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KS3 Bitesize

Maths

Percentages

'Percent' means 'per 100'. If 70 percent of the population own a pet, this means that 70 out of every hundred people own a pet. The symbol '%' means 'percent'.

Introduction

This Revision Bite covers:

Concept of a percentage

In this diagram, 30 out of 100 squares have been shaded. So 30% has been shaded.

Percentages

Percentage examples

What percentage has been shaded? 72 out of 100 squares have been shaded

What percentage has been shaded?

Percentage examples

72 percent has been shaded

72% has been shaded

Percentage examples

What percentage has been shaded? 6 out of 10 have been shaded in

What percentage has been shaded?

Percentage examples

60 percent has been shaded in

60% has been shaded in

Percentage examples

Half a circle has been shaded in. What percentage has been shaded?

What percentage has been shaded?

Percentage examples

50 percent has been shaded - half a circle has been shaded

50% has been shaded

Percentage examples

A quarter of a circle is shaded. What percentage is shaded?

What percentage is shaded?

Percentage examples

25 percent has been shaded

25% has been shaded.

Percentage of a quantity

It's often useful to be able to find a percentage of a quantity. For example, you might be told that bus fares are going up by 5% and you need to know how much more you will need each week.

Here are a couple of ways you could do it:

Find 1% of the quantity by dividing it by 100.

Find x% of a quantity by multiplying 1% of the quantity by x.

Method 1

Question

Rakesh has a box containing 60 pens. 20% of the pens are red. How many is that?

Answer

You need to find 20% of 60.

1% of 60 is 60 ÷ 100 = 0.6

So 20% of 60 is 0.6 × 20 = 12

Method 2

Find x% of a quantity by multiplying that quantity by x/100

This combines the division and multiplication of Method 1 into one sum.

Question

Q1. In a class of 25 pupils, 24% live in a flat. How many pupils live in a flat?

Q2. Last year Sam earned £20,000. This year her pay has increased by 8%.
a) By how much money has Sam's pay increased?
b) What is her new salary?

Answer

A1. 24% is equivalent to 24/100
24% of 25 = 24/100 × 25 = 6
Therefore 6 pupils live in a flat.

A2.
a) Method 1:
1% of 20000 = 20000 ÷ 100 = 200
8% of 20000 = 8 × 200 = 1600.

Method 2:
8/100 × 20000 = 1600.

b)Therefore, her new salary is:
£20000 + £1600 = £21600.

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