Practise Using Common Denominators to Order Mixed and Improper Fractions

Before we compare fractions, they need the same denominators.

We do this by using lowest common multiples.

Suppose we wish to compare the mixed numbers 1 7/9 and 1 4/6.

Here, we know each fraction has one whole, so we only need to compare the fraction part of the mixed number. 

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 1 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 we now we can compare the fractions. 

14/18 > 12/18

1 7/9 > 1 4/6 

Let's try an example question. 

Example

Place these fractions in ascending order of size.

2 5/8, 2 1/2 and 2 2/3.

Answer

All three fractions have the same whole number in front of them (2), so we can ignore that when comparing their size.

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 like this:

12/24 < 15/24 < 16/24

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

2 1/2 < 2 5/8 < 2 2/3 

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