Find Common Denominators to Order Fractions

Before we compare fractions, they need the same denominators.

We do this by using lowest common multiples.

Suppose we wish to compare 7/9 and 4/6.

We look for the smallest number that 9 and 6 go into.

This is called the lowest common multiple (LCM).

This will be 18, so we want to change both fractions into 18ths.

We multiply the numerator and the denominator of 7/9 by 2:

7/9 = 14/18

We multiply the numerator and the denominator of 4/6 by 3:

4/6 = 12/18

So now we can compare the fractions. 

14/18 > 12/18

7/9 > 4/6 

Let's try an example question. 

Example

Place these fractions in ascending order of size.

5/8, 1/2 and 2/3.

Answer

The lowest common multiple of 8, 2 and 3 is 24. 

3 × 8 = 24

12 × 2 = 24

8 × 3 = 24

We multiply the numerator and the denominator of 5/8 by 3:

5/8 = 15/24

We multiply the numerator and the denominator of 1/2 by 12:

1/2 = 12/24

We multiply the numerator and the denominator of 2/3 by 8:

2/3 = 16/24

We can order the equivalent fractions in ascending order like this:

12/24 < 15/24 < 16/24

The last step is to place our three original fractions in ascending order as shown below:

1/2 < 5/8 < 2/3 

Remember that ascending order means from lowest to highest - like going upstairs!

It's time for you to have a go at some questions now.