Fractions on the number line
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We've already seen that if we take a whole, and in this example, the whole is this entire green circle. And if we were to split it into 5 equal sections-- 1, 2, 3, 4, 5. So we've split it into 5 equal sections-- and if we were to select 1 of those 5 equal sections. So let's say we select this section right over here, that we have selected 1/5 of the whole, 1 out of the 5 equal sections. We could do the exact same thing on a number line. Everything we've been doing so far has to deal with shapes, but we could do the exact same idea on a number line. So let me draw a number line here. So let me draw it pretty big so we get a sense of things. So it will go all the way to there. And let's say that this is 0, this is 1, and this is 2. And of course, we could keep going if we had more space to 3, 4, and on and on and on. And what I want to do, instead of taking a circle and dividing it into 5 equal sections, I want to take the section of our number line between 0 and 1 and divide it into 5 equal sections. So let me see if I can do this. So 1, 2, 3, 4, 5. That looks pretty good. I'm drawing it as exact as I can with my hand. But let's just assume these are 5 equal sections. So what would you think would be a good label for this number right over here? Well, it's the exact same idea. Between 0 and 1, I've traveled 1 out of the 5 equal sections towards 1. And actually, let me make it a little bit neater than that. We could make the equal sections look a little bit better. 1, 2, 3, 4, 5. And what we're thinking about is this. What should we call this number here? This number is clearly between 0 and 1. It's clearly closer to 0. And we've gone 1 out of the 5 equal sections towards 1. Well, it makes complete sense that, look, we had 5 equal sections here. And we've traveled 1 of them towards 1. So we should call this number right over here 1/5. So when we're talking about a fraction, 1/5, it's not just talking about, hey, what part of a pizza pie have I eaten or something like that. This is actually a number. This is a number. And we can actually plot it on the number line. Now you might say, OK, well, that's fair about 1/5. But what about all these other slashes? What numbers would we call that? Well, we can make the exact same idea. If up here, instead of shading in 1 out of the 5 equal sections, if I shaded in 2 of the 5 equal sections, then I wouldn't say this is 1/5 any more. I would say that this 2/5. And so if I go 2 of the equal sections towards 1, then I should call this number right over here 2/5. And I could keep going. This right over here should be 3, 3/5. This right over here, I've gone 1, 2, 3, 4 out of the 5 sections towards 1. So I could call this 4/5. And I could keep going. I could call this right over here-- I've traveled 5 out of the 5 equal sections towards 5, so I could call this right over here 5. Let me do it in that red color. I could call this right over here 5/5. You might say, wait, but 5/5, we've gotten to 1. And that's exactly right. If I were to shade in 5 things over here-- let me do that little bit cleaner. That's not the color I want to use. If I were to shade in 5 things over here, we've already seen that shading in 5 things-- let me make this a little bit neater-- if this is now 5 over 5 or 5/5, we've already seen that this is a whole. And over here, if we've traveled 5/5 of the way towards 1, we've gotten to the whole 1. 5/5 is the exact same thing as 1. It is equal to a whole.