Working with Percentages

Writing percentages as fractions ‘Percent’ means ‘out of 100’. To write a percentage as a fraction we write it over a hundred. For example: 46% = Cancelling: = % = Cancelling: = = % = Cancelling: = 3 =

Writing percentages as decimals We can write percentages as decimals by dividing by % = = 46 ÷ 100= % = = 7 ÷ 100 = % = = 130 ÷ 100 = % = = 0.2 ÷ 100= 0.002

Writing fractions as percentages To write a fraction as a percentage, we can find an equivalent fraction with a denominator of For example: = × 5 and = % = = × × and = %

Writing decimals as percentages To write a decimal as a percentage you can multiply it by 100%. For example: 0.08 = 0.08 × 100% = 8% = × 100% = 137.5%

Using a calculator We can also convert fractions to decimals and percentages using a calculator = 5 ÷ 16 × 100% = 31.25% 4 7 = 4 ÷ 7 × 100% = 57.14% (to 2 d.p.) 13 ÷ 8 × 100%= 162.5% 5 8 =1= 13 8

Calculating percentages using fractions Remember, a percentage is a fraction out of % of 90, means “16 hundredths of 90”, or × 90 = = 72 5 = × = 14.4

Using a calculator By writing a percentage as a decimal, we can work out a percentage using a calculator. Suppose we want to work out 38% of £65. 38% =0.38 So we key in: 0.38×65= And get an answer of We write the answer as £24.70.

What is 34 % of 82? 10 % = 82 ÷ 10 = 8.2 So: 30% = 8.2 x 3 = 24.6 Also: 2% = 8.2 ÷ 5 = 1.64 So: 4% = 1.64 x 2 = 3.28 Therefore: 34% = = 27.88

Now try these: Calculate the following by finding 10% first: 1.22% of % of % of % of % of % of % of % of 9 Calculate the following using fractions: 1.18% of % of % of % of % of % of % of % of 900 Calculate the following by using a calculator: 1.12% of % of % of % of % of % of 23

Answers: Calculate the following by finding 10% first: 1.22% of 55 = % of 180 = % of 400 = % of 60 = % of 300 = % of 94 = % of 78 = % of 9 = 1.17 Calculate the following using fractions: 1.18% of 45 = % of 90 = % of 35 = % of 2.44 = % of 130 = % of 320 = % of 8 = % of 900 = 315 Calculate the following by using a calculator: 1.12% of 67 = % of 89 = % of 12 = % of 43 = % of 15 = % of 23 = 28.29