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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.

'Adding and Subtracting Fractions with Unrelated Denominators' worksheet

Key stage:  KS 2

Curriculum topic:   Number: Fractions, Decimals and Percentages

Curriculum subtopic:   Add/Subtract Fractions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Before we add or subtract fractions, they need to have the same denominators by using lowest common multiples.

 

We can't subtract these fractions until the denominators are the same:

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

 

The answer is:

22
45

 

 

Example

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

2  +  3
3 4

 

Answer

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.

 

The answer is:

1 5
12
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