Maths

Addition, subtraction, multiplication and division - Foundation

For your exam, you will need to feel confident when dealing with fractions. This section will help you to recognise equivalent fractions and practise simple calculations.

Adding and subtracting fractions

added fraction

It is easy to add fractions when the numbers on the bottom are the same.

All you need to do is add the tops of the fractions together.

So 2/9 + 5/9 = 7/9

Sometimes you need to cancel down the answer to its simplest terms.

3/10 + 1/10 = 4/10 = 2/5

When the numbers on the bottom are not the same to start with, you use equivalent fractions to make them the same.

Question

3/5 + 1/4

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Answer

The numbers on the bottom of the fractions are not the same. You can use equivalent fractions to make them both equal 20.

3/5 = 12/20 and 1/4 = 5/20

Now you can add them together.

12/20 + 5/20 = 17/20

Subtraction

You subtract using the same methods you use for adding.

Question

Calculate: 3/5 - 1/5

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Answer

3/5 - 1/5 = 2/5

Question

Calculate5/8 - 3/10

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Answer

8 and 10 both divide into 40. So re-write the fractions using 40 as the number on the bottom of each one.

5/8 - 3/10 = 25/40 - 12/40 = 13/40

Multiplying and dividing fractions

To multiply fractions, you need to multiply the top numbers together, and multiply the bottom numbers together. Remember that you cannot cancel numbers that are both on the top of a fraction. Have a look at the example below.

4/5 × 5/6

Multiply then cancel:4 over 5 x 5 over 6 = 20 over 30 = 2 over 3

OR cancel between the top and the bottom then multiply:

4 over 5 x 5 over 6 = 2 over 3

Question

Calculate: 5/6 × 5/8

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Answer

5/6 × 5/8 = 25/48

The 5s do not cancel because they are both on the top of the fraction.

Dividing a fraction by a whole number

3/4 divided by 3 should be 1/3 of the original fraction, which would make the answer 1/4.

So 3/4 ÷ 3

= 3/4 ÷ 3/1    (writing 3 as 3/1)

= 1/4.

Dividing by a fraction

The rule to remember when dividing fractions is that you turn the fraction you are dividing by upside down, and multiply.

So going back to the previous example we can work this out by turning the 3/1 upside down.

3/4 ÷ 3/1 = 3/4 × 1/3 = 1/4

Dividing by 3 is the same as multiplying by 1/3.

It works with all fractions. For example dividing by 3/4 is the same as multiplying by 4/3.

Question

Calculate: 3/8 ÷ 3/4

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Answer

3/8 ÷ 3/4

= 3/8 × 4/3

= 1/2

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