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# Creating equivalent fractions

Sal creates equivalent fractions by dividing a fraction model and number line into smaller parts. Created by Sal Khan.

Video transcript

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.