Grade DE Proportion and ratio Understand use proportion

Grade D/E Proportion and ratio Understand use proportion as equality of ratios If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Ratio Proportion Parts Common units

How to work with proportion and ratio 1) Alice is making smoothie from strawberries, bananas, yoghurt and honey in the ratio 5 : 3 : 1. She puts in 123 g yoghurt. She wants to fill her jug that holds 480 g drink. Can she fill her jug? Yoghurt refers to 3 parts. 123 ÷ 3 = 41 g each part 41 x 5 = 205 g strawberries 41 x 3 = 123 g bananas 41 x 1 = 41 g honey 205 + 123 + 41 = 492 g Yes, she can fill her jug.

How to work with proportion and ratio 2) Here are the ingredients for 12 cupcakes. Julie wants to make 40 cupcakes. She has 650 g flour and plenty of other ingredients. Can she make 40 cupcakes? 200 g flour 150 g sugar 125 g butter 3 eggs 50 g cocoa powder For every 12 cupcakes, she uses 200 g flour 200 ÷ 12 = 16. 6 g flour needed for each cupcake 16. 6 g x 40 = 666. 6 g needed for 40 cupcakes No she can’t make 40 cupcakes, she is 16. 6 g short of flour.

How to work with proportion and ratio 3) Imran makes lemonade by mixing lemon juice, sugar and water in the ratio 8 : 3 : 13. He wants to make 3 litres of lemonade. How much of each ingredient does 8 + 3 + 13 = 24 parts altogether he need? 3 litres = 3000 ml 3000 ÷ 24 = 125 ml each part 8 x 125 = 1000 ml = 1 litre lemon juice 3 x 125 = 375 ml sugar 13 x 125 = 1625 ml = 1. 625 litre water Imran is not happy with the taste. So he adds 250 ml of sugar and 175 ml water to the mixture. What is the new ratio? 375 + 250 = 625 sugar 1625 + 175 = 1800 ml water simplified (÷ 25) 40 : 25 : 72 1000 : 625 : 1800

Work with proportion and ratio – Now you try… 1) The cost of 24 pens is £ 39. 60. Find the cost of 10 pens. 2) One litre of shampoo costs £ 8. 20. What is the cost for 325 ml? 3) In a class of forty people, three in every eight people have brown hair. How many people have brown hair? 4) Leyla gets pocket money every week. She gets triple the amount of her sister Amy and their brother James gets twice as much as Leyla. If they were given £ 54 in total, how much would they each get?

Work with proportion and ratio – Now you try… 1) The cost of 24 pens is £ 39. 60. Find the cost of 10 pens. 1) 16. 50 2) One litre of shampoo cost £ 8. 20. What is the cost for 325 ml? 2) £ 2. 67 3) In a class of forty, three in every eight people have brown hair. How many people have brown hair? 3) 15 4) Leyla gets pocket money every week. She gets triple the amount of her sister Amy and their brother James gets twice as much as Leyla. If they were given £ 54 in total, how much would they each get? 4) Amy = £ 5. 40 Leyla = £ 16. 20 James = £ 32. 40

Problem Solving and Reasoning In 2011, the ratio of John’s age to Pamela’s age was 5 : 4. In 2014, the ratio changed to 11 : 9. How old was Pamela in 2014?

Problem Solving and Reasoning In 2011, the ratio of John’s age to Pamela’s age was 5 : 4. In 2014, the ratio changed to 11 : 9. How old was Pamela in 2014? Let’s assume John’s age as 5 a and Pamela’s age as 4 a. After 3 years, John is 5 a + 3 and Pamela is 4 a + 3 5 a + 3 = 11 4 a + 3 9 9 (5 a + 3) = 11 (4 a + 3) 45 a + 27 = 44 a + 33 a=6 In 2014, Pamela’s age => 4 a + 3 = (4 x 6) + 3 = 27 years old.

Problem Solving and Reasoning In a school of 320 pupils, 30% play a musical instrument. Out of this 30%, the ratio of pupils who play violin to piano is 3 : 5. 1/6 of pianists also play guitar. How many children play guitar?

Problem Solving and Reasoning In a school of 320 pupils, 30% play a musical instrument. Out of this 30%, the ratio of pupils who play violin to piano is 3 : 5. 1/6 of pianists also play guitar. How many children play guitar? 30% of 320 = 96 pupils play instruments 3 + 5 = 8 parts is equal to 96. One part => 96 ÷ 8 = 12 Pianists 5 parts => 5 x 12 = 60 pupils 1/6 x 60 = 10 pupils play guitar

Reason and explain • What is the difference between definitions of ratio and proportion? • It takes two weeks for 5 builders to paint a house. How long would it take 8 builders to paint a house? What do we call this type of proportion? • Coffee is mixed with water and milk in the following ratios. Which coffee is strongest? 2: 3: 1 3: 4: 0 3: 3: 1 4: 5: 2