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### Unit 14: Lesson 6

Equivalent fractions on the number line# Equivalent fraction visually

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

## 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.