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.

Example: which is bigger: 38 or 512 ?

Convert each fraction to a decimal.

We can use a calculator (3÷8 and 5÷12), or the method on Converting Fractions to Decimals.

Anyway, these are the answers I get:

38 = 0.375, and 512 = 0.4166...

So 512 is bigger.

The Same Denominator Method

fraction

The denominator is the bottom number in a fraction.

It shows how many equal parts the item is divided into

When two fractions have the same denominator they are easy to compare:

Example:

49 is less than 59 (because 4 is less than 5)

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

Example: Which is larger: 38 or 512 ?

Look at this:

  • When we multiply 8 × 3 we get 24,
  • and when we multiply 12 × 2 we also get 24,

so let's try that (important: what we do to the bottom we must also do to the top):

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

We can see that 924 is smaller than 1024 (because 9 is smaller than 10).

so 512 is the larger fraction.

Making the Denominators the Same

There are two main methods to make the denominator the same:

They both work, use which one you prefer!

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

Using the Common Denominator method  we multiply each fraction by the denominator of the other:

  × 15  
5  =  75
6 90
  × 15  
and
  × 6  
13  =  78
15 90
  × 6  

We can see that 78 90 is the larger fraction

so 13 15 is the larger fraction.