 # Adding and Subtracting Fractions with Related Denominators

In this worksheet, students add and subtract fractions, where the denominator of one fraction is 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 3

We look for the smallest number that 9 and 3 go into.

This will be 9, so we change both fractions into 9ths.

(Note that the first fraction is already in 9ths so won't need to be changed.)

We multiply top and bottom of 2 thirds by 3:

 2 = 6 3 9

So we now have:

 8 - 6 9 9

 2 9

Example

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

 7 + 4 15 30

The lowest common multiple of 15 and 30 is 30, because 2 × 15 = 30.

We multiply top and bottom of 7 fifteenths by 2:

 7 = 14 15 30

So we now have:

 14 + 4 30 30

This gives:

 18 30

But this must be reduced by dividing top and bottom by 2.

 9 15

which we write as   9/15.

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

 1 + 1 2 8

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

 2 - 1 3 9

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

 3 - 2 5 10

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

 3 + 1 4 12

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

 5 + 1 6 12

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

 7 - 2 15 5

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

 3 - 7 5 20

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

 3 + 4 14 7

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

 5 + 2 8 16

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

 7 - 1 10 30
• Question 1

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

 1 + 1 2 8
5/8
EDDIE SAYS
The lowest common multiple of 2 and 8 is 8.
This gives 4/8 + 1/8 = 5/8.
• Question 2

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

 2 - 1 3 9
5/9
EDDIE SAYS
The lowest common multiple of 3 and 9 is 9.
This gives 6/9 - 1/9 = 5/9.
• Question 3

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

 3 - 2 5 10
2/5
EDDIE SAYS
The lowest common multiple of 5 and 10 is 10.
This gives 6/10 - 2/10 = 4/10 = 2/5.
• Question 4

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

 3 + 1 4 12
5/6
EDDIE SAYS
The lowest common multiple of 4 and 12 is 12.
This gives 9/12 + 1/12 = 10/12 = 5/6.
• Question 5

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

 5 + 1 6 12
11/12
EDDIE SAYS
The lowest common multiple of 6 and 12 is 12.
This gives 10/12 + 1/12 = 11/12.
• Question 6

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

 7 - 2 15 5
1/15
EDDIE SAYS
The lowest common multiple of 15 and 5 is 15.
This gives 7/15 - 6/15 = 1/15.
• Question 7

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

 3 - 7 5 20
1/4
EDDIE SAYS
The lowest common multiple of 5 and 20 is 20.
This gives 12/20 - 7/20 = 5/20 = 1/4.
• Question 8

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

 3 + 4 14 7
11/14
EDDIE SAYS
The lowest common multiple of 14 and 7 is 14.
This gives 3/14 + 8/14 = 11/14.
• Question 9

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

 5 + 2 8 16
3/4
EDDIE SAYS
The lowest common multiple of 8 and 16 is 16.
This gives 10/16 + 2/16 = 12/16 = 3/4.
• Question 10

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

 7 - 1 10 30
2/3
EDDIE SAYS
The lowest common multiple of 10 and 30 is 30.
This gives 21/30 - 1/30 = 20/30 = 2/3.
---- OR ----

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