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## Arithmetic (all content)

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

Lesson 5: Comparing fractions- Comparing fractions with > and < symbols
- Comparing fractions with like numerators and denominators
- Compare fractions with the same numerator or denominator
- Comparing fractions
- Comparing fractions 2 (unlike denominators)
- Compare fractions with different numerators and denominators
- Comparing and ordering fractions
- Ordering fractions
- Order fractions

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# Comparing fractions

Comparing Fractions. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Why did Sal, in the 54/81 problem at1:51make a dot, erase it, and then write x?(115 votes)
- well, the reason he did that because in some school districs they teach their students that a dot means to multiply (x). Its like a little easier shorter thing for them to write. If you have any more questions just ask me! :D(13 votes)

- Can't you simplify fractions even though you, like can't? Take 5/12, for example. Can't you simplify that using what you know about decimals? 🤔🤔🤔(1 vote)
- You can convert a simplified fraction to a decimal, but you cannot make a simplified fraction into an even more simplified fraction.(5 votes)

- Why would u have to do the 9 divided by 9 if u dont actually use it?(1 vote)
- You very well might need the fraction 9/9. It may be equal to 1, but it has straightforward applications. You are splitting 9 gumballs among 9 friends? How many gumballs does each friend get? The answer is one, because 9/9 = 1.(5 votes)

- 24367/6 in lowest tearms(3 votes)
- This fraction fraction cannot be reduced only put into a mixed fraction which is 4061 1/6.(1 vote)

- 5 Goes equally into both 30 and 45 and is less than 15, so why didn't he use 5?(3 votes)
- Because by using the GREATEST of the common factors, you end up with the fraction in its lowest terms. 5 would not have accomplished that.(1 vote)

- Do you have to make the denominators the same to find the comparison?(2 votes)
- Not always. There are several ways to compare fractions. The most general method, that always works for any fractions, is to change to equivalent fractions with a common denominator and then compare the numerators. This works because you are expressing both numbers with a common unit (like halves, thirds, fourths, etc.), and then seeing which has more of that unit.

If fractions have the same numerator, you can reason about which is bigger:

3/4 or 3/5?

A denominator of 5 means a whole has been cut into 5 equal pieces, while 4 means a SAME size whole has been cut into 4 equal pieces. Which piece would be bigger? It makes sense that more pieces means that each piece will be smaller, right? So 1/5 is smaller than 1/4, which means that 3/5 is less than 3/4 - you have the same number of pieces but each piece is smaller.

Another method is to see if you can compare fractions to 1/2 or to 1.

For example, which is bigger, 3/5 or 5/12?

Well, 3/5 is more than 1/2 (if you had to fairly share 5 cookies with your brother, you would each get 1/2 of 5, or 2 and 1/2 cookies), but 5/12 is less than 1/2 (if you were sharing 12 cookies with your brother you would each get 6). So 3/5 is greater than 5/12.

Another example, which is greater 4/5 or 5/6?

They are each missing one unit to get to 1. But how close is each to 1?

4/5 is 1/5 away from 1

5/6 is 1/6 away from 1.

But we know that 1/5 is bigger than 1/6, so 4/5 is farther away from one than 5/6.

Since 5/6 is closer to 1, then it is bigger.(3 votes)

- find perimeter and area figure(2 votes)
- This i one of the best parts about fractions(2 votes)
- this can gt a bit confusing sometimes(2 votes)
- Your videos are amazing and actually help me learn! The only thing that, well it doesn't bother me I just thought I should bring it up is that i'm not from the US i'm from the UK and sometimes things that you learn in America is different to things that i learn. :'D(2 votes)

## Video transcript

Determine whether
30/45 and 54/81 are equivalent fractions. Well, the easiest way I can
think of doing this is to put both of these fractions into
lowest possible terms, and then if they're the same
fraction, then they're equivalent. So 30/45, what's the largest
factor of both 30 and 45? 15 will go into 30. It'll also go into 45. So this is the same thing. 30 is 2 times 15 and
45 is 3 times 15. So we can divide both the
numerator and the denominator by 15. So if we divide both the
numerator and the denominator by 15, what happens? Well, this 15 divided by 15,
they cancel out, this 15 divided by 15 cancel out, and
we'll just be left with 2/3. So 30/45 is the same
thing as 2/3. It's equivalent to 2/3. 2/3 is in lowest possible terms,
or simplified form, however you want to
think about it. Now, let's try to do 54/81. Now, let's see. Nothing really jumps
out at me. Let's see, 9 is divisible
into both of these. We could write 54 as being 6
times 9, and 81 is the same thing as 9 times 9. You can divide the numerator
and the denominator by 9. So we could divide both
of them by 9. 9 divided by 9 is 1, 9 divided
by 9 is 1, so we get this as being equal to 6/9. Now, let's see. 6 is the same thing
as 2 times 3. 9 is the same thing
as 3 times 3. We could just cancel these 3's
out, or you could imagine this is the same thing as dividing
both the numerator and the denominator by 3, or multiplying
both the numerator and the denominator by 1/3. These are all equivalent. I could write divide by
3 or multiply by 1/3. Actually, let me write
divide by 3. Let me write divide
by 3 for now. I don't want to assume you
know how to multiply fractions, because we're going
to learn that in the future. So we're going to divide by 3. 3 divided by 3 is just 1. 3 divided by 3 is 1, and
you're left with 2/3. So both of these fractions, when
you simplify them, when you put them in simplified form,
both end up being 2/3, so they are equivalent
fractions.