# Order Fractions

In this worksheet, students use common denominators to place fractions in ascending order of size.

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Fractions

Difficulty level:

#### Worksheet Overview

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

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

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