.

1, 2, 3, 4, 5, 6. So we need to move it to 3 of those 4 sections. 1, 2, 3. Let’s check our answer.

Let’s do a couple more of these. Move the orange dot to 2/4 on the number line. So we have 1, 2, 3, 4 equal sections. We need to move it to 1, 2 of them.

If they didn’t divide it into 4 equal sections for us, then it wouldn’t have been so easy to just count 2. The number of sections has to be the number in the denominator. And then the number in the numerator’s how many of those we move the dot to.

Let’s do one more of this. This is a lot of fun. Move the orange dot to 1/4 on the number line. Well, we already did that when we were drawing it out.

There’s 1, 2, 3, 4 equal sections. And we are going to move to 1/4.

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