# Unit 17 Section 3 : Introduction to Percentages

In this section we introduce the idea of a percentage.
Percentages are another way of representing fractions and decimals.

The word 'percentage' means 'per hundred', so 50% means 50 per hundred, or ½.
Look at the table on the right for some common percentages:

## Percentages of Shapes

Example 1
Look at the two shapes below.
In each case, we need to work out what percentage of the shape is shaded.

Common Percentages
 100% = 100100 = 1 75% = 75100 = ¾ 50% = 50100 = ½ 25% = 25100 = ¼ 1% = 1 100 = 0.01 0% = 0 100 = 0
Example 2
In the two shapes above, what percentage of the shape was not shaded?
The whole of any object or shape is 100%.
(a) If 71% of the square is shaded, 29% must be not shaded.
(b) If 60% of the rectangle is shaded, 40% must be not shaded.

## Finding a percentage of an amount

To find a particular percentage of an amount, convert the percentage to a fraction, then multiply by the amount.

Example
Find 30% of 40 metres.

30% of 40 metres is 12 metres.

Practice Questions
Work out the answer to each of these questions then click on the button marked to see whether you are correct.
(a) What is 5% of 100 kg?

(b) What is 20% of 40 litres?

(c) What is 25% of £80?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Questions 1 & 2
Look at the shapes below:
 Question 1 Write down what percentage of each shape is shaded. (a) % (b) % (c) % (d) % (e) % (f) % Question 2 Write down what percentage of each shape is not shaded. (a) % (b) % (c) % (d) % (e) % (f) %

Question 3
76% of a rectangle is shaded.
%

Question 4
Look at the shapes below:
 Write down what percentage of each shape is shaded. (a) % (b) % (c) % (d) % (e) % (f) % (g) %

Question 5
35% of a class are girls.
What percentage are boys?
%

Question 6
88% of a class pass their maths test.
What percentage failed the test?
%

Question 7
Calculate the following (be careful with units).

(a) 50% of £200
£

(b) 30% of 500 kg
kg

(c) 60% of 50p
p

(d) 5% of £2
p

(e) 15% of 10 kg
kg

(f) 25% of 120 metres
metres

(g) 2% of £400
£

(h) 26% of £2
p

(i) 20% of £300
£

(j) 75% of 200 kg
kg

You have now completed Unit 17 Section 3
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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