Page 114 - Mathematics Coursebook

11.1 Simple percentages

11.1 Simple percentages
Useful conversions
1
Per cent just means ‘out of 100’. 2 = 50%
1
t 25% means ‘25 parts out of 100’. 4 1 = 25%
1
1
t 25% is another way to write . 3 = 33 %
3
4 1 = 10%
So a percentage is just a di# erent way of writing a fraction. 10 1
You have already learnt how to write some simple fractions as 100 = 1%
decimals in Unit 7.

Worked example 11.1

a What percentage of this shape is shaded?
b What percentage is not shaded?

8
a The fraction shaded is 20 . There are 20 identical squares. 8 are shaded.
2
8
20 = 5 8 and 20 have a common factor of 4. Divide them both by 4.
40
2 = 100 = 40% shaded Look for a fraction out of 100. 5 × 20 = 100 so multiply by 20.
5
b So 60% is not shaded. The whole shape is 100%. 100% − 40% = 60%

) Exercise 11.1

1 Write down the fraction shaded in each diagram. Then write each fraction as a percentage.
a b

c d

2 Write each percentage as a fraction. Write the answers as simply as possible.
a 75% b 20% c 30% d 90% e 5%
1
3 If 25% = , what fraction is 12.5%?
4

11 Percentages 113