1 Percentages MENU Judging fractions and percentages Percentage Trails Percentages to Fractions questions Percentages of quantities Calculator Percentages of quantities Calc questions 10% of quantities Non calc. 10% of quantities Non calc questions 1% of a quantity Non calc. 1% of a quantity Non calc questions Using 10% & 1% to make other percentages. Non calc Using 10% & 1% to calculate percentages questions. Non calc Writing one number as a percentage of another Writing one number as a % of another questions One number as a % of another.10 quickfire A One number as a % of another.10 quickfire B Percentages of quants. 10 quickfire A Percentages of quants. 10 quickfire B Starters Main Menu Writing one number as a percentage of another - Calc Writing one number as a percentage of another – Calc questions Compound Interest questions % Increase / Decrease % Profit / Loss % Increase / Decrease % Profit / Loss questions Calculating an Original amount after a % change Calculating an Original amount after a % change questions Multiplying Factors for % change. Increasing, Decreasing & questions Teacher’s notes on quickfire

2 ½ How full is it ? (as a fraction ) FULL Menu

3 1/3 FULL How full is it ? (as a fraction) Menu

4 ¾ FULL How full is it ? (as a fraction) Menu

5 ¼ FULL How full is it ? (as a fraction ) Menu

6 2/3 FULL How full is it ? (as a fraction) Menu

7 ½ ¼ ¾ 1/3 2/3 How full is it ? (as a fraction ) It is very difficult to be precise ! What about using Percentages ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

8 How full is it ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

9 How full is it ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

10 How full is it ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

11 How full is it ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

12 How full is it ? 50 % 10 % 20 % 30 % 40 % 60 % 70 % 80 % 90 % 100 % Full FULL Menu

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14 I know that 100 % ( full ) of the bottle = 200 ml. What else can I work out ? 200 ml Contents 100 % full = 200 ml 50 % full = 100 ml 25 % full = 50 ml 75 % full = 150 ml 12.5 % full = 25 ml 10 % full = 20 ml 5 % full = 10 ml 2.5 % full = 5 ml 17.5 % full = 35 ml 1 % full = 2 ml 2 % full = 4 ml 0.5 % full = 1 ml 2.5 % full = 5 ml Menu

15 I know that 100 % ( full ) of the bottle = 500 ml. What else can I work out ? 500 ml Contents 100 % full = 500 ml 50 % full = 250 ml 25 % full = 125 ml 75 % full = 375 ml 12.5 % full = 62.5 ml 10 % full = 50 ml 5 % full = 25 ml 2.5 % full = 12.5 ml 17.5 % full = 87.5 ml 1 % full = 5 ml 2 % full = 10 ml 0.5 % full = 2.5 ml 2.5 % full = 12.5 ml Menu

16 I know that 100 % ( full ) of the bottle = 800 ml. What else can I work out ? 800 ml Contents 100 % full = 800 ml 50 % full = 400 ml 25 % full = 200 ml 75 % full = 600 ml 12.5 % full = 100 ml 10 % full = 80 ml 5 % full = 40 ml 2.5 % full = 20 ml 17.5 % full = 140 ml 1 % full = 8 ml 2 % full = 16 ml 0.5 % full = 4 ml 2.5 % full = 20 ml Copy and Complete : Menu Answers

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18 1% There are 100 in one whole. 100 There are 100 % in one whole. So 100 % = and 1 % = = 50 % = 25 % = 20 % = 10 % Menu

19 Convert the following Percentages to Fractions in their Simplest form. 1)40 %2)30%3)70 % 4)45 %5)35 %6)15 % 7)42 %8)82 %9)5 % 10)168 %11)254 %12)500 % Menu Answers

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21 What is 24 % of £ 14 ? 1% If I divide by 100 I will know what 1 % is. £ 0.14 or 14 p £ 0.14 But I want 24 % So multiply by 24 x 24= £ 3.36 £14 Menu

22 1% What is 74 % of £ ? If I divide by 100 I will know what 1% is. 100 £0.382 or 38.2p £0.382 But I want 74 of them. So I multiply by 74 x 74 = £ = £ to the nearest penny £38.20 Menu

23 Use a calculator to work out the following. (Give your answers to the nearest penny. 2 decimal places) 1)22% of £13.252)38% of £ )8% of £11.554)64% of £240 5)18% of £34.996)12.5% of £ )20% of £2.498)33% of £ )41.5% of £9.9910)5.5% of £ )17.5% of £ )82% of 99p 13)45% of 25p14)23.5% of 89p 15)11% of 33p 16)3.5% of 23p £ 2.92£ p or £ 0.92£ £ 6.30 £ p or £ 0.50£ £ p or £ 0.99 £ p or £ p 21p or £ p or £ 0.041p or £ 0.01 Menu Answers

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25 1% Working out 10% is easy ! 10% is the same as 1 10 What is 10% of £ 200 ? So divide by 10 Menu

26 £ Move the digits one place to the right ! £ You may prefer to move the decimal point 1 place to the left ! What is 10% of £ 200 ? Answer = £20 Menu

27 £ 1 5 Move the digits one place to the right ! £ 1 5 You may prefer to move the decimal point 1 place to the left ! What is 10% of £ 15 ? Answer = £1.50 Menu

Move the digits one place to the right ! You may prefer to move the decimal point 1 place to the left ! What is 10% of £ 1.20 ? Answer = £0.12 or 12p £0 £0 Menu

29 £ Move the digits one place to the right ! £ You may prefer to move the decimal point 1 place to the left ! What is 10% of £ ? Answer = £1.82 Menu

30 Work out the following: 1) 10% of £4002) 10% of £650 3) 10% of £554) 10% of £1000 5) 10% of £6.206) 10% of £ ) 10% of £0.508) 10% of £0.10 9) 10% of 2435 g10) 10% of 4552 secs 11) 10% of litres 12) 10% of 0.34 Km 13) 10% of 0.04 cm14) 10% of 34.5 °C £40£65 £5.50£100 62p or £0.62£1.24 5p or £0.051p or £ g secs litres0.034 Km cm3.45°C Menu Answers

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32 1% Working out 1% is easy ! 1% is the same as What is 1% of £ 200 ? So divide by 100 Menu

33 £ Move the digits two places to the right ! £ You may prefer to move the decimal point 2 places to the left ! What is 1% of £ 200 ? Answer = £2 Menu

Move the digits two places to the right ! 1 5 You may prefer to move the decimal point 2 places to the left ! What is 1% of £ 15 ? Answer = £0.15 or 15p £ 0 £0 Menu

35 Work out the following: 1) 1% of £3002) 1% of £450 3) 1% of £254) 1% of £14 5) 1% of £65006) 1% of £100 7) 1% of £758) 1% of £18 9) 1% of £110) 1% of £810 11) 1% of 24 g12) 1% of 3453 secs 13) 1% of Km14) 1% of 0.3 litres £3£ p or £0.2514p or £0.14 £65 £1 75p or £0.7518p or £0.18 1p or £0.01 £ g34.53 secs Km litres Menu Answers

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37 The two most important Percentages are 10 % and 1 %. From these we can easily work out lots of other percentages. 20 % 5 % 15 % 2.5 % 12.5 % 11 % 17.5 % 21 % 6 % 17 % 31 % 29 % Two lots of 10 % Half of 10 % 10 % plus 5 % Half of 5 % ( Half 10 % and then half again ) 10 % plus 2.5 % 10 % plus 1 % 10 % plus 5 % plus 2.5 % Two lots of 10 % plus 1 % 5 % ( Half of 10 % ) plus 1 % 10 % plus 5 % plus two lots of 1 % Three lots of 10 % plus 1 % Three lots of 10 % then subtract 1 % Which combinations of 10 % and 1 % could you use to make the above percentages ? Menu

38 What is 5% of £80 ? How will I make 5% ? By halving 10% 10% of £80 = £8 So 5% of £80 = £4 What is 5% of 40p ? 10% of 40p = 4p So 5% = 2p Menu

39 What is 15% of £80 ? How will I make up 15% ? By putting together a 10% and a 5% ! 10% of £80 = £8 5% of £80 = £4 15% = = £12 What is 15% of £2.40 ? 10% of £2.40 = £0.24 or 24p 5% = £0.12 or 12p 15% = = 36p Menu

40 What is 20% of £140 ? How will I make 20% ? By doubling 10% ! 10% of £140 = £14 So 20% of £140 = £28 What is 20% of £1.20 ? 10% of £1.20 = 12p So 20% = 24p Menu

41 What is 11% of £420 ? How will I make 11% ? By putting together a 10%and a 1% ! 10% of £420 = £42 1% of £420 = £4.20 What is 11% of £2000 ? 10% of £2000 = £200 1% of £2000 = £20 So 11% = = £46.20 So 11% = = £220 Menu

42 Work out the following. Don’t forget to properly write the answers in money. 1) 5% of £402) 5% of £1.803) 5% of £ ) 20% of £2.105) 20% of £6006) 20% of £3.40 7) 15% of £1408) 15% of £2.409) 15% of 80p 10) 2.5% of £60 11) 2.5% of £40012) 2.5% of 40p 13) 12.5% of £20014) 12.5% of £1.6015) 12.5% of £ ) 17.5% of £5017) 17.5% of 80p18) 17.5% of £ ) 11% of £30020) 6% of £2421) 2% of £350 22) 12% of £18023) 19% of £42024) 16% of £5 25) ½% of £300026) 5.5% of £20027) 99% of £500 28) 39% of £80029) 1.5% of £10030) ¼% of £6000 £29p or £ p or £ p or £0.42£12068p or £0.68 £2136p or £0.3612p or £0.12 £1.50£101p or £0.01 £2520p or £0.2055p or £0.55 £8.7514p or £0.14£350 £33 £1.44£7 £21.60£ p or £0.80 £15 £11£495 £312£1.50£15 Menu Answers

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44 1% What is 5 out of 10 as a percentage ? 5 10 = or 50% x 10 Menu

45 1% What is 32 out of 50 as a percentage ? = 64 or 64% 100 x 2 Menu

46 1% What is 8 out of 20 as a percentage ? 8 20 = 40 or 40% 100 x 5 Menu

47 1% What is 18 out of 25 as a percentage ? = 72 or 72% 100 x 4 Menu

48 1% What is 3 out of 5 as a percentage ? 3 5 = 60 or 60% 100 x 20 Menu

49 What about these ? 6 out of 10 ? 7 out of 20 ? 40 out of 50 ? 2 out of 5 ? 12 out of 25 ? 6 = 10 7 = = 50 2 = 5 12 = x or 60% x 5 35or 35% x 2 or 80%80 x 20 40or 40% x 4 48or 48% 30 out of 40 ? 80 out of 200 ? 400 out of 1000 ? 60 out of 300 ? 120 out of 600 ? 30 = = = = = x or 75% ÷ 2 40or 40% ÷ 10 40or 40% ÷ 3 20or 20% ÷ 6 20 or 20% Menu

50 Write the following as percentages. {First write them as fractions} 1) 9 out of 10 2) 6 out of 103) 2 out of 10 4) 1 out of 5 5) 4 out of 5 6) 2 out of 5 7) 11 out of 20 8) 3 out of 20 9) 18 out of 20 10) 28 out of 50 11) 14 out of 50 12) 35 out of 50 13) 8 out of 25 14) 20 out of 25 15) 14 out of 25 16) 10 out of 40 17) 14 out of 40 18) 22 out of 40 19) 160 out of ) 90 out of ) 10 out of ) 180 out of ) 180 out of ) 44 out of ) 45 out of ) 670 out of ) 420 out of ) 800 out of ) 1200 out of ) 3500 out of % 60% 20% 80%40% 55%15%90% 56%28%70% 32%80%56% 25%35%55% 80%45%5% 60%30% 11% 9% 67%42% 40%20%70% Menu Answers

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52 1% What is 5 out of 10 as a percentage ? 5 10 of the 100% 5 10 × 100 = 50% Menu = 50%

53 What is 24 out of 37 as a percentage ? 24 × 100 = 65 % to the nearest percent. 37 Menu

54 Use a calculator to work out the following as percentages. {Give your answers to the nearest whole number} 1)8 out of 142)15 out of 32 3)45 out of 1214)62 out of 885)13 out of 41 6)134 out of 2067)57 out of 908)76 out of 234 9)½ out of ¾ 10)8 ½ out of 11 ¼ 11)56 ¾ out of % 47 % 37 %70 %32 % 65 %63 %32 % 67 %76 %39 % Menu Answers

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£ 500 is put into a bank account paying 5% interest per annum. How much will there be after 2 years ? End of year × 5 = £ 25 interest 100 New total amount = = £ End of year × 5 = £ interest Total amount after 2 years = = £ Menu

57 £ 2000 is put into a bank account paying 12% interest per annum. How much will there be after 3 years ? End of year × 12 = £ 240 interest 100 New total amount = = £ End of year × 12 = £ interest New total amount = = £ End of year × 12 = £ interest Total amount after 3 years = = £ Menu

58 Work out the final total amounts of money. 1) £ 240 at 10 % p.a. for 2 years. 2) £ 800 at 4 % p.a. for 2 years. 3) £ at 8 ½ % p.a. for 2 years. 4) £ 7000 at 15 % p.a. for 3 years. 5) £ at 12 ¼ % p.a. for 3 years. £ £ £ £ £ Menu Answers

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60 An aircraft increases its speed from 500 m.p.h to 800 m.p.h. Calculate the percentage increase in speed. % increase or decrease = Actual Increase or decrease × 100 Start Amount You will need to memorise this ! % increase = 300 × = 60 % Menu

61 A house was bought for £ and then sold for £ Calculate the percentage loss. % increase or decrease = Actual Increase or decrease × 100 Start Amount You will need to memorise this ! % loss = × = 11.1 % loss Menu

62 Work out the following % increases / profits or decreases / losses. { Round answers to the nearest whole number } 1)A population of 400,000 increases to 900,000. 2)A salary of £ increases to £ )A car was bought for £ 9500 and sold for £ )The water level dropped from 8 metres to 7 metres. 5)The temperature rose from 12°C to 19°C. 6)A man’s weight fell by 15 Kg and became 70 Kg. 7)A train traveling at 130 m.p.h. increases its speed by 40 m.p.h. 8)After increasing by £ 5000 a woman’s salary becomes £ )A supermarket increases its floor space by square feet. It now has a total of square feet. 125 % increase 50 % increase 35 % loss 13 % drop 58 % increase 18 % decrease 31 % increase 17 % increase 900 % increase Menu Answers

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64 Due to inflation a camcorder’s price rises by 10%. It now costs £ 600. What did it used to cost ? That’s easy ! 10 % of £ 600 = £ 60 So it has gone up by £ 60. It must have cost £ 540 ! But that’s not right ! 10 % of £ 540 = £ 54 So new price would be = £ 594 !! You originally pay 100% of the price. You now pay 110% and it now costs £ % = £ % = Original price = 600 × = £ to the nearest penny Menu

65 The price of a drill increases by 12 ½ %. It now costs £ 80. What was the original price ? You originally pay 100% of the price. You now pay % and it now costs £ % = £ 80 1 % = Original Price = 80 × = £ to the nearest penny Menu

66 A car decreases in value by 5 %. It is now worth £ What was the original value ? You originally pay 100% of the price. You now pay 95 % and it now costs £ % = £ % = Original Price = × = £ to the nearest penny. Menu

67 In a 12 ½ % ‘off everything’ sale a jacket now costs £ 35. How much did it used to cost ? You originally pay 100% of the price. You now pay 87.5 % and it now costs £ % = £ 35 1 % = Original Price = 35 × = £ 40 Menu

68 1)In a 10 % ‘off everything’ sale a wristwatch now costs £ 60. How much did it used to cost ? 2)The water level in a reservoir drops by 5 % and is now 30 metres above sea level. What was the original level ? 3)Due to inflation the price of microwaves increases by 7 % and they now cost £ 55. How much did they used to cost ? 4)A drinks manufacturer increases the volume of its cans by 25 %. They now hold 450 ml. How much did they used to hold ? 5)The share prices of Ian Ramsey Bank fall by 15 ½ % and are now worth 70 pence per share. What was the original price ? 6)A helicopter increases its speed by 6 ¼ %. It now travels at 260 m.p.h. What was its original speed ? 7)Paul is charged £ 430 including V.A.T. at 17 ½ % for car repairs. What would it have cost without the tax ? 8)A supermarket sells potatoes in 1 ¼ Kg bags after decreasing the weight by 5 ½ %. What was the original weight of the bags ? 9)Debbie gets a 200 % pay increase due to promotion at work. She now earns £ p.a. What did she used to earn ? £ metres £ ml 83 p m.p.h. £ Kg £ Menu Answers

69 { This is a calculator exercise } Menu

70 A yacht costing £ 20,000 is to have its price increased by %. What will the new price be ? 10 % of £ 20,000 = £ 2000 So new price = 20, = £ 22,000. See if you can multiply £ 20,000 by a single number and get an answer of £ 22, × = 22000?1.1 Original Price % IncreaseNew Price Multiplying Factor £ 20,0001 % £ 20,0005 % £ 20,00010 % £ 20,00015 % £ 20,00020 % £ 20,00025 % £ 22, % of £ 20,000 = £ 4000 New Price = 20, = £ 24,000 £ 24, % of £ 20,000 = £ 200 New Price = 20, = £ 20,200 £ 20, % of £ 20,000 = £ 1000 New Price = 20, = £ 21,000 £ 21, % of £ 20,000 = £ 3000 New Price = 20, = £ 23,000 £ 23, % of £ 20,000 = £ 5000 New Price = 20, = £ 25,000 £ 25,000 Now work out the other Multiplying Factors Menu

71 Work out the new increased totals. Show your working. Ex. Increase £ 30 by 5 % : 30 × 1.05 = £ {Round answers to the nearest whole number} 1)Increase £ 300 by 10 %2)Increase 200 g by 5 % 3)Increase 680 ml by 15 %4)Increase £ 35 by 25 % 5)Increase $ 400 by 1 %6)Increase 80 cm by 20 % 7)Increase £ 6000 by 12 % 8)Increase 9 Kg by 22 % 9)Increase 365 days by 17 %10)Increase 330 mg by 3 % 11)Increase £ 5000 by ½ %12)Increase 4000 g by 5 ½ % 13)Increase 2500 litres by 2 ½ %14)Increase $ 30,000 by 20 ½ % 15)Increase 1000 cm by 1 ¼ %16)Increase £ by 15 ¼ % 300 × 1.1 = £ × 1.05 = 210 g 680 × 1.15 = 782 ml35 × 1.25 = £ × 1.01 = $ × 1.2 = 96 cm 6000 × 1.12 = £ × 1.22 = 11 Kg 365 × 1.17 = 427 days330 × 1.03 = 340 mg 5000 × = £ × = 4220 g 2500 × = 2563 litres30000 × = $ × = 1013 cm65000 × = £ Menu Answers

72 Original Price % decreaseNew Price Multiplying Factor £ 40,0001 % £ 40,0005 % £ 40,00010 % £ 40,00015 % £ 40,00020 % £ 40,00025 % A car costing £ 40,000 has its value decreased by %. What will the new price be ? % of £ 40,000 = £ 4000 New Price = 40, = £ 36,000 £ 36, % of £ 40,000 = £ 8000 New Price = 40, = £ 32,000 £ 32, % of £ 40,000 = £ 2000 New Price = 40, = £ 38,000 £ 38, % of £ 40,000 = £ 6000 New Price = 40, = £ 34,000 £ 34, % of £ 40,000 = £ New Price = 40, = £ 30,000 £ 30, % of £ 40,000 = £ 400 New Price = 40,000 – 400 = £ 39,600 £ 39,600 See if you can multiply £ 40,000 by a single number and get an answer of £ 36, × = 36000?0.9 Now work out the other Multiplying Factors Menu

73 Work out the new decreased totals. Show your working. Ex. Decrease £ 30 by 5 % : 30 × 0.95 = £ {Round answers to the nearest whole number} 1)Decrease £ 300 by 10 %2)Decrease 200 g by 5 % 3)Decrease 680 ml by 15 %4)Decrease £ 35 by 25 % 5)Decrease $ 400 by 1 %6)Decrease 80 cm by 20 % 7)Decrease £ 6000 by 12 % 8)Decrease 9 Kg by 22 % 9)Decrease 365 days by 17 %10)Decrease 330 mg by 3 % 11)Decrease £ 5000 by ½ %12)Decrease 4000 g by 5½ % 13)Decrease 2500 litres by 2½ %14)Decrease $ 30,000 by 20½ % 15)Decrease 1000 cm by 1¼ %16)Decrease £ by 15¼ % 300 × 0.9 = £ × 0.95 = 190 g 680 × 0.85 = 578 ml35 × 0.75 = £ × 0.99 = $ × 0.8 = 64 cm 6000 × 0.88 = £ × 0.78 = 7 Kg 365 × 0.83 = 303 days330 × 0.97 = 320 mg 5000 × = £ × = 3780 g 2500 × = 2438 litres30000 × = $ × = 988 cm65000 × = £ Menu Answers

74 Teacher’s Notes on quickfire questions Quickfire questions are designed as a straight forward starter where pupils quickly work out the answers (possibly in the backs of their books). The teacher should then review each question giving out the answers and reminding pupils of the techniques / ideas behind the topic. Menu

75 One Number as a Percentage of Another Number 10 Quick-fire A Questions Menu

76 Question 1 What is 6 out of 10 as a Percentage ? Menu

77 Question 2 What is 45 out of 50 as a Percentage ? Menu

78 Question 3 What is 8 out of 20 as a Percentage ? Menu

79 Question 4 What is 3 out of 5 as a Percentage ? Menu

80 Question 5 What is 4 out of 10 as a Percentage ? Menu

81 Question 6 What is 8 out of 25 as a Percentage ? Menu

82 Question 7 What is 16 out of 20 as a Percentage ? Menu

83 Question 8 What is 2 out of 5 as a Percentage ? Menu

84 Question 9 What is 7 out of 10 as a Percentage ? Menu

85 Question 10 What is 4 out of 20 as a Percentage ? Menu

86 One Number as a Percentage of Another Number 10 Quick-fire B Questions Menu

87 Question 1 What is 22 out of 25 as a Percentage ? Menu

88 Question 2 What is 1 out of 5 as a Percentage ? Menu

89 Question 3 What is 1 out of 10 as a Percentage ? Menu

90 Question 4 What is 14 out of 20 as a Percentage ? Menu

91 Question 5 What is 30 out of 40 as a Percentage ? Menu

92 Question 6 What is 10 out of 25 as a Percentage ? Menu

93 Question 7 What is 16 out of 40 as a Percentage ? Menu

94 Question 8 What is 2 out of 20 as a Percentage ? Menu

95 Question 9 What is 17 out of 50 as a Percentage ? Menu

96 Question 10 What is 22 out of 40 as a Percentage ? Menu

97 10 Quickfire A Percentage Questions Menu

98 10 % of £ 30 Question 1 Menu

99 20 % of £ 80 Question 2 Menu

100 5 % of £ 1.80 Question 3 Menu

101 20% of £ 300 Question 4 Menu

% of £ 200 Question 5 Menu

103 5 % of £ 2.40 Question 6 Menu

% of £ 40 Question 7 Menu

% of £ 400 Question 8 Menu

% of £ 20 Question 9 Menu

% of £ 200 Question 10 Menu

Quickfire B Percentage Questions Menu

% of £ 1.80 Question 1 Menu

% of £ 2000 Question 2 Menu

% of £ 200 Question 3 Menu

% of £ 500 Question 4 Menu

113 6 % of £ 50 Question 5 Menu

% of £ 30 Question 6 Menu

% of £ 400 Question 7 Menu

% of £ 4.80 Question 8 Menu

% of £ 8.40 Question 9 Menu

% of £ 76 Question 10 Menu

119 End of Percentages Presentation. Return to previous slide.