1. Working with Percentages

2. 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% = 46 100 Cancelling: 46 100 = 23 50 23 50 180% = 180 100 Cancelling: 180 100 = 9 5 9 5 = 1 4 5 7.5% = 7.5 100 Cancelling: 15 200 3 40 = 3 = 15 200

3. Writing percentages as decimals We can write percentages as decimals by dividing by 100. 46% = 46 100 = 46 ÷ 100= 0.46 7% = 7 100 = 7 ÷ 100 = 0.07 130% = 130 100 = 130 ÷ 100 = 1.3 0.2% = 0.2 100 = 0.2 ÷ 100= 0.002

4. Writing fractions as percentages To write a fraction as a percentage, we can find an equivalent fraction with a denominator of 100. 85 For example: = 17 20 100 × 5 and = 100 85 85% 1 7 25 = = 32 25 × 4 100 × 4 128 and = 100 128 128%

5. 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% 1.375 = 1.375 × 100% = 137.5%

6. Using a calculator We can also convert fractions to decimals and percentages using a calculator. 5 16 = 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

7. Calculating percentages using fractions Remember, a percentage is a fraction out of 100. 16% of 90, means “16 hundredths of 90”, or 16 100 × 90 = = 72 5 = 14 2 5 4 25 × 90 5 18 = 14.4

8. 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 24.7. We write the answer as £24.70.

9. 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% = 24.6 + 3.28 = 27.88

10. Now try these: Calculate the following by finding 10% first: 1.22% of 562. 34% of 1803. 17.5% of 400 4. 56% of 60 5. 65% of 3006. 110% of 947. 86% of 78 8. 13% of 9 Calculate the following using fractions: 1.18% of 452. 35% of 903. 26% of 354. 75% of 2.44 5. 67% of 1306. 110% of 320 7. 92% of 8 8. 35% of 900 Calculate the following by using a calculator: 1.12% of 672. 56% of 893. 15.7% of 124. 8% of 43 5. 3.6% of 156. 123% of 23

11. Answers: Calculate the following by finding 10% first: 1.22% of 55 = 12.1 2. 34% of 180 = 61.23. 17.5% of 400 = 70 4. 56% of 60 = 33.65. 65% of 300 = 1956. 110% of 94 = 103.4 7. 86% of 78 = 67.088. 13% of 9 = 1.17 Calculate the following using fractions: 1.18% of 45 = 8.12. 35% of 90 = 31.53. 26% of 35 = 9.1 4. 75% of 2.44 = 1.835. 67% of 130 = 87.16. 110% of 320 = 352 7. 92% of 8 = 7.368. 35% of 900 = 315 Calculate the following by using a calculator: 1.12% of 67 = 8.042. 56% of 89 = 49.843. 15.7% of 12 = 1.884 4. 8% of 43 = 3.445. 3.6% of 15 = 0.546. 123% of 23 = 28.29