For full tracking and unlimited access to thousands of activities

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 

 

girl has an idea

 

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!

 

girl going upstaris

 

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

10 questions