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2. What do we mean when we say two quantities are in proportion or directly proportional ? It means that if: one of them doubles, the other one also doubles. one of them trebles, the other one also trebles. one of them x4, the other one also x4. one of them halves, the other one also halves. one of them ÷4, the other one also ÷4. Can you give examples of directly proportional quantities from every day life?

3. © T Madas Directly proportional quantities: They increase or decrease at the same rate More formally: Two quantities are directly proportional if the ratio between them remains constant.

5. Laps in Racing Cars A racing car does 2 laps every 5 minutes How long does it take to cover 17 laps? How many laps does it cover in 1 hour? L T 2 : 5 17 laps in 42½ minutes In 1 hour it does 24 laps 1 : 2.5 ÷2÷2 ÷2÷2 17 : 42.5 x 17 L T 2 : 5 0.4 : 1 ÷5÷5 ÷5÷5 24 : 60 x 60

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7. Calculating Earnings A plumber earns £51 in 6 hours How much does he earn in a 41 hour week? In many hours does he earn £1000? H £ 6 : 51 £348.50 in 41 hours approximately 118 hours 1 : 8.5 ÷6÷6 ÷6÷6 41 : 348.5 x 41 H £ 6 : 51 0.1176 : 1 ÷51 117.6 : 1000 x 1000

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9. Converting Currency If £5 are worth €7 How many € are £8 worth? How many £ are €3 worth? £ € 5 : 7 £8 = € 11.20 1 : 1.4 ÷5÷5 ÷5÷5 8 : 11.2 x8x8 x8x8 £ € 5 : 7 0.7143 : 1 ÷7÷7 ÷7÷7 2.14 : 3 x3x3 x3x3 € 3 ≈ £ 2.14

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11. In a chemical reaction solution A must be combined with solution B in the ratio of 5 : 8, to form a certain compound. How many ml of solution B must be used, if 5.5 ml of solution A is to be used? Chemistry Experiments A B 5 : 8 8.8 ml of solution B must be mixed with 5.5 ml of solution A 1 : 1.6 ÷5÷5 ÷5÷5 5.5 : 8.8 X 5.5

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14. Laps in Racing Cars A racing car does 2 laps every 5 minutes How long does it take to cover 17 laps? How many laps does it cover in 1 hour? L M 17 laps in 42½ minutes M L In 1 hour it does 24 laps

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16. Calculating Earnings A plumber earns £51 in 6 hours How much does he earn in a 41 hour week? In many hours does he earn £1000? h £ He earns £348.50 £ h He earns it in 118 hours

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18. Converting Currency If €7 are worth £5 How many £ are €3 worth? How many € are £8 worth? € £ €3 ≈ £2.14 £ € £8 = €11.20

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20. In a chemical reaction solution A must be combined with solution B in the ratio of 5 : 8, to form a certain compound. How many ml of solution B must be used, if 5.5 ml of solution A is to be used? Chemistry Experiments A B 8.8 ml of solution B must be used

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22. 12 kg of flour cost £15. How much do 28 kg cost? 12 kg of flour cost £15. How many Kg do £120 buy?

23. © T Madas 600 Mb require a 72 minute CD. How many minutes do 700 Mb need? 600 Mb require a 72 minute CD. How many Mb correspond to 60 minutes?

24. © T Madas In a pie chart 7200 voters are represented by 144°. How many voters do 120° represent? In a pie chart 7200 voters are represented by 144°. By how many degrees are 1000 voters represented?

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26. 40y 8024x The variables in the table are directly proportional. Find the missing value. 8 20 45y 18x 21.6 54y 3690x

27. © T Madas 120 80 y 9060 x The variables in the table are directly proportional. Find the missing value. 40 60 y 1218 x 24 50 75 y 36 x

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29. 20 litres of petrol cost £16. 1. Work out the cost of 1 litre of petrol. 2. Work out the cost of 7 litres of petrol. litres 20 10 1 7 cost 16 8 0.8 5.6 : : : : : £0.80 £5.60

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31. Toca-Cola costs £1.24 for a 2 litre bottle. Sepsi-Cola costs £0.90 for a 1.5 litre bottle. Work out which brand is the cheapest. 2 lt £1.24 1.5 lt £0.90 lt£: 21.24: ÷2÷2 ÷2÷2 10.62: Toca-Cola 1 lt costs 62 pence, lt£: 1.50.90: ÷1.5 10.60: Sepsi-Cola 1 lt costs 60 pence, Sepsi-Cola is the cheapest

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33. 18 pens cost £2.16. Calculate the cost of 24 pens. pens£: 182.16: ÷18 1 unimportant : x 24 242.88: pens£: 182.16: ÷3÷3 ÷3÷3 6 0.72: x 4 242.88: £2.88

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35. Look at the nutritional information shown on the label opposite. How many grams of carbohydrate do 100 grams of these beans provide? Bono Baked Beans Each 150 g provides 108 kcal 6.9 g 19.5 g 0.3 g 0.5 g Energy Protein Carbohydrate Fat Salt beanscarbs: 15019.5: ÷3÷3 ÷3÷3 506.5: x2x2 x2x2 10013: 100 grams of beans provide 13 grams of carbohydrate

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37. Look at the nutritional information shown on the label opposite. Calculate how many grams of carbohydrate do 100 grams of these beans provide, giving your answer correct to 3 significant figures. Chilli Baked Beans Each 215 g provides 161 kcal 10 g 30.5 g 0.2 g 0.6 g Energy Protein Carbohydrate Fat Salt beanscarbs: 21530.5: ÷215 10.1419: x100 10014.19: 100 grams of beans provide 14.2 grams of carbohydrate

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39. Hojo Apple Pie Each 175 g provides 434 kcal 6.9 g 79.5 g 9.9 g 0.5 g Energy Protein Carbohydrate Fat Salt Mojo Apple Pie Each 150 g provides 375 kcal 6.7 g 70.5 g 5.3 g 0.5 g Energy Protein Carbohydrate Fat Salt Look at the nutritional information shown on the two labels. Rohan eats the same amount from each apple pie. Which apple pie provides Rohan with more energy. gramsenergy: 175434: ÷175 12.48: gramsenergy: 150375: ÷150 12.5: each gram provides 2.48 kcal each gram provides 2.5 kcal

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41. Mr Green sells a 2.4 kg bag of apples for £1.80 while Mr Red sells a 2.5 kg bag of apples for £2. Who sells the cheaper apples? kg£: 2.41.80: ÷2.4 10.75: at Mr Green’s 1 kg costs 75 pence, kg£: 2.52: ÷2.5 10.8: at Mr Red’s 1 kg costs 80 pence, Mr Green sells the cheaper apples

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43. The exchange rate between Sterling and Euros is: £1 = €1.60 1. How many Euros do we get if we change £150? 2. How many Pounds do we get if we change €32.64? £€: 11.6: x150 150240: £150 = €240 £€: 11.6: ÷1.6 Who cares? 1: €32.64= £20.40 x32.64 20.432.64:

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45. The exchange rate between Sterling and Euros is: £1 = €1.60 How many Pounds do we get if we change €32.64? £ 1 2 10 20 40 0.4 20.4 € 1.6 3.2 16 32 64 0.64 32.64 : : : : : : : :

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