Order Fractions

Before we compare fractions, they need 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 want to change both fractions into 18ths.

 

We multiply top and bottom of 7 ninths by 2:

7	=	14
9		18

 

We multiply top and bottom of 4 sixths by 3:

4	=	12
6		18

 

So we now have:

14	and	12
18		18

 

Clearly:

14	>	12
18		18

 

So:

7	>	4
9		6

 

 

Example

Place these fractions in ascending order of size.

5		1		2
8		2		3

 

Answer

The lowest common multiple of 8, 2 and 3 is 24, because 3 × 8 = 24 and 12 × 2 = 24 and 8 × 3 = 24.

We multiply top and bottom of 5 eighths by 3:

5	=	15
8		24

 

We multiply top and bottom of 1 half by 12:

1	=	12
2		24

 

We multiply top and bottom of 2 thirds by 8:

2	=	16
3		24

 

Clearly:

12	<	15	<	16
24		24		24

 

So the ascending order is:

1		5		2
2		8		3