Before we compare fractions, we try to get them to have the same denominators.

We do this by using lowest common multiples.

 

Suppose we wish to compare:

 

7	and	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 the numerator and 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	and	12
18		18

 

14	>	12
18		18

 

7	>	4
9		6

 

 

Example

Which is bigger?

 

12	or	11
8		6

 

Answer

The lowest common multiple of 8 and 6 is 24, because 3 × 8 = 24 and 4 × 6 = 24.

We multiply the numerator and the denominator of 12/8 by 3:

 

12	=	36
8		24

 

We multiply the numerator and the denominator of 11/6 by 4:

 

11	=	44
6		24

 

 

44	>	36
24		24

 

11	is bigger
6

 

 

Let's move on to the questions now.