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Ratio and Percentages

Ratio and Percentages. Percentage/Decimal/Fraction. These are different ways of saying how much of something you have E.g. 100% = 1.0 = 1 50%= 0.5 = ½ What is 25%? 0.25 and ¼ What is 10%? 0.1 and 1/10. Percentage/Decimal/Fraction. What is 1/3? 33.3% and 0.33 What is 2/3?

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Ratio and Percentages

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  1. Ratio and Percentages

  2. Percentage/Decimal/Fraction • These are different ways of saying how much of something you have • E.g. 100% = 1.0 = 1 • 50%= 0.5 = ½ • What is 25%? • 0.25 and ¼ • What is 10%? • 0.1 and 1/10

  3. Percentage/Decimal/Fraction • What is 1/3? • 33.3% and 0.33 • What is 2/3? • 66.67% and 0.67 • What is 150%? • 1 ½ and 1.5 • What is 7%? • 0.07 and 7/100

  4. Simplifying Fractions • Fractions should always be simplified • E.g. 2/4 is ½ • What are these: • 10/100? • 1/10 • 2/100? • 1/5 • 4/6? • 2/3

  5. Try these • Change these percentages to fractions: • 70% • 5% • 15% • 2% • 12 ½ % • 6 ¼ % • 66 2/3 %

  6. Answers • 7/10 • 5/100 which is 1/20 • 15/100 which is 3/20 • 2/100 which is 1/50 • 1/8 • 1/16 • 2/3

  7. Converting Fractions to Percentages • To convert a fraction into a percentage there are two ways: • Type the fraction into your calculator and multiply by 100 • Divide the top part of the fraction by the bottom part and multiply by 100 e.g. • ½ is ½ x 100 = 50% • ¼ is • 25%

  8. Try these • Convert these fractions to percentages: • 71/80 • 4/5 • 56/60 • 16/40 • 23/28 • 112/125

  9. Answers • 88.75% • 80% • 93.3% • 40% • 82.1% • 89..6%

  10. Sales • Often sales are 25% off or 50% off • This means you can work out what the sale price is • E.g. If a football costs £12 and there is 25% off • You type in 12 x 25% on your calculator • This is £3 • The football is £12-3 = £9

  11. Work out these: • What are the prices of these if there is a 25% off sale; • A £6 football pump • £7 tennis balls • £20 fishing rod • If there is 10% off these; • £108 tent • £12 airbed • £16 gas cooker

  12. Answers • £4.50 • £5.25 • £15 • £97.20 • £10.80 • £14.40

  13. Working out the % of something • If you are asked to find the percentage of something e.g. 12% of 300g • Type 300 x 12% into the calculator • 36g • There is another method • 300 ÷ 100 gives you 1%, then multiply your answer by 12 • 300 ÷ 100 = 3g • 3g x 12 = 36g

  14. Try these • Find 18% of 250cm • Find 8% of 600cm • Find 45% of 120g • Find 34% of 350m • Find 12.5% of £150 • Find 15% of £450 • Find 9.75% of £420

  15. Answers • 45cm • 48cm • 54g • 14m • £18.75 • £67.50 • £39.90

  16. Ratio • Ratio is when you want to split something unevenly between several people • E.g. You have 10 sweets and 2 friends and yourself to share them with • You want the most and then your best friend gets the next most • You could split them 5 to you: 3 to your best friend: 2 to the other friend • The ratio is 5:3:2

  17. Simplifying ratios • Ratios are really fractions and they need to be simplified • 20:5 • Both can be divided by 5 so it becomes • 4:1 • 6:4:2? • All can be divided by 2 • 3:2:1

  18. Try these • Simplify these ratios; • 10:5:20 • 5:5 • 7:7:14 • 12:6:6 • 9:3:6:3 • 24:16:8:80

  19. Answers • 2:1:4 • 1:1 • 1:1:2 • 2:1:1 • 3:1:2:1 • 3:2:1:10

  20. Ratios with n • If you are asked to convert ratios into the form 1:n you must divide the first number down to 1 and divide the other side by this same number • E.g. • 7:14 • Both sides are divided by 7 • So the answer is 1:2

  21. Try these • Convert these to the form 1:n • 4:5 • 2:3 • 3:7.5 • 7:2 • 16:11 • Convert these to the form n:1 • 3:4 • 2:3 • 10:20

  22. Answers • 1:1.25 • 1:1.5 • 1:2.5 • 1:0.29 • 1:0.69 • 0.75:1 • 0.67:1 • 0.5:1

  23. Using ratios • If you want to split £21 in the ratio 2:1:4 • How much does everybody get? • Ratios are like fractions so what do all these parts add up to? • 2+1+4= 7 • This means that they get 2/7:1/7:4/7 • 1/7 of £21 is £3 • 2/7 of £21 is £6 • And 4/7 of £21 is £12 • This is £6:£3:£12

  24. Work out these • £27 – 8:10 • £3 – 4:4:2 • £34 – 7:10 • £4.40 – 2:8:10 • 70p – 18:9:3

  25. Answers • £12 : £15 • £1.20 : £1.20 : £0.60 • £14 : £20 • £0.44 : £1.76 : £2.20 • 42p : 21p : 7p

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