Use Common Multiples to Find Common Denominators

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.