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### Course: Arithmetic (all content) > Unit 5

Lesson 7: Equivalent fractions on the number line# Creating equivalent fractions

Learn about equivalent fractions. It demonstrates how to find equivalent fractions using visuals, like dividing a whole into equal sections and shading them. The video also shows how to represent equivalent fractions on a number line. The examples used include 2/3, 4/6, and 6/9, which are all equivalent fractions. Created by Sal Khan.

## Want to join the conversation?

- What does equivalent mean?(90 votes)
- Equivalent means "the same as". One is equivalent to 1. Or one is the same as 1.(52 votes)

- Is there any formula for quickly creating row of equivalent fractions? I realized that if we take 2/3, next fraction will be 4/6.. and there is formula like 2+2/3+3=4/6 and this formula continues to the infinity. In this fraction it's just adding +2 to the numerator and +3 to the denominator. Is there so me general formula or pattern for every fraction?(7 votes)
- Yes you are just multiplying (adding) the fractions times 2.

The way you are doing it is the way I've done it all my life.

I hope my answer helps you.(7 votes)

- you guys are so smart(4 votes)
- that is good to know(1 vote)

- do you have to draw lines inside of the shape(5 votes)
- Yes but shade the ones you need to shade so if your fraction is 5/6 I would shade 5 of the sixths(0 votes)

- What's the difference of "equivalent" and same?(0 votes)
- In terms of math, I don't think there is a difference.

We use all of these phrases to mean that items are equal.

X is equal to Y

X is the same as Y

X is equivalent to Y(12 votes)

- what does equvilent mean(2 votes)
- did you know that an improper fraction is greater than an hole?(2 votes)
- What's t he app he's using?(2 votes)
- Probably annotate.(1 vote)

- Why is there hard math also my name is gisselle(2 votes)

## 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.