# Adding and Subtracting Fractions with Unrelated Denominators

In this worksheet, students add and subtract fractions, where the denominator of one fraction is not a multiple of the other.

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Fractions

Difficulty level:

### QUESTION 1 of 10

Before we add or subtract fractions, we try to get them to have the same denominators.

We do this by using lowest common multiples.

Suppose we wish to subtract:

 8 - 2 9 5

We look for the smallest number that 9 and 5 go into.

This will be 45, so we change both fractions into 45ths.

5 × 9 = 45 and 9 × 5 = 45

We multiply top and bottom of 8 ninths by 5:

 8 = 40 9 45

We multiply top and bottom of 2 fifths by 9:

 2 = 18 5 45

So we now have:

 40 - 18 45 45

 22 45

Example

Work out the following, remembering to give your answer in its lowest terms.

 2 + 3 3 4

The lowest common multiple of 3 and 4 is 12, because 4 × 3 = 3 × 4 = 12.

We multiply top and bottom of 2 thirds by 4:

 2 = 8 3 12

We multiply top and bottom of 3 quarters by 3:

 3 = 9 4 12

So we now have:

 8 + 9 12 12

This gives:

 17 12

But this must be changed to a mixed number.

17 ÷ 12 = 1 remainder 5.

 1 5 12

Work out the following, remembering to give your answer in its lowest terms.

 1 + 1 2 3

Work out the following, remembering to give your answer in its lowest terms.

 1 + 2 2 5

Work out the following, remembering to give your answer in its lowest terms.

 3 - 1 4 5

Work out the following, remembering to give your answer in its lowest terms.

 3 - 1 5 4

Work out the following, remembering to give your answer in its lowest terms.

 6 - 2 7 4

Work out the following, remembering to give your answer in its lowest terms.

 2 + 3 5 6

Work out the following, remembering to give your answer in its lowest terms.

 3 + 2 7 5

Work out the following, remembering to give your answer in its lowest terms.

 7 - 1 9 5

Work out the following, remembering to give your answer in its lowest terms.

 3 - 2 10 7

Work out the following, remembering to give your answer in its lowest terms.

 6 + 2 9 8
• Question 1

Work out the following, remembering to give your answer in its lowest terms.

 1 + 1 2 3
5/6
EDDIE SAYS
The lowest common multiple of 2 and 3 is 6.
This gives 3/6 + 2/6 = 5/6.
• Question 2

Work out the following, remembering to give your answer in its lowest terms.

 1 + 2 2 5
9/10
EDDIE SAYS
The lowest common multiple of 2 and 5 is 10.
This gives 5/10 + 4/10 = 9/10.
• Question 3

Work out the following, remembering to give your answer in its lowest terms.

 3 - 1 4 5
11/20
EDDIE SAYS
The lowest common multiple of 4 and 5 is 20.
This gives 15/20 - 4/20 = 11/20.
• Question 4

Work out the following, remembering to give your answer in its lowest terms.

 3 - 1 5 4
7/20
EDDIE SAYS
The lowest common multiple of 4 and 5 is 20.
This gives 12/20 - 5/20 = 7/20.
• Question 5

Work out the following, remembering to give your answer in its lowest terms.

 6 - 2 7 4
5/14
EDDIE SAYS
The lowest common multiple of 7 and 4 is 28.
This gives 24/28 - 14/28 = 10/28 = 5/14.
• Question 6

Work out the following, remembering to give your answer in its lowest terms.

 2 + 3 5 6
9/10
EDDIE SAYS
The lowest common multiple of 5 and 6 is 30.
This gives 12/30 + 15/30 = 27/30 = 9/10.
• Question 7

Work out the following, remembering to give your answer in its lowest terms.

 3 + 2 7 5
29/35
EDDIE SAYS
The lowest common multiple of 7 and 5 is 35.
This gives 15/35 + 14/35 = 29/35.
• Question 8

Work out the following, remembering to give your answer in its lowest terms.

 7 - 1 9 5
26/45
EDDIE SAYS
The lowest common multiple of 9 and 5 is 45.
This gives 35/45 - 9/45 = 26/45.
• Question 9

Work out the following, remembering to give your answer in its lowest terms.

 3 - 2 10 7
1/70
EDDIE SAYS
The lowest common multiple of 10 and 7 is 70.
This gives 21/70 - 20/70 = 1/70.
• Question 10

Work out the following, remembering to give your answer in its lowest terms.

 6 + 2 9 8
11/12
EDDIE SAYS
The lowest common multiple of 9 and 8 is 72.
This gives 48/72 + 18/72 = 66/72 = 33/36 = 11/12.
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