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:

QUESTION 1 of 10

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 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

Place these fractions in ascending order of size.

 1 1 3 2 4 4

Column B

1. (smallest)
1/4
2.
1/2
3. (largest)
3/4

Place these fractions in ascending order of size.

 5 1 3 8 2 4

Column B

1. (smallest)
3/4
2.
1/2
3. (largest)
5/8

Place these fractions in ascending order of size.

 5 1 3 6 2 4

Column B

1. (smallest)
1/2
2.
3/4
3. (largest)
5/6

Place these fractions in ascending order of size.

 5 5 3 8 6 4

Column B

1. (smallest)
3/4
2.
5/8
3. (largest)
5/6

Place these fractions in ascending order of size.

 3 7 1 5 10 2

Column B

1. (smallest)
7/10
2.
3/5
3. (largest)
1/2

Place these fractions in ascending order of size.

 5 7 4 6 18 9

Column B

1. (smallest)
7/18
2.
4/9
3. (largest)
5/6

Place these fractions in ascending order of size.

 2 3 7 3 4 12

Column B

1. (smallest)
2/3
2.
7/12
3. (largest)
3/4

Place these fractions in ascending order of size.

 4 7 9 5 8 10

Column B

1. (smallest)
7/8
2.
4/5
3. (largest)
9/10

Place these fractions in ascending order of size.

 5 3 5 6 4 9

Column B

1. (smallest)
5/9
2.
3/4
3. (largest)
5/6

Place these fractions in ascending order of size.

 5 4 11 6 5 15

Column B

1. (smallest)
11/15
2.
4/5
3. (largest)
5/6
• Question 1

Place these fractions in ascending order of size.

 1 1 3 2 4 4

Column B

1. (smallest)
1/4
2.
1/2
3. (largest)
3/4
EDDIE SAYS
The lowest common multiple of 2, 4 and 4 is 4.
The fractions change to 2/4, 1/4 and 3/4.
• Question 2

Place these fractions in ascending order of size.

 5 1 3 8 2 4

Column B

1. (smallest)
1/2
2.
5/8
3. (largest)
3/4
EDDIE SAYS
The lowest common multiple of 8, 2 and 4 is 8.
The fractions change to 5/8, 4/8 and 6/8.
• Question 3

Place these fractions in ascending order of size.

 5 1 3 6 2 4

Column B

1. (smallest)
1/2
2.
3/4
3. (largest)
5/6
EDDIE SAYS
The lowest common multiple of 6, 2 and 4 is 12.
The fractions change to 10/12, 6/12 and 9/12.
• Question 4

Place these fractions in ascending order of size.

 5 5 3 8 6 4

Column B

1. (smallest)
5/8
2.
3/4
3. (largest)
5/6
EDDIE SAYS
The lowest common multiple of 8, 6 and 4 is 24.
The fractions change to 15/24, 20/24 and 18/24.
• Question 5

Place these fractions in ascending order of size.

 3 7 1 5 10 2

Column B

1. (smallest)
1/2
2.
3/5
3. (largest)
7/10
EDDIE SAYS
The lowest common multiple of 5, 10 and 2 is 10.
The fractions change to 6/10, 7/10 and 5/10.
• Question 6

Place these fractions in ascending order of size.

 5 7 4 6 18 9

Column B

1. (smallest)
7/18
2.
4/9
3. (largest)
5/6
EDDIE SAYS
The lowest common multiple of 6, 18 and 9 is 18.
The fractions change to 15/18, 7/18 and 8/18.
• Question 7

Place these fractions in ascending order of size.

 2 3 7 3 4 12

Column B

1. (smallest)
7/12
2.
2/3
3. (largest)
3/4
EDDIE SAYS
The lowest common multiple of 3, 4 and 12 is 12.
The fractions change to 8/12, 9/12 and 7/12.
• Question 8

Place these fractions in ascending order of size.

 4 7 9 5 8 10

Column B

1. (smallest)
4/5
2.
7/8
3. (largest)
9/10
EDDIE SAYS
The lowest common multiple of 5, 8 and 10 is 40.
The fractions change to 32/40, 35/40 and 36/40.
• Question 9

Place these fractions in ascending order of size.

 5 3 5 6 4 9

Column B

1. (smallest)
5/9
2.
3/4
3. (largest)
5/6
EDDIE SAYS
The lowest common multiple of 6, 4 and 9 is 36.
The fractions change to 30/36, 27/36 and 20/36.
• Question 10

Place these fractions in ascending order of size.

 5 4 11 6 5 15

Column B

1. (smallest)
11/15
2.
4/5
3. (largest)
5/6
EDDIE SAYS
The lowest common multiple of 6, 5 and 15 is 30.
The fractions change to 25/30, 24/30 and 22/30.
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