1 Ratio MENU Equivalent Ratios Main Menu Sharing with a total amount given Sharing with a total given amount given questions Sharing with a part amount given Sharing with a part amount given questions Teacher’s notes on sharing with ratio Equivalent Ratios Questions Ratios in the form 1 : n Ratios in the form 1 : n questions Ratios in the form n : 1 Ratios in the form n : 1 questions Starters Simplifying Ratios 1 10 quickfire Simplifying Ratios 2 10 quickfire Writing Ratios 1 : n (1) 10 quickfire Writing Ratios n : 1 (2) 10 quickfire Writing Ratios n : 1 (1) 10 quickfire Writing Ratios 1 : n (2) 10 quickfire Proportion. Adapting recipes Proportion. Adapting recipes questions Proportion. General problems Proportion. General problems questions Best Value for money Best Value for money questions Teacher’s notes on quickfire

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3 Flour Sugar I like simple cakes made only out of flour and sugar. I mix it using a ratio of 2 : 1 21: But the cake will not be big enough ! Repeat the process ! But now my cake is 4 : 2 !!! 4 : : 2 But the cake tastes exactly the same ! Both ratios are equivalent. They can be simplified in the same way as fractions are simplified. Two goes into both 4 and Menu

4 Flour Sugar I’m going to try a cake using flour and sugar in a ratio of 2 : 3 23 : But the cake will not be big enough ! Repeat the process. But now my cake has used a ratio of 4 : 6 !!! 46 But the cake will taste exactly the same ! Two goes into 4 and : 3 is a simplified version of 4 : 6 Menu

5 Write the following ratios in their simplest form. 1)4 : 82)8 : 12 3)4 : 12 4)6 : 95)10 : 206)8 : 10 7)2 : 88)14 : 69)30 : 20 10)7 : 2111)8 : 2212)9 : 6 13)2000 g : 1 Kg14)50 mm : 2 cm 15)4000 ml : 6 litres16)3 Km : m 17)40 g : mg18)6 tonnes : 8000 Kg 19)180 secs : 2 mins20)3 mins : 200 secs 21)3 hours : 120 mins22)1 hour 15 mins : 2 hours 23)4 hours : 2 hours 20 mins 24) 2 hours 10 mins : 1 hour 5 mins 1 : 22 : 31 : 3 2 : 31 : 24 : 5 1 : 47 : 33 : 2 1 : 34 : 113 : 2 2 : 15 : 2 2 : 31 : 4 1 : 23 : 4 3 : 29 : 10 3 : 25 : 8 12 : 72 : 1 Menu Answers

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7 2 Flour Sugar : 3 FlourSugar But I only want to use 1 spoonful of flour ! 1 or This is now in the form of 1 : n or : 31 : 3 2 Menu

8 5 Flour Sugar : 4 FlourSugar But I only want to use 1 spoonful of flour ! 1 or This is now in the form of 1 : n 5 : 41 : 4 5 Menu

9 Write the following ratios in the form of 1 : n 1)3 : 42)2 : 5 3)6 : 74)5 : 35)4 : 7 6)3 : 107)7 : 28)8 : 5 9)100 secs : 2 mins10)3 Kg : 2000 g11)200 cm : 3 m 12)5000 ml : 8 litres13)2 tonnes : 9000 Kg 14)2 hours 10 mins : 5 hours 20 mins15)½ hour : 45 mins 1 : 4/3 1 : 5/2 1 : 7/61 : 3/51 : 7/4 1 : 10/31 : 2/71 : 5/8 1 : 6/5 1 : 2/31 : 3/2 1 : 8/51 : 9/2 1 : 32/13 1 : 3/2 Make sure these are in their simplest form ! Menu Answers

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11 33 Flour Sugar 2 : 3 FlourSugar 2 : But I only want to use 1 spoonful of sugar ! 2 3 : 1 This is now in the form of n : 1 1 or Menu

12 44 Flour Sugar FlourSugar 5 : But I only want to use 1 spoonful of sugar ! 5 : : 1 or This is now in the form of n : 1 Menu

13 Write the following ratios in the form of n : 1 1)3 : 42)2 : 5 3)6 : 74)5 : 35)4 : 7 6)3 : 107)7 : 28)8 : 5 9)100 secs : 2 mins10)3 Kg : 2000 g11)200 cm : 3 m 12)5000 ml : 8 litres13)2 tonnes : 9000 Kg 14)2 hours 10 mins : 5 hours 20 mins15)½ hour : 45 mins 3/4 : 1 2/5 : 1 6/7 : 15/3 : 14/7 : 1 3/10 : 17/2 : 18/5 : 1 5/6 : 1 3/2 : 12/3 : 1 5/8 : 12/9 : 1 13/32 : 1 2/3 : 1 Make sure these are in their simplest form ! Menu Answers

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15 Birthday cake recipe. { Serves 4 people } 400 g of flour. 200 g of sugar 100 g of butter 2 eggs. But I need a cake for 6 children ! Work out how much you need for 1 child and then multiply up the quantities by 6. people = 400 g of flour41 1 person = 100 g of flour 6 people need 100 × 6 = 600 g of flour 4 people = 200 g of sugar 1 person = 200 of sugar 4 1 person = 50 g of sugar 6 people need 50 × 6 = 300 g of sugar 4 people = 100 g of butter 1 person = 100 of butter 4 1 person = 25 g of butter 6 people need 25 × 6 = 150 g of sugar 4 people = 2 eggs 1 person = 2 eggs 4 {0.5 eggs} 6 people need 0.5 × 6 = 3 eggs Menu

16 Murghal Shredded Duck Curry Recipe { Serves 5 } 500 g skinned duck breasts 60 ml vegetable oil 125 g cashew nuts 155 ml natural yoghurt 6 tablespoons of cream But I want to cook for 12 people ! 5 people = 500 g duck 1 person = people need 100 × 12 = 1200 g of duck = 100 g 5 people = 60 ml of vegetable oil 1 person = 60 5 = 12 ml 12 people need 12 ×12 = 144 ml of vegetable oil 5 people = 125 g cashew nuts 1 person = = 25 g 12 people need 25 ×12 = 300 g of cashew nuts 5 people = 155 ml of natural yoghurt 1 person = = 31 ml 12 people need 31 ×12 = 372 ml of natural yoghurt 5 people = 6 tablespoons of cream 1 person = 6 5 = 1.2 tablespoons 12 people need 1.2 ×12 = 14.4 tablespoons of cream Menu

17 Adapt the following recipes. Fresh Mango Chutney { Serves 2 } 2 Mangoes 1 red chilli 30 g raisins ½ teaspoon cumin ADAPT IT FOR 6 PEOPLE Lime Pickle { Serves 3 } 12 Limes 250 ml sunflower oil 6 teaspoons chilli powder 2 teaspoons turmeric ADAPT IT FOR 10 PEOPLE Curried Chick Peas { Serves 4 } 185 g chick peas 2 cloves crushed garlic 1 onion ½ teaspoon chilli powder ADAPT IT FOR 9 PEOPLE Chicken Tikka { Serves 5 } 800 g chicken 180 ml yoghurt 6 teaspoons lime juice 2 ½ cm root ginger ADAPT IT FOR 3 PEOPLE g 1 ½ ml g 4 ½ 2 ¼ g 108ml ½ Menu Answers

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19 5 Pairs of socks £ 3.20 But I only want to buy 3 pairs ! 5 pairs = £ pair = = £ pairs cost 0.64 × 3 = £ 1.92 First of all always work out what is needed for ONE then simply multiply up to what is needed. Menu

20 8 paint brushes £ 4.99 But I want 10 brushes ! 8 brushes = £ brush = = £ brushes cost × 10 = £ = £ 6.24 to the nearest penny Menu

21 I bought $ 38 using a £ 20 note. How many dollars could I buy for £ 15 ? £ 20 = $ 38 £ 1 = = $ 1.9 £ 15 = 1.9 × 15 = $ Menu

22 Work out the following. {Round your answers sensibly} 1)12 pens cost 75p. How much would 15 pens cost ? 2)5 apples weigh 600g. How much would 7 apples weigh ? 3)200g of gold costs £4000. How much would 550g cost ? 4)A car can travel 150Km on 30 gallons of petrol. How far could it travel on 45 gallons ? 5)If 30 oranges can be bought for £2. How many could be bought for £8.50 ? 6)A pack of 20 blank compact discs cost £ How much should a pack of 30 cost ? 7)35 workers make 230 pairs of shoes in a day. How many shoes should 50 workers be able to produce ? 8)To make a 1 litre orange drink you need 150ml of orange and the rest water. How much orange would you need for a 800 ml drink ? 94 p 840 g £ Km 127 £ ml Menu Answers

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24 Germ Killer 5 litres £ 2.99 Germ Killer 4 litres £ 2.49 But which one is best value for money ? Work out how much 1 penny buys. Whichever one buys most must be best value ! 299 p = 5000 ml 1 p = p = ml 249 p = 4000 ml 1 p = p = ml The yellow gives more per penny. So best value ! Menu

cm of thread £ metres of thread 80 p But which one is best value for money ? 80 p = 200 cm 1 p = p = 2.5 cm 125 p = 300 cm 1 p = p = 2.4 cm The ‘2 metre thread’ gives more per penny. So best value. Menu

26 Work out which is ‘Best Value For Money’. Clearly show and explain, with a sentence, all of your working out. 1)200 g of butter for £ 1.35 or 240 g for £ )2 litres of apple juice for 95 p or 2.2 litres for £ )1850 sheets of toilet roll for £ 1.75 or 1100 sheets for £ )3 ½ Kg of potatoes for £ 1.35 or 2200 g for 90 p. 5)40 nappies for £ 3.35 or 65 nappies for £ )300 g of coffee for £ 1.70 or 350 g for £ )A dozen eggs for 89 p or 14 eggs for £ )A 6 mile taxi fare costing £ 8.30 or an 8 ½ mile journey costing £ )A 450 ml tub of ice-cream for £ 1.60 or a 1 litre tub for £ )A pack of 4 batteries for £ 3.75 or a pack of 6 for £ )0.8 Kg of flour for 55 p or 1 Kg for 70 p. 12)A 125 g tin of tuna for 57 p or a 140 g for 65 p. 240 g : 1p = 1.71 g 2 litres : 1p = ml 1850 sheets : 1p = sheets 3 ½ Kg : 1p = g 65 nappies : 1p = 0.12 nappies 300g : 1p = g Dozen eggs : 1p = eggs 8 ½ : 1p = miles 1 litre : 1p = ml Pack of 6 : 1p = batteries 0.8 Kg : 1p = g 125 g : 1p = 2.19 g Menu Answers

27 Teacher’s Notes on Ratio : The idea of the following slides is that the pupils, in effect, work out for themselves what they have to do with the numbers, or parts, in order to solve problems involving ratio. Each pupil needs to be given small piles of blue, orange and yellow pieces of card. Pupils then simply share out the card as instructed and answer the questions. After a few have been completed the pupils should start to be able to answer the questions WITHOUT using the card for help. Menu

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29 Share out Blue and Orange card in the ratio of 1 : 2. Use a TOTAL of 9 cards. How many of each colour are given out ? There are now 9 cards. 3 blue and 6 orange. Menu

30 Share out Blue, Orange and Yellow card in the ratio of 2 : 1 : 3 Use a TOTAL of 12 cards. How many of each colour are given out ? There are now 12 cards. 4 blue, 2 orange and 6 yellow. Menu

31 In each of the following work out how many of each colour have been shared out : 1)Share out BLUE to ORANGE cards in the ratio of 2 : 1 {Use 6 cards} 2)Share out BLUE to YELLOW cards in the ratio of 3 : 1 {Use 8 cards} 3)Share out ORANGE to YELLOW cards in the ratio of 1 : 4 {Use 10 cards} 4)Share out BLUE to YELLOW cards in the ratio of 2 : 3 {Use 10 cards} 5)Share out ORANGE to YELLOW cards in the ratio of 3 : 5 {Use 16 cards} 6)Share out BLUE and YELLOW cards in the ratio of 2 : 1 {Use 9 cards} 7)Share out ORANGE and YELLOW cards in the ratio of 1 : 3 {Use 12 cards} 8)Share out BLUE and YELLOW cards in the ratio of 3 : 2 {Use 15 cards} 9)Share out ORANGE and BLUE cards in the ratio of 4 : 3 {Use 28 cards} 10)Share out BLUE and YELLOW cards in the ratio of 3 : 1 {Use 16 cards} 11)Share out ORANGE, BLUE and YELLOW cards in the ratio of 3 : 2 : 1 {Use 12 cards} 12)Share out ORANGE, BLUE and YELLOW cards in the ratio of 2 : 1 : 4 {Use 14 cards} 13)Share out ORANGE, BLUE and YELLOW cards in the ratio of 3 : 2 : 4 {Use 18 cards} 14)Share out ORANGE, BLUE and YELLOW cards in the ratio of 4 : 1 : 3 {Use 24 cards} 15)Share out BLUE, YELLOW and ORANGE cards in the ratio of 2 : 1 : 3 {Use 36 cards} 4 blue & 2 orange 6 blue & 2 yellow 2 orange & 8 yellow 4 blue & 6 yellow 6 orange & 10 yellow 6 blue & 3 yellow 3 orange & 9 yellow 9 blue & 6 yellow 16 orange & 12 blue 12 blue & 4 yellow 6 orange, 4 blue & 2 yellow 4 orange, 2 blue & 8 yellow 6 orange, 4 blue & 8 yellow 12 orange,3 blue & 9 yellow 12 blue 6 yellow & 18 orange Menu Answers

32 1)I have 16 sweets. I share them out between Joe and Sam in the ratio of 3 : 1 How many sweets does each get ? 2)8 pens are shared out between Sue and Mike using the ratio of 1 : 3. How many pens do they each get ? 3)15 coins are shared out between Paul and Steve in the ratio of 2 : 1. How many coins did Paul get ? 4)32 biscuits are shared out between Mike, Fred, and Gareth using the ratio of 2 : 5 : 1. How many biscuits did Fred get ? 5)42 cards are given to Debbie, Jane and Sarah using the ratio of 3 : 2 : 2. Who got the most cards and how many did she get ? 6)36 crisps are shared out between Max, Ian and Tim using the ratio of 5 : 1 : 3 How many did Tim get ? 7)48 Litres of lemonade are given to Martin, Clive, Paul and Tom using the ratio of 4 : 3 : 2 : 3. Who got the SAME amount and how much did they get ? 8)45 presents are shared out between Mark, Daniel, Peter and Emma using the ratio of 2 : 1 : 1 : 1. How many presents did Emma get ? Joe = 12, Sam = 4 Sue = 2, Mike = 6 Paul = 10 Fred = 20 Debbie = 18 Tim = 12 Clive & Tom = 12 Emma = 9 Menu Answers

33 1)Share out £168 between Paul and Mike using the ratio 3 : 5. 2)Share out 126 litres of water between Sue and Bob using the ratio of 7 : 2. 3) Give 957 marbles to Ian and David using the ratio of 8 : 3. 4)Share out 1044 Kg of hay between Dobbin, Clover and Rusty using the ratio of 6 : 7 : 5. 5)140,736 votes were cast at an election. The Labour, Conservative and Liberals shared the vote in the ratio of 9 : 5 : 2 respectively. How many votes did the Labour Party win ? 6)Find the largest share when £12,327 is shared out in the ratio of 6 : 2 : 3 : 10. 7)Find the smallest share when $1008 is shared out using the ratio of 2 : 2 : 1 : 3 : 4. 8)Find the largest share when £ 31,251 is shared out using the ratio of 6 : 14 : 11 : 2. Paul = £63, Mike = £ 105 Sue = 98 litres, Bob = 28 litres Ian = 696 marbles, David = 261 marbles Dobbin = 232 Kg, Clover =406 Kg, Rusty = 290 Kg 79,164 votes £ 5870 $ 84 £ 13,258 Menu Answers

34 1)£ 27 is shared out between Paul and Debbie. Paul gets twice as much as Debbie. How much does Paul get ? 2)£ 128 is shared out between Mark and Sarah. Sarah gets three times as much as Mark. How much did Sarah receive ? 3)£ 235 is shared out between Joe and Daniel. Joe has ¼ as much as Daniel. How much does Joe get ? 4)£ 686 is shared out between David, Steve and Mike. Mike gets twice as much as Steve who gets twice as much as David. How much does Mike get ? 5)£ 150 is shared out between Helen, Ruth and Jessica. Helen gets twice as much as Jessica and Jessica has a third as much as Ruth. How much does Helen get ? 6)£ 456 is shared out between Daniel, Adam and Richard. Richard gets six times as much as Daniel and Daniel gets 1/5 as much as Adam. Who gets the most and how much do they get ? 7)£ 5232 is shared out between Joanne, Mary, Hannah and Sophie. Mary gets twice as much as Sophie. Sophie gets ½ as much as Joanne. Hannah gets 1½ times as much as Mary. How much does Joanne get ? £ 18 £ 96 £ 47 £ 392 £ 50 Richard = £ 228 £ 1308 Menu Answers

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36 Blue and orange cards are shared out in the ratio of 2 : 1. If 4 blue cards are given out how many orange cards will also be given out ? There are now 4 blue cards and there are 2 orange cards. Menu

37 Blue, orange and yellow cards are shared out in the ratio of 1 : 3 : 2 If 9 orange cards are given out how many blue and yellow cards will also be given out ? There are now 9 orange cards. There are 3 blue and 6 yellow cards ! Menu

38 1)Blue and orange card is shared out in the ratio of 2 : 1. There are 4 blue cards. How many orange cards are there ? 2)Yellow and blue card is given out in the ratio of 1 : 3. There are 3 yellow cards. How many blue cards are there ? 3)Blue and orange cards are shared out in the ratio of 3 : 2. There are 9 blue cards. How many orange cards are there ? 4)Blue and yellow cards are shared out using the ratio of 2 : 7. There are 8 blue cards. How many yellow cards are there ? 5)Blue, yellow and orange cards are shared out in the ratio of 1 : 2 : 3. There are 4 yellow cards. How many orange cards are there ? 6)Orange, blue and yellow cards are shared out in the ratio of 3 : 5 : 6.There are 40 blue cards. How many orange cards are there ? 7)Blue, yellow and orange cards are shared out in the ratio of 3 : 5 : 7.There are 18 blue cards. How many cards are there ALTOGETHER ? 8)Blue, orange and yellow cards are shared out in the ratio of 9 : 2 : 5.There are 12 orange cards. How many cards are there ALTOGETHER ? Menu 2 orange 9 blue 6 orange 28 yellow 6 orange 24 orange 90 altogether 96 altogether Answers

39 1)In a field the ratio of cows to sheep is 2 : 3. There are 8 cows. How many sheep are there ? 2)In a classroom the ratio of boys to girls is 4 : 5. There are 15 girls. How many boys are there ? 3)In a pencil case the ratio of pens to pencils is 7 : 5. There are 21 pens. How many pencils are there ? 4)In an orchard the ratio of apple trees to pear trees is 6 : 11. There are 60 apple trees. How many pear trees are there ? 5)Money is shared out between Paul and Helen in the ratio of 3 : 4. Paul receives £27. How much did Helen receive ? 6)Money is shared out between Bob, Sam and Mike using the ratio of 2 : 5 : 3. Mike received £24. How much did Sam receive ? 7)Paint is mixed using yellow, red and green paint in the ratio of 2 : 3 : litres of red paint is used. How much paint was mixed altogether ? 8)Jane has lessons in Maths, English, History and Science in the ratio of 7 : 6 : 4 : 5. She has already had 24 History lessons. How many lessons has she had altogether ? Menu 12 sheep 12 boys 15 pencils 110 pear trees £ 36 £ litres 132 lessons Answers

40 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

41 Simplifying Ratios Quickfire questions Menu

42 Simplify 4 : 2 Question 1 Menu

43 Simplify 10 : 15 Question 2 Menu

44 Simplify 7 : 21 Question 3 Menu

45 Simplify 6 : 18 Question 4 Menu

46 Simplify 8 : 12 Question 5 Menu

47 Simplify 9 : 3 Question 6 Menu

48 Simplify 3 : 15 Question 7 Menu

49 Simplify 8 : 20 Question 8 Menu

50 Simplify 10 : 6 Question 9 Menu

51 Simplify 5 : 20 Question 10 Menu

52 Simplifying Ratios Quickfire questions Menu

53 Simplify 12 : 14 Question 1 Menu

54 Simplify 8 : 2 Question 2 Menu

55 Simplify 4 : 10 Question 3 Menu

56 Simplify 7 : 35 Question 4 Menu

57 Simplify 24 : 6 Question 5 Menu

58 Simplify 18 : 12 Question 6 Menu

59 Simplify 11 : 33 Question 7 Menu

60 Simplify 20 : 10 Question 8 Menu

61 Simplify 6 : 6 Question 9 Menu

62 Simplify 201 : 201 Question 10 Menu

63 Writing ratios in the form of 1 : n (1.) 10 Quickfire questions Menu

64 Write 3 : 6 in the form of 1 : n Question 1 Menu

65 Write 5 : 15 in the form of 1 : n Question 2 Menu

66 Write 7 : 16 in the form of 1 : n Question 3 Menu

67 Write 2 : 5 in the form of 1 : n Question 4 Menu

68 Write 6 : 14 in the form of 1 : n Question 5 Menu

69 Write 10 : 5 in the form of 1 : n Question 6 Menu

70 Write 9 : 3 in the form of 1 : n Question 7 Menu

71 Write 10 : 3 in the form of 1 : n Question 8 Menu

72 Write 12 : 5 in the form of 1 : n Question 9 Menu

73 Write 6 : 4 in the form of 1 : n Question 10 Menu

74 Writing ratios in the form of 1 : n (2.) 10 Quickfire questions Menu

75 Write 6 : 9 in the form of 1 : n Question 1 Menu

76 Write 8 : 3 in the form of 1 : n Question 2 Menu

77 Write 10 : 18 in the form of 1 : n Question 3 Menu

78 Write 6 : 2 in the form of 1 : n Question 4 Menu

79 Write 15 : 8 in the form of 1 : n Question 5 Menu

80 Write 4 : 3 in the form of 1 : n Question 6 Menu

81 Write 10 : 100 in the form of 1 : n Question 7 Menu

82 Write 8 : 7 in the form of 1 : n Question 8 Menu

83 Write 3 : 10 in the form of 1 : n Question 9 Menu

84 Write 5 : 7 in the form of 1 : n Question 10 Menu

85 Writing ratios in the form of n : 1 (1.) 10 Quickfire questions Menu

86 Write 8 : 4 in the form of n : 1 Question 1 Menu

87 Write 2 : 4 in the form of n : 1 Question 2 Menu

88 Write 5 : 15 in the form of n : 1 Question 3 Menu

89 Write 6 : 10 in the form of n : 1 Question 4 Menu

90 Write 4 : 9 in the form of n : 1 Question 5 Menu

91 Write 8 : 3 in the form of n : 1 Question 6 Menu

92 Write 7 : 10 in the form of n : 1 Question 7 Menu

93 Write 4 : 24 in the form of n : 1 Question 8 Menu

94 Write 11 : 3 in the form of n : 1 Question 9 Menu

95 Write 5 : 4 in the form of n : 1 Question 10 Menu

96 Writing ratios in the form of n : 1 (2.) 10 Quickfire questions Menu

97 Write 2 : 9 in the form of n : 1 Question 1 Menu

98 Write 7 : 5 in the form of n : 1 Question 2 Menu

99 Write 4 : 5 in the form of n : 1 Question 3 Menu

100 Write 6 : 9 in the form of n : 1 Question 4 Menu

101 Write 10 : 9 in the form of n : 1 Question 5 Menu

102 Write 4 : 15 in the form of n : 1 Question 6 Menu

103 Write 8 : 5 in the form of n : 1 Question 7 Menu

104 Write 5 : 20 in the form of n : 1 Question 8 Menu

105 Write 30 : 80 in the form of n : 1 Question 9 Menu

106 Write 9 : 9 in the form of n : 1 Question 10 Menu

107 End of Ratio and Proportion Presentation. Return to previous slide.