Relating number lines to fraction bars

We are asked what fraction is located at point A on the number line, and we can see point A right there. Pause this video and see if you can answer that.

All right, now there's a bunch of ways that you could think about it. You could see that the space between zero and one is split into one, two, three, four equal spaces, and this has gone three of those four equal spaces from zero to one. So that's one interesting way to think about it.

Another thing that might help us is a bit of a visualization. If this rectangle represents a whole, notice it goes from zero to one, so you could view one as a whole. We have split it into four equal sections, so each of these equal sections you would consider a fourth. So that's a fourth right over there, that's another fourth right over there, this is another fourth right over there.

So how many of these fourths have been shaded in? Well, three of them have been shaded in. When you look at the number line, you see the same idea. When we see the space between zero and one, it has been split into fourths, so this is a fourth, and then another fourth, and then another fourth, and another fourth.

And where is point A? Well, we have gone 1/4, 2/4, 3/4 past 0, or from 0 to 1, which is a whole. So what fraction is located at point A on the number line? 3/4.

Let's do another example. So here we're told which point is at 2/6 on the number line. Pause this video and see if you can answer on your own before we work through it together.

And I'll give you a little bit of a hint. Let's imagine that this rectangle represents a whole. Notice it is divided into six equal sections, so each of those sections is a sixth. And so if I start at zero, how many would I fill in to get 2/6 and what would be the corresponding point on the number line?

All right, let's do it together. So if each of these is a sixth and we have 6/6 there, so that would be a whole. And that's good because it goes from 0 to 1, and you could view 1 as a whole. 2/6 is so that's 1/6 right over there, and then that is 2/6.

And so you could see on the number line the thing that gets us 2/6 of the way to 1 is at point B. It corresponds to how much we've filled up that rectangle—point B right over there.

Now, another way that you could think about it—you could see that the space between zero and one is split up into six equal sections: one, two, three, four, five, six equal sections. And we want to go to 2/6.

So each of those equal sections we are increasing by a sixth, so we're going from 0 to 1/6 to 2/6. Once again, we end up at point B.