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### 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

Math>

Arithmetic (all content)>

Fractions>

Comparing fractions

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

## Want to join the conversation?

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Alexandria Murray

12 years agoPosted 12 years ago. Direct link to Alexandria Murray's post “Why did Sal, in the 54/81...”

Why did Sal, in the 54/81 problem at

1:51

make a dot, erase it, and then write x?•

(115 votes)

Lauren

12 years agoPosted 12 years ago. Direct link to Lauren's post “well, the reason he did t...”

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)

Ethan

7 years agoPosted 7 years ago. Direct link to Ethan's post “Can't you simplify fracti...”

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)

Joe Williams

7 years agoPosted 7 years ago. Direct link to Joe Williams's post “You can convert a simplif...”

You can convert a simplified fraction to a decimal, but you cannot make a simplified fraction into an even more simplified fraction.

(5 votes)

Layla Fox

7 years agoPosted 7 years ago. Direct link to Layla Fox's post “Why would u have to do th...”

Why would u have to do the 9 divided by 9 if u dont actually use it?

•

(1 vote)

Whiskers467

7 years agoPosted 7 years ago. Direct link to Whiskers467's post “You very well might need ...”

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)

Liam Porter

11 years agoPosted 11 years ago. Direct link to Liam Porter's post “24367/6 in lowest tearms”

24367/6 in lowest tearms

•

(3 votes)

00015651

11 years agoPosted 11 years ago. Direct link to 00015651's post “This fraction fraction ca...”

This fraction fraction cannot be reduced only put into a mixed fraction which is 4061 1/6.

(1 vote)

Quinn

4 years agoPosted 4 years ago. Direct link to Quinn's post “5 Goes equally into both ...”

5 Goes equally into both 30 and 45 and is less than 15, so why didn't he use 5?

•

(3 votes)

Ivye Hayes

4 years agoPosted 4 years ago. Direct link to Ivye Hayes's post “Because by using the GREA...”

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)

krithi2001

9 years agoPosted 9 years ago. Direct link to krithi2001's post “Your videos are amazing a...”

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

•

(3 votes)

Bri

11 years agoPosted 11 years ago. Direct link to Bri's post “Do you have to make the d...”

Do you have to make the denominators the same to find the comparison?

•

(2 votes)

lisa

11 years agoPosted 11 years ago. Direct link to lisa's post “Not always. There are sev...”

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)

Judy Odhiambo

4 years agoPosted 4 years ago. Direct link to Judy Odhiambo's post “find perimeter and area f...”

find perimeter and area figure

•

(2 votes)

noralavin

5 years agoPosted 5 years ago. Direct link to noralavin's post “This i one of the best pa...”

This i one of the best parts about fractions

•

(2 votes)

Evelyn

4 years agoPosted 4 years ago. Direct link to Evelyn's post “this can gt a bit confusi...”

this can gt a bit confusing sometimes

•

(2 votes)

## Video transcript

Determine whether30/45 and 54/81 are equivalent fractions. Well, the easiest way I canthink of doing this is to put both of these fractions intolowest possible terms, and then if they're the samefraction, then they're equivalent. So 30/45, what's the largestfactor 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 and45 is 3 times 15. So we can divide both thenumerator and the denominator by 15. So if we divide both thenumerator and the denominator by 15, what happens? Well, this 15 divided by 15,they cancel out, this 15 divided by 15 cancel out, andwe'll just be left with 2/3. So 30/45 is the samething as 2/3. It's equivalent to 2/3. 2/3 is in lowest possible terms,or simplified form, however you want tothink about it. Now, let's try to do 54/81. Now, let's see. Nothing really jumpsout at me. Let's see, 9 is divisibleinto both of these. We could write 54 as being 6times 9, and 81 is the same thing as 9 times 9. You can divide the numeratorand the denominator by 9. So we could divide bothof them by 9. 9 divided by 9 is 1, 9 dividedby 9 is 1, so we get this as being equal to 6/9. Now, let's see. 6 is the same thingas 2 times 3. 9 is the same thingas 3 times 3. We could just cancel these 3'sout, or you could imagine this is the same thing as dividingboth the numerator and the denominator by 3, or multiplyingboth the numerator and the denominator by 1/3. These are all equivalent. I could write divide by3 or multiply by 1/3. Actually, let me writedivide by 3. Let me write divideby 3 for now. I don't want to assume youknow how to multiply fractions, because we're goingto 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, andyou're left with 2/3. So both of these fractions, whenyou simplify them, when you put them in simplified form,both end up being 2/3, so they are equivalentfractions.