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

Lesson 5: Comparing fractions

# 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 at make a dot, erase it, and then write x?
• 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
• 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.
• 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.
• 24367/6 in lowest tearms
• 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?
• 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)
• 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
• Do you have to make the denominators the same to find the comparison?
• 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.