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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

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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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
CORRECT ANSWER
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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