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.