# 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: 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

 The denominator is the bottom number in a fraction. It shows how many equal parts the item is divided into

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

### 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

It is now easy to see that 9/24 is smaller than 10/24, (because 9 is smaller than 10).

so 5/12 is the larger fraction.

## 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 the larger fraction

so 13/15 is the larger fraction.