Compare Fractions by Finding the Common Denominator

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.