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Equivalent fraction visually

Sal uses number lines and fraction models to show equivalent fractions. Created by Sal Khan.

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Video transcript

So what I want you to do is pause this video and think about what fraction the red part represents in each of these shapes. Or what fraction of the whole does the red part represent? And I also want to plot it out on a number line, to plot that fraction as a number on a number line. So let's go through each of these. So in this pie right over here, we have 1, 2, 3, 4, 5 equal sections. And 1 of those 5 equal sections is shaded in. So we could say that 1/5 of this pie is shaded in. Now over here, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal sections, and 2 of them are shaded in. So we could say that 2/10 are shaded in. And then, finally, right over here, once again, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal sections, and 2 of them are shaded in red. So in this situation, the red slices represent 2/10 of the whole. And if we were to try to plot this on a number line, so right over here, we do a quick one right over here. Let me do it like this. Let me make a big number line here. And let's take the section between 0 and 1, that's what we want to focus on, and I'm going to divide it into 5 equal sections. So 1, 2, 3, 4, 5 equal sections and then that gets us to 1. So this right over here, 1/5, that would be 1 out of the 5 equal sections. So that would get us right over there. So this would be 1/5. Now, what I want to do, let me copy and paste this same number line since I've already drawn it. So copy and paste it. So let me put it right over here. But now, I'm going to divide it into 10 equal sections. Let's see. Let me divide it into 10 equal sections on the top one. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So I've divided it into 10 equal sections. And I want to figure out where 2/10 goes. So I'm going to go 2 of those equal sections, so 1, 2. So once again, I've got to that exact same point. So this 1/5 I could also represent as 2/10. So I could represent this as 2/10, this point right over here. And you might be saying, hey, wait, but that means that those are the same number. They're the exact same point on the number line. And if you said that, you would be absolutely correct. 1/5 is equal to 2/10. They represent the exact same number. And it makes sense even when you visually look at them as a fraction of these pies. Here going from this slice to this slice, if you were just divide all of these slices into 2, you see that you have the exact same fraction shaded in as this one right over here. They've become identical. I didn't shade in anything else. I haven't taken any of the red away. I haven't any of the red. I just divided all of those pieces of pie into 2. And so you see that the exact same part of the whole pie is shaded in. And here it's not quite as obvious, but if you imagine taking this, dividing it into 2 and then splitting them up so that they look like this, you still have the same part of the circle shaded in red. So it makes complete sense that they represent the same number on the number line. That this number right over here, it's not only 1/5, it also is 2/10. 1/5 is equal to 2/10.