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Percentages Objectives: D GradeIncrease or decrease a quantity by a given percentage C GradeWork out a percentage increase or decrease Prior knowledge: Understand : Finding percentages of quantities – calculator and non calculator Use of percentage multipliers to find the percentage of a quantity Percent to decimal conversion (i.e. percent ÷ 100)

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Percentages Percentage increase Find the percentage of the quantity and add it to the original Example 1: Increase 200 by 12% 12 × 200 100 2 = 24 cancel common factors 200 + 24 = 224 Example 2: Increase 270 by 40% cancel common factors 270 + 108 = 378 40 × 270 100 4 10 ≡ = 108

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Percentages Percentage decrease Find the percentage of the quantity and subtract it from the original Example 1: Decrease 200 by 12% 12 × 200 100 2 = 24 cancel common factors 200 - 24 = 176 Example 2: Decrease 270 by 40% cancel common factors 270 - 108 = 162 40 × 270 100 4 10 ≡ = 108

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Percentages Now do these: 1.Increase 250 by 10% 2. Decrease 500 by 6% 3. Decrease 24 by 25% 4. Increase 80 by 30% 5. Increase £4.20 by 15% 275 470 18 104 £4.83

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Percentages Percentage increase When calculating a percentage increase of a quantity we are starting with 100% and then we add the percentage asked for. e.g.Increase a quantity by 23% 100 % + 23 % = 123 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 + 23 = 123 100 100 100 Now 123 = 1.23 100 This is called the percentage multiplier for a percentage increase

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Percentages Example : Increase 345 by 56% the percentage multiplier is 1.56 100 % + 56 % = 156 % 156 = 1.56 100 345 × 1.56 = 538.2

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Percentages Now do these: 1.Increase 125 by 16% 2. Increase 340 by 9% 3. Increase 575 by 22% 4. Increase 84 by 1.3% 5. Increase £6.30 by 17.5% Percentage multiplier is 1.16 125 × 1.16 = 145 Percentage multiplier is 1.09 340 × 1.09 = 370.6 Percentage multiplier is 1.22 575 × 1.22 = 701.5 Percentage multiplier is 1.013 80 × 1.013 = 81.04 Percentage multiplier is 1.175 6.30 × 1.175 = £7.40

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Percentages Percentage decrease When calculating a percentage decrease of a quantity we are starting with 100% and then we subtract the percentage asked for. e.g.decrease a quantity by 23% 100 % - 23 % = 77 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 - 23 = 77 100 100 100 Now 77 = 0.77 100 This is called the percentage multiplier for a percentage decrease

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Percentages Example : Decrease 345 by 56% the percentage multiplier is 0.44 100 % - 56 % = 44 % 44 = 0.44 100 345 × 0.44 = 151.8

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Percentages Now do these: 1.Decrease 137 by 13% 2. Decrease 78 by 6% 3. Decrease 623 by 37% 4. Decrease 467 by 1.3% 5. Decrease £7.45 by 17.5% Percentage multiplier is 0.87 137 × 0.87 = 119.19 Percentage multiplier is 0.94 78 × 0.94 = 73.32 Percentage multiplier is 0.63 623 × 0.63 = 392.49 Percentage multiplier is 0.987 467 × 0.987 = 460.929 Percentage multiplier is 0.825 7.45 × 0.825 = £6.15

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Percentages To summarise percentage calculations Original quantity × percentage multiplier = new quantity By understanding how to rearrange equations you can find any of the three if you know the other two.

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Percentages Worksheet 1 Mixed Non-Calculator 1.Todd is paid £350 per week. He gets a 4% pay rise. What is his new weekly pay? 2.A package holiday is priced at £660. Julie gets a 10% discount for booking before the end of January. How much does she pay? 3.Chris has 50 books on his shelves. Jenny has 12% more books. How many books has Jenny got? 4.A train ticket is priced at £48. In the new year the cost increases by 2½ %. What is the new cost of the train ticket? 5.A music centre costs £280. VAT is added at 17 ½ %. What is the total cost £364 £594 £56 £49.20 £329

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Percentages Worksheet 2 Mixed Calculator 1.Sarah’s salary is £13 575 per year. Her annual bonus is 1¾% of her salary. How much does she earn altogether? 2.Jack sells computers. He is paid commission of 8¼% on his sales. Last year he sold computers worth £85 496. How much was his commission? 3.Nathan buys a new Fiat for £12 499. Over 2 years it depreciates by 45%. What is the value after 2 years 4.The population of Newtown was 74 970 in 2008. By 2009 the population had decreased by 27%. What is the population in 2009. 5.Decrease £9.55 by 12% £13 812.56 £7 053.42 £6 874.45 54 728 £7.40

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Percentages Worksheet 1 Mixed Non-Calculator 1.Todd is paid £350 per week. He gets a 4% pay rise. What is his new weekly pay? 2.A package holiday is priced at £660. Julie gets a 10% discount for booking before the end of January. How much does she pay? 3.Chris has 50 books on his shelves. Jenny has 12% more books. How many books has Jenny got? 4.A train ticket is priced at £48. In the new year the cost increases by 2½ %. What is the new cost of the train ticket? 5.A music centre costs £280. VAT is added at 17 ½ %. What is the total cost

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Percentages Worksheet 2 Mixed Calculator 1.Sarah’s salary is £13 575 per year. Her annual bonus is 1¾% of her salary. How much does she earn altogether? 2.Jack sells computers. He is paid commission of 8¼% on his sales. Last year he sold computers worth £85 496. How much was his commission? 3.Nathan buys a new Fiat for £12 499. Over 2 years it depreciates by 45%. What is the value after 2 years 4.The population of Newtown was 74 970 in 2008. By 2009 the population had decreased by 27%. What is the population in 2009. 5.Decrease £9.55 by 12%

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