Maths

Fraction basics

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.

Fractions of a quantity

How do we find 3/5 of 20?

Method 1 is to find 1/5 of 20, then multiply by 3.

1/5 of 20 is 20 ÷ 5 = 4.

We need 3/5 of 20, so we multiply 4 by 3.

3/5 of 20 = 4 × 3 = 12.

Method 2 is to multiply 3/5 by 20 (more on multiplying fractions here and here).

3/5 × 20 = 3/5 × 20/1 = 60/5 = 12

Question

Use either method to find 3/7 of 35.

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Answer

The answer is 15.

(1/7 of 35 is 5.)

Equivalent fractions

Refresh your memory on fractions in the activity below.

A fraction can be written in different ways and still mean the same thing. These are called equivalent fractions. Look at the shaded areas in this rectangle.

two sets of fractions

so 3 over 5 = 6 over 10

You can produce lots of equivalent fractions by multiplying or dividing the top and bottom by the same number.

multiplied fraction

If you are asked to fill in a missing number, remember that the top and bottom must be multiplied or divided by the same number.

Question

What is the missing number? 4 over 5 = ? over 15

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Answer

Here, the bottom is multiplied by 3, so you must multiply the top by 3.4 over 5 = 12 over 15

Cancelling fractions

Sometimes you can divide the top and bottom of a fraction by the same number. This is called cancelling down. It is also called simplifying the fraction. You often have to write a fraction in its simplest terms. This means that you have to cancel it down until it cannot be canceled down any more

Question

Write this fraction in its simplest form:12 over 16

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Answer

Dividing by 4: 12 over 16 = 3 over 4

You could do this in two stages.

Dividing top and bottom by 2, to get 6/8.

Then dividing the top and bottom by 2 again, to get 3/4.

12 over 16 = 6 over 8 = 3 over 4

When you have worked out a fraction question, you should always cancel down the answer.

One number as a fraction of another

Imagine that there are 10 questions in a test and you get 7 of them correct. You would say that you got 7 over 10

7 as a fraction of 10 is 7 over 10

In the same way, 4 as a fraction of 12 is 4 over 12 or 1 over 3 and 20 as a fraction of 48 is 20 over 48 or 5 over 12

Easy? Yes, but just be careful with the units.

For example, 20p as a fraction of £2 is not 20 over 2 or 20 over 200 (£2 = 200p). And 30cm as a fraction of 5m is 30 over 500 (5m = 500cm).

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