Page 116 - Mathematics Coursebook

11.2 Calculating percentages

11.2 Calculating percentages

You should be able to $nd simple percentages of a quantity without using a calculator.
You can easily $nd 50%, 25% or 10% because they are simple fractions. You can use these to

$nd other percentages.

Worked example 11.2

Find 35% of 80 kg.

Method 1
35% = 25% + 10%, which are easy percentages to work out.
1
25% of 80 = 4 of 80 = 20 Divide by 4 to work out 1 4 .
1
1
10% of 80 = 10 of 80 = 8 Divide by 10 to work out 10 .
35% of 80 kg = 28 kg 25% + 10% = 20 + 8 You should be able to use either method.

Method 2
35 7
35% = 100 = 20 Write 35% as a fraction and simplify it, cancelling by 5.
7 1 7
20 of 80 = 80 ÷ 20 × 7 = 28 kg Divide by 20 to fi nd 20 . Multiply by 7 to fi nd 20 .

) Exercise 11.2

1 a Write 20% as a fraction in its simplest terms.
b Work out 20% of: i 25 ii 40 iii 50 iv 65 v 120.

2 a Write each of these percentages as fractions, as simply as possible.
i 30% ii 85% iii 64% iv 8%
b Work out: i 30% of 40 ii 85% of 20 iii 64% of 50 iv 8% of 200.

3 Work out the following.
a 10% of 80 m b 15% of 60 kg c 44% of $200 d 85% of 40 cm
4 A man has a mass of 120 kg. He reduces his mass by 15%. How many kilograms is that?
5 30% of the mass of an object is 24 kilograms. Use this fact to find:

a 60% of the mass b 10% of the mass
c 50% of the mass d the whole mass of the object.
6 There were 300 people at a football match and 35% were adults. The rest were children.
a What percentage were children? b How many children were present?

7 Find the missing numbers.
a 25% of 80 m = % of 40 m b 60% of $25 = % of $50 c 12% of 300 = 6% of

11 Percentages 115