Before we add or subtract fractions, we try to get them to have the same denominators.

We do this by using lowest common multiples.

 

Suppose we wish to subtract:

 

7	-	4
9		6

 

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

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

 

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

 

7	=	14
9		18

 

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

 

4	=	12
6		18

 

So we now have:

 

14	-	12
18		18

 

The answer is:

 

2	=	1
18		9

 

 

Example

When we work out this calculation, what is the lowest common denominator we should choose for both fractions?

 

7	-	4
15		10

 

Answer

The lowest common multiple of 15 and 10 is 30, because 2 × 15 = 30 and 3 × 10 = 30.

So the answer is 30.

 

We need to multiply both the numerator and denominator of 7/15 by 2, which gives us 14/30

We need to multiply both the numerator and denominator of 4/10 by 3, which gives us 12/30

14/30 - 12/30 = 2/30 which can be simplified to 1/15.

 

Now it's time to try some questions.