Creating equivalent fractions

So we've got this fraction written here, 2/3. What I want you to do is pause this video and try to think of any other fractions that are the same that are equivalent to this fraction right over here that essentially represent the same number. So to do that, let's visualize what 2/3 is. So let me draw a whole here. Let me draw a whole, and I'm going to divide it into three equal sections. So that is my whole. I'm drawing three equal sections I'm going to try to draw and make them as equal as i-- I can do a little better job than that. So that's 1, 2, 3. Three equal sections. And so 2/3 would represent two out of those three equal sections. So actually I can spray paint this. So that's 1/3 right over here, and then this is 2/3. So we have two of the three equal sections. So that is 2/3. And now let me copy and paste that so we can think about other ways to represent this fraction. So copy. And then let me paste it. I'll do it once, and then I'll do it another time. And I could do this multiple times, but I'll do it two other times right over here. So there's a couple of things we could do. The first option is we could take this and we could draw a horizontal line that divides each of these three sections into two sections. So let's do that. So now, how many equal sections do I have? I have 1, 2, 3, 4, 5, 6 equals sections. And how many of those equal sections are actually shaded in now. Well, we see it's 1, 2, 3, 4. 4/6. So notice, 4/6 is the exact same fraction of the whole as 2/3. These are equivalent fractions. We could say that 2/3 is equal to 4/6. Now, we could do something very similar. Instead of dividing each of these thirds into two, we could divide each of these thirds into three. So I could draw three horizontal lines here. So let's see 1, 2, 3. So now I have divided what was in three equal sections, I now have three times as many sections. I have 1, 2,, 3, 4, 5, 6, 7, 8, 9 equals sections. And then which of those are actually shaded in? We have 1, 2, 3, 4, 5, 6. 6. So 2/3, which is equal to 4/6, is also equal to 6/9. All three of these are equivalent fractions, 2/3, 4/6, and 6/9. And if you were to put them on the number line, the same thing would happen. So let's do that. Let's draw a number line here. Let's say that's 0. And I'm just going to focus on between 0 and 1. And obviously we can go beyond that. And let's divide it first into thirds. So this is 1/3 and 2/3. So we already know this would represent 1/3 and this is 2/3. We've gone two of the equal spaces of the three on the way to 1. We've divided the section between 0 and 1 into three equal spaces. Now, what for 4/6 be? Well, now we would just have to divide this into 6 equal spaces. So 1, 2, 4, 4, 5, 6. And 4/6, that would be 4 out of the 6 spaces on the way to 1. So 1, 2, 3, 4. So this number is also equal to 4/6. And you could do the same thing if you want to think about ninths. So what we could do, we could put 1, 2, 3, 4, 5, 6, 7, 8, 9. Now I've split this part of our number line between 0 and 1 into 9 equal spaces. Well, what would 6/9 be? Well, 1, 2, 3, 4, 5, 6. Once again, the exact same point on the number line. It's an equivalent fraction. 6/9 is equal to 2/3 is equal to 4/6.