1 / 15

Percentages

Percentages. Objectives: D Grade Increase or decrease a quantity by a given percentage. C Grade Work out a percentage increase or decrease. Prior knowledge:. Understand :. Finding percentages of quantities – calculator and non calculator .

dominique
Download Presentation

Percentages

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Percentages Objectives: D Grade Increase or decrease a quantity by a given percentage C Grade 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

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

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

  4. 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

  5. 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: This is called the percentage multiplier for a percentage increase 100 + 23 = 123 100 100 100 Now 123 = 1.23 100

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

  7. 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% 125 × 1.16 = 145 Percentage multiplier is 1.16 340 × 1.09 = 370.6 Percentage multiplier is 1.09 575 × 1.22 = 701.5 Percentage multiplier is 1.22 80 × 1.013 = 81.04 Percentage multiplier is 1.013 6.30 × 1.175 = £7.40 Percentage multiplier is 1.175

  8. 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: This is called the percentage multiplier for a percentage decrease 100 - 23 = 77 100 100 100 Now 77 = 0.77 100

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

  10. 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% 137 × 0.87 = 119.19 Percentage multiplier is 0.87 78 × 0.94 = 73.32 Percentage multiplier is 0.94 623 × 0.63 = 392.49 Percentage multiplier is 0.63 467 × 0.987 = 460.929 Percentage multiplier is 0.987 7.45 × 0.825 = £6.15 Percentage multiplier is 0.825

  11. 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.

  12. 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

  13. 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

  14. 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

  15. 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%

More Related