Main content

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

Lesson 8: Equivalent fractions 2- Equivalent fractions
- Visualizing equivalent fractions
- Equivalent fractions (fraction models)
- More on equivalent fractions
- Equivalent fractions
- Equivalent fractions
- Equivalent fractions 2
- Equivalent fractions review
- Equivalent fractions and different wholes
- Equivalent fractions and different wholes
- Simplify fractions

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Equivalent fractions

Learn how to write equivalent fractions. Created by Sal Khan.

## Want to join the conversation?

- what will i add to make 5/8 to make it equal to 1?(157 votes)
- Yes, 1/2, ,2/4, and 4/8 are all equal because if they are all one half, then they are equal.(87 votes)

- What is the numerator?(49 votes)
- The top number is the numerator

The bottom number is the denominator(118 votes)

- what country came up with the word fraction?and what does it mean in there country or city?(34 votes)
- By now you have probably found out already, but here you go. The earliest evidence of using fractions dates back to ancient Egypt and ancient Greece.

However, the English word "fraction" is based on the Latin (the language of the ancient Romans) word "fractus", which literally means "broken". This is surely related to other English words such as fracture, fractured etc.

Language evolves in a very gradual way, over decades and centuries. Sometimes it's possible to say with accuracy where a word comes from and who supposedly first used it, but usually the best you can do is say what roots the word stems from, like in this case. It's very hard to say at what point in time the word "fraction" crept into English with its mathematical significance.(45 votes)

- 4:17I am pretty sure that example confused many people, they are like, how 3:5 X 1 = 21/35 ? because anything X 1 is the same thing but the result is different, how can that be....?(26 votes)
- "anything X 1 is the same thing", and in fact you are right : )

Although 3/5 and 21/35 use different numbers, they represent the same QUANTITY. For example 10/5 and 50/25, are two ways to represent the exact same quantity (i just multiplied 10/5 five times).

So although it seems that it doesn't make sense (and anyway i think you'll never fine yourself doing it), you could write: 3/5 x 1 = 9/15, or 3/5 x 1 = 12/20, or 3/5 x 1 = 21/35: because all those different fractions are still the same quantity of 3/5! (9/15 is 3/5 x 3, 12/20 is 3/5 x 4, 21/35 is 3/5 x 7)

It's more of a "metaphor" that actual math anyway, if you don't want to confuse yourself just write 3/5 x 7 and don't start wondering about 7/7 or 1s or whatever : )(23 votes)

- so an Equivalent fraction is something that is a same thing as the other one but made in a different way(18 votes)
- Yes. Equivalent fractions are interchangeable in every way, so they are a useful way of simplifying equations. The fraction 1/5 is equivalent to the fraction 12589/62945, but it's much easier to use!(17 votes)

- what is equivalent to 4 2/3?(6 votes)
- There is a mixed number and infinite improper fractions that are equivalent to 4 2/3.

The mixed number is 14/3. Some examples of equivalent improper fractions are 4 4/6, 4 6/9, and 4 8/12.

Hope this helps!(6 votes)

- what is an equivalent fraction?(1 vote)
- An equivalent fraction is a fraction that is the same as another fraction with a different denominator(7 votes)

- this video is good for beginners but are there videos showing and explaining the hard stuff?(4 votes)
- Is the numerator on the top or bottom?(4 votes)
- top

the denominater is on the bottom(1 vote)

- After I watched the equivalent fraction video they made more since.(3 votes)

## Video transcript

Welcome to my presentation
on equivalent fractions. So equivalent fractions
are, essentially what they sound like. They're two fractions that
although they use different numbers, they actually
represent the same thing. Let me show you an example. Let's say I had
the fraction 1/2. Why isn't it writing. Let me make sure I get
the right color here. Let's say I had
the fraction 1/2. So graphically, if we to draw
that, if I had a pie and I would have cut it
into two pieces. That's the denominator
there, 2. And then if I were to eat
1 of the 2 pieces I would have eaten 1/2 of this pie. Makes sense. Nothing too complicated there. Well, what if instead of
dividing the pie into two pieces, let me just draw
that same pie again. Instead of dividing it in two
pieces, what if I divided that pie into 4 pieces? So here in the denominator I
have a possibility of-- total of 4 pieces in the pie. And instead of eating one
piece, this time I actually ate 2 of the 4 pieces. Or I ate 2/4 of the pie. Well if we look at these two
pictures, we can see that I've eaten the same
amount of the pie. So these fractions
are the same thing. If someone told you that they
ate 1/2 of a pie or if they told you that they ate 2/4 of a
pie, it turns out of that they ate the same amount of pie. So that's why we're saying
those two fractions are equivalent. Another way, if we actually
had-- let's do another one. Let's say-- and that pie is
quite ugly, but let's assume it's the same type of pie. Let's say we divided
that pie into 8 pieces. And now, instead of eating 2
we ate 4 of those 8 pieces. So we ate 4 out of 8 pieces. Well, we still ended up eating
the same amount of the pie. We ate half of the pie. So we see that 1/2 will equal
2/4, and that equals 4/8. Now do you see a pattern here
if we just look at the numerical relationships
between 1/2, 2/4, and 4/8? Well, to go from 1/2 to 2/4 we
multiply the denominator-- the denominator just as review is
the number on the bottom of the fraction. We multiply the
denominator by 2. And when you multiply the
denominator by 2, we also multiply the numerator by 2. We did the same thing here. And that makes sense because
well, if I double the number of pieces in the pie, then I have
to eat twice as many pieces to eat the same amount of pie. Let's do some more examples
of equivalent fractions and hopefully it'll
hit the point home. Let me erase this. Why isn't it letting me erase? Let me use the regular mouse. OK, good. Sorry for that. So let's say I had
the fraction 3/5. Well, by the same principle,
as long as we multiply the numerator and the denominator
by the same numbers, we'll get an equivalent fraction. So if we multiply the numerator
times 7 and the denominator times 7, we'll get 21-- because
3 times 7 is 21-- over 35. And so 3/5 and 21/35 are
equivalent fractions. And we essentially, and I don't
know if you already know how to multiply fractions, but all we
did is we multiplied 3/5 times 7/7 to get 21/35. And if you look at this, what
we're doing here isn't magic. 7/7, well what's 7/7? If I had 7 pieces in a pie
and I were to eat 7 of them; I ate the whole pie. So 7/7, this is the
same thing as 1. So all we've essentially
said is well, 3/5 and we multiplied it times 1. Which is the same thing as 7/7. Oh boy, this thing
is messing up. And that's how we got 21/35. So it's interesting. All we did is multiply the
number by 1 and we know that any number times 1
is still that number. And all we did is we figured
out a different way of writing 21/35. Let's start with
a fraction 5/12. And I wanted to write that with
the denominator-- let's say I wanted to write that with
the denominator 36. Well, to go from 12 to 36, what
do we have to multiply by? Well 12 goes into
36 three times. So if we multiply the
denominator by 3, we also have to multiply the numerator by 3. Times 3. We get 15. So we get 15/36 is the
same thing as 5/12. And just going to our original
example, all that's saying is, if I had a pie with 12
pieces and I ate 5 of them. Let's say I did that. And then you had a pie, the
same size pie, you had a pie with 36 pieces and
you ate 15 of them. Then we actually ate the
same amount of pie.