Comparing Fractions

Sometimes we need to compare two fractions to discover which is larger or smaller. There are two easy ways to compare fractions: using decimals; or using the same denominator

The Decimal Method of Comparing Fractions

Just convert each fraction to decimals, and then compare the decimals.

Which is bigger: 3/8 or 5/12 ?

You need to convert each fraction to a decimal. You can do this using your calculator (3÷8 and 5÷12), or you can read about Converting Fractions to Decimals. Anyway, these are the answers I get:

3/8 = 0.375, and 5/12 = 0.4166...

So, 5/12 is bigger.

The Same Denominator Method

If two fractions have the same denominator (the bottom number) then they are easy to compare.

For example 4/9 is less than 5/9 (because 4 is less than 5)

But if the denominators are not the same you need to make them the same (using Equivalent Fractions).

Example: Which is larger: 3/8 or 5/12 ?

If you multiply 8 × 3 you get 24 , and if you multiply 12 × 2 you also get 24, so let's try that (important: what you do to the bottom, you must also do to the top):

  × 3  
3  =  9
   
8 24
  × 3  
and,
  × 2  
5  =  10
   
12 24
  × 2  

so it is now easy to see that 10/24 is bigger than 9/24, so 5/12 must be bigger.

How to Make the Denominators the Same

The trick is to find the Least Common Multiple of the two denominators. In the previous example, the Least Common Multiple of 8 and 12 was 24.

Then it is just a matter of changing each fraction to make it's denominator the Least Common Multiple.

Example: Which is larger: 5/6 or 13/15?

The Least Common Multiple of 6 and 15 is 30. So, let's do some multiplying to make each denominator equal to 30 :

  × 5  
5  =  25
   
6 30
  × 5  
and,
  × 2  
13  =  26
   
15 30
  × 2  

Now we can easily see that 26/30 is larger than 25/30, so 13/15 is the larger fraction.