Transcript Document
Percentages Objectives: D Grade C Grade Increase or decrease a quantity by a given percentage Work out a percentage increase or decrease Prior knowledge: Understand : Finding percentages of quantities – calculator and non calculator Percent to decimal conversion (i.e. percent ÷ 100) Use of percentage multipliers to find the percentage of a quantity Percentages Percentage increase Find the percentage of the quantity and add it to the original Example 1: Increase 200 by 12% cancel common factors Example 2: Increase 270 by 40% cancel common factors 2 12 × 200 = 24 100 200 + 24 = 224 4 × 270 = 108 40 ≡ 100 10 270 + 108 = 378 Percentages Percentage decrease Find the percentage of the quantity and subtract it from the original Example 1: Decrease 200 by 12% cancel common factors Example 2: Decrease 270 by 40% cancel common factors 2 12 × 200 = 24 100 200 - 24 = 176 4 × 270 = 108 40 ≡ 100 10 270 - 108 = 162 Now do these: Percentages 1. Increase 250 by 10% 275 2. Decrease 500 by 6% 470 3. Decrease 24 by 25% 18 4. Increase 80 by 30% 104 5. Increase £4.20 by 15% £4.83 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 % 100 % + 23 % = 123 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 + 23 = 123 Now 123 = 1.23 This is called the percentage multiplier for 100 100 100 100 a percentage increase Percentages Example : Increase 345 by 56% 100 % + 56 % = 156 % 156 = 1.56 100 the percentage multiplier is 1.56 345 × 1.56 = 538.2 Now do these: 1. 2. 3. 4. 5. Percentages Increase 125 by 16% 125 × 1.16 = 145 Percentage multiplier is 1.16 340 × 1.09 = 370.6 Increase 340 by 9% Percentage multiplier is 1.09 575 × 1.22 = 701.5 Increase 575 by 22% Percentage multiplier is 1.22 Increase 84 by 1.3% 80 × 1.013 = 81.04 Percentage multiplier is 1.013 Increase £6.30 by 17.5% 6.30 × 1.175 = £7.40 Percentage multiplier is 1.175 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 % 100 % - 23 % = 77 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 - 23 = 77 Now 77 = 0.77 This is called the percentage multiplier for 100 100 100 100 a percentage decrease Percentages Example : Decrease 345 by 56% 100 % - 56 % = 44 % 44 = 0.44 100 the percentage multiplier is 0.44 345 × 0.44 = 151.8 Now do these: 1. 2. 3. 4. 5. Percentages Decrease 137 by 13% 137 × 0.87 = 119.19 Percentage multiplier is 0.87 78 × 0.94 = 73.32 Decrease 78 by 6% Percentage multiplier is 0.94 623 × 0.63 = 392.49 Decrease 623 by 37% Percentage multiplier is 0.63 Decrease 467 by 1.3% 467 × 0.987 = 460.929 Percentage multiplier is 0.987 Decrease £7.45 by 17.5% 7.45 × 0.825 = £6.15 Percentage multiplier is 0.825 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. Worksheet 1 Percentages Mixed Non-Calculator 1. Todd is paid £350 per week. He gets a 4% pay rise. What is his new weekly pay? £364 2. 3. 4. 5. A package holiday is priced at £660. Julie gets a 10% discount for booking before the end of January. How much does she pay? £594 Chris has 50 books on his shelves. Jenny has 12% more books. How many books has Jenny got? £56 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? £49.20 A music centre costs £280. VAT is added at 17 ½ %. What is £329 the total cost Worksheet 2 1. 2. Percentages Mixed Calculator Sarah’s salary is £13 575 per year. Her annual bonus is 1¾% of her salary. How much does she earn altogether? £13 812.56 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? £7 053.42 3. Nathan buys a new Fiat for £12 499. Over 2 years it depreciates by 45%. What is the value after 2 years £6 874.45 4. The population of Newtown was 74 970 in 2008. By 2009 the population had decreased by 27%. What is the population in 2009. 54 728 5. Decrease £9.55 by 12% £7.40 Worksheet 1 Percentages 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 Worksheet 2 1. Percentages Mixed Calculator 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%