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Relating number lines to fraction bars

Video transcript

- [Instructor] 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 could 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 and 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. And 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 zero or from zero to one, 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 and notice it is divided into six equal sections so each of those sections is 1/6. 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, now 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 zero to one and you can view one as a whole. 2/6 is, so that's 1/6 right over there and then that is 2/6. And so you can see on the number line, the thing that gets us 2/6 of the way to one 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. 2/6. So each of those equal sections, we are increasing by a sixth. So we're going from zero to 1/6 to 2/6. Once again we end up at point B.