1 / 61

KS3 Mathematics

KS3 Mathematics. N7 Percentages. N7 Percentages. Contents. A1. N7.2 Calculating percentages mentally. A1. N7.3 Calculating percentages on paper. A1. N7.1 Equivalent fractions, decimals and percentages. N7.4 Calculating percentages with a calculator. A1. N7.5 Comparing proportions. A1.

aloysius
Télécharger la présentation

KS3 Mathematics

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. KS3 Mathematics N7 Percentages

  2. N7 Percentages Contents • A1 N7.2 Calculating percentages mentally • A1 N7.3 Calculating percentages on paper • A1 N7.1 Equivalent fractions, decimals and percentages N7.4 Calculating percentages with a calculator • A1 N7.5 Comparing proportions • A1 N7.6 Percentage change • A1

  3. Percentages 1900 - 2000 Many words begin with ‘cent’:

  4. Percentages “Percent” means . . . “out of a hundred”

  5. Percentages 1% 1 part per hundred 1 0.01 100 A percentage is just a special type of fraction. means or =

  6. Percentages 10% 10 parts per hundred 10 1 0.1 100 10 A percentage is just a special type of fraction. means or = =

  7. Percentages 25% 25 parts per hundred 25 1 0.25 100 4 A percentage is just a special type of fraction. means or = =

  8. Percentages 50% 50 parts per hundred 50 1 0.5 100 2 A percentage is just a special type of fraction. means or = =

  9. Percentages 100% 100 parts per hundred 100 1 100 A percentage is just a special type of fraction. means or =

  10. Percentages of shapes

  11. Estimating percentages

  12. Estimating percentages

  13. Equivalentfractions,decimalsand percentages

  14. Writing percentages as fractions 180 46 46 23 = 100 100 100 50 180 = = 9 4 1 7.5 15 3 100 15 = = 5 5 100 200 40 200 ‘Per cent’ means ‘out of 100’. To write a percentage as a fraction we write it over a hundred. For example, 23 46% = Cancelling: 50 9 180% = Cancelling: 5 3 Cancelling: 7.5% = 40

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

  16. Percentages as fractions and decimals

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

  18. Writing fractions as percentages 3 3 1 = = 3 ÷ 8 8 2 8 37.5 = 100 37 % = To write a fraction as a percentage you can change to a decimal and see how many hundredths : ( first two digits from decimal point) For example, = 0.375

  19. Writing decimals as percentages To write a decimal as a percentage you can see how many hundredths – first two figures to right of decimal point. For example, 0.08 = 0.08 1.375 = 1.375 = 8% = 137.5%

  20. Using a calculator 5 = 4 = 16 7 5 13 1 = = 8 8 We can also convert fractions to decimals and percentages using a calculator. For example, = 31.25% 5 ÷ 16 = 0.3125 = 57.14% (to 2 d.p.) 4 ÷ 7 13 ÷ 8 = 162.5%

  21. Table of equivalences

  22. Table of equivalences

  23. Ordering on a number line

  24. Dominoes

  25. N7 Percentages Contents N7.1 Equivalent fractions, decimals and percentages • A1 • A1 N7.3 Calculating percentages on paper • A1 N7.2 Calculating percentages mentally N7.4 Calculating percentages with a calculator • A1 N7.5 Comparing proportions • A1 N7.6 Percentage change • A1

  26. Calculating percentages mentally Some percentages are easy to work out mentally: 1% Divide by 100 To find 10% Divide by 10 To find 25% Divide by 4 To find 50% Divide by 2 To find

  27. Calculating percentages mentally 20% 30% 60% 15% 75% 11% 2% 49% 150% 17.5% 0.5 % We can use percentages that we know to find other percentages. Suggest ways to work out:

  28. Spider diagram

  29. N7 Percentages Contents N7.1 Equivalent fractions, decimals and percentages • A1 N7.2 Calculating percentages mentally • A1 • A1 N7.3 Calculating percentages on paper N7.4 Calculating percentages with a calculator • A1 N7.5 Comparing proportions • A1 N7.6 Percentage change • A1

  30. Calculating percentages 16% of 90, means “16 hundredths of 90”. 10% of 90 is 9 “ 10 hundredths of 90”. 1% of 90 is 0.9 “ 1 hundredth of 90”. 5% of 90 is 4.5 “ 5 hundredths of 90”. 16% of 90 = 9 + 0.9 + 4.5 = 14.4

  31. Calculating percentages 87% of 125, means “87 hundredths of 125”. 10% of 125 is 12.5 50 % of 125 is 62.5. 1 % of 125 is 1.25 87% ( 50% + (3X10%) + (7X1%) ) 62.5 + 37.5 + 8.75 = 108.75

  32. Calculating percentages using decimals What is 4% of 9? We can also calculate percentages using an equivalent decimal operator. 4% of 9 = 0.04 × 9 = 4 × 9 ÷ 100 = 36 ÷ 100 = 0.36

  33. N7 Percentages Contents N7.1 Equivalent fractions, decimals and percentages • A1 N7.2 Calculating percentages mentally • A1 N7.3 Calculating percentages on paper • A1 N7.4 Calculating percentages with a calculator • A1 N7.5 Comparing proportions • A1 N7.6 Percentage change • A1

  34. Estimating percentages We can find more difficult percentages using a calculator. It is always sensible when using a calculator to start by making an estimate. For example, estimate the value of: 19% of £82  20% of £80 = £16 27% of 38m  25% of 40m = 10m 73% of 159g  75% of 160g = 120g

  35. Using a calculator 0 . 3 8 × 6 5 = 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: And get an answer of 24.7. We write the answer as £24.70.

  36. Using a calculator 57 100 5 7 ÷ 1 0 0 × 8 = 0 We can also work out a percentage using a calculator by converting the percentage to a fraction. Suppose we want to work out 57% of £80. 57% = = 57 ÷ 100 So we key in: And get an answer of 45.6. We write the answer as £45.60.

  37. Using a calculator 0 . 5 9 × 3 7 . = 5 We can also work out percentage on a calculator by finding 1% first and multiplying by the required percentage. Suppose we want to work out 37.5% of £59. 1% of £59 is £0.59 so, 37.5% of £59 is £0.59 × 37.5. We key in: And get an answer of 22.125. We write the answer as £22.13 (to the nearest penny).

  38. N7 Percentages Contents N7.1 Equivalent fractions, decimals and percentages • A1 N7.2 Calculating percentages mentally • A1 N7.3 Calculating percentages on paper • A1 N7.5 Comparing proportions N7.4 Calculating percentages with a calculator • A1 • A1 N7.6 Percentage change • A1

  39. Using percentages to compare proportions Matthew sat tests in English, Maths and Science. His results were: English Maths Science 74 17 66 80 20 70 Which test did he do best in? To compare the marks we can write each fraction as a percentage.

  40. Using percentages to compare proportions = 74 74 66 66 17 17 = 80 80 20 70 70 20 = English × 100% = 74 ÷ 80 × 100% = 92.5% Maths × 100% = 17 ÷ 20 × 100% = 85% Science × 100% = 66 ÷ 70 × 100% = 94.3% (to 1 d.p.) We can see that Matthew did best in his Science test.

  41. Using percentages to compare proportions Chocolate Cookies Cheesy Crisps Nutrition Information Nutrition Information Typical Value Per 10g biscuit Typical Value Per 23g bag Energy Protein Carbohydrate Fat Fibre Sodium 233kj 0.6g 6.7g 2.2g 0.2g <0.05g Energy Protein Carbohydrate Fat Fibre Sodium 504kj 1.6g 13g 7g 0.3g 0.2g Which product contains the smallest percentage of carbohydrate?

  42. Using percentages to compare proportions 6.7 10 13 23 The chocolate cookies contain 6.7g of carbohydrate for every 10g of biscuits. 6.7g out of 10g = × 100% = 6.7 ÷ 10 × 100% = 67% The cheesy crisps contain 13g of carbohydrate for every 23g of crisps. 13g out of 23g = × 100% = 13 ÷ 23 × 100% = 56.5% (to 1 d.p) The cheesy crisps contain a smaller percentage of carbohydrate.

  43. N7 Percentages Contents N7.1 Equivalent fractions, decimals and percentages • A1 N7.2 Calculating percentages mentally • A1 N7.3 Calculating percentages on paper • A1 N7.6 Percentage change N7.4 Calculating percentages with a calculator • A1 N7.5 Comparing proportions • A1 • A1

  44. Percentage increase and decrease House prices predicted to fall by 2% next month SALE 20% off all marked prices! PC now only £568 Plus 17 % VAT Orange Shampoo 25% extra free! 1 2 Factory workers demand 15% pay increase Bus fares set to rise by 30%

  45. Percentage increase Method 1 We can work out 20% of £150 000 and then add this to the original amount. The value of Frank’s house has gone up by 20% since last year. If the house was worth £150 000 last year how much is it worth now? There are two methods to increase an amount by a given percentage. The amount of the increase = 20% of £150 000 = 0.2 × £150 000 = £30 000 The new value = £150 000 + £30 000 = £180 000

  46. Percentage increase Method 2 If we don’t need to know the actual value of the increase we can find the result in a single calculation. We can represent the original amount as 100% like this: 100% 20% When we add on 20%, we have 120% of the original amount. Finding 120% of the original amount is equivalent to finding 20% and adding it on.

  47. Percentage increase So, to increase £150 000 by 20% we need to find 120% of £150 000. 120% of £150 000 = 1.2 × £150 000 = £180 000 In general, if you start with a given amount (100%) and you increase it by x%, then you will end up with (100 + x)% of the original amount. To convert (100 + x)% to a decimal multiplier we have to divide (100 + x) by 100. This is usually done mentally.

  48. Percentage increase What happens if we increase an amount by 100%? We take the original amount and we add on 100%. 100% 100% We now have 200% of the original amount. This is equivalent to 2 times the original amount.

  49. Percentage increase What happens if we increase an amount by 200%? We take the original amount and we add on 200%. 100% 200% We now have 300% of the original amount. This is equivalent to 3 times the original amount.

  50. Percentage increase Here are some more examples using this method: Increase £50 by 60%. Increase £86 by 17.5%. 160% × £50 = 1.6 × £50 117.5% × £86 = 1.175 × £86 = £80 = £101.05 Increase £24 by 35% Increase £300 by 2.5%. 135% × £24 = 1.35 × £24 102.5% × £300 = 1.025 × £300 = £32.40 = £307.50

More Related