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Ratio

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Objectives Understand how to use ratios to find specific quantities Simplify ratios by identifying common factors Demonstrate a medium level of understanding of multiplication and division

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A ratio is a comparison between two numbers or two quantities of different items. A ratio can be written as 3:2 and is said to be 3 to 2. If you have 2 biscuits and 1 cups of tea, the ratio of biscuits to cups of tea would be 2:1. Ratio is also a way in which quantities can be divided or shared.

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Simplifying Ratios Like fractions, ratios can be simplified by finding common factors. The factors of a number are those numbers that divide into it exactly. E.g 1 × 12 = 12 2 × 6 = 12 3 × 4 = 12 So the factors of 12 are 1, 2, 3, 4, 6 and 12.

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Example There are 15 males and 12 females in a group. What is the ratio of males to females? Give your example in its simplest form. So the ratio of males to females is 15:12. However, both sides of the ratio can be divided by 3. Dividing 15 and 12 by 3 gives 5:4. 5:4 is the ratio in its simplest form.

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Simplifying Ratios QUIZ Write 1 to ten in your margin 10 seconds for each question

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Simplify- 4:10 Q1 End

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Q2 Simplify- 6:12 End

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Q3 Simplify- 9:12 End

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Q4 Simplify- 15:25 End

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Q5 Simplify- 6:18 End

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Q6 Simplify- 50:70 End

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Q7 Simplify- 27:30 End

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Q8 Simplify- 36:48 End

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Q9 Simplify- 4:10:12 End

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Q10 Simplify- 6:12:21 End

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Answers 1)2:5 2)1:2 3)3:4 4)3:5 5)1:3 6)5:7 7)9:10 8)3:4 9)2:5:6 10)3:4:7

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Adrian is building a barbecue and needs 300g of mortar. He needs to mix cement and sand in a ratio of 2:1. How much of each does he need? Ratios and finding quantities

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Ask yourself 3 questions: a)How many parts are there? a)3 (2 of cement, 1 of sand) b)How much is 1 share worth? a)300g ÷ 3 = 100g c)How much of each is needed? a)2 parts cement = 2 x 100g = 200g b)1 part sand = 1 x 100g = 100g How do you split 300g in the ratio 2:1?

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The next job Adrian runs a job renovating a house. He employs painters, carpenters and brickies. They earn £600 for the day. Adrian decides to pay out his painters, carpenters and brickies in the ratio 1:2:3 (painters get 1, carpenters 2 and brickies 3) How do they split it?

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Ask yourself 3 questions: a)How many shares are there? a)6 (3 for Brickies, 2 for Carpenters and 1 for Painters) b)How much is 1 share worth? a)600 ÷ 6 = £100 c)How much do they get? a)Brickies get 3 x 100 = £300 b)Carpenters get 2 x 100 = £200 c)Painters get 1 x 100 = £100 How do you split £600 in the ratio 1:2:3?

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Sharing in Ratios 10 multiple choice questions to be answered in pairs 20 seconds for each question

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£5 £4 £3 £1 A)B) C)D) £20 is shared in the ratio 1:3 How much is 1 share worth? End

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£6 £1£5 £2 A)B) C)D) £30 is shared in the ratio 2:3 How much is 1 share worth? End

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£6£3 £18£2 A)B) C)D) £18 is shared in the ratio 1:2 How much is 1 share worth? End

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£5£9 £4£6 A)B) C)D) £45 is shared in the ratio 4:5 How much is 1 share worth? End

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£15 £16£12 £3 A)B) C)D) £20 is shared in the ratio 1:3 How much is 3 shares worth? End

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£18£12 £15£20 A)B) C)D) £30 is shared in the ratio 2:3 How much is 3 shares worth? End

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£12£6 £18£3 A)B) C)D) £18 is shared in the ratio 1:2 How much is 2 share worth? End

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£25 £18 £20 £15 A)B) C)D) £45 is shared in the ratio 4:5 How much is 5 shares worth? End

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Tom- £5 Ellie- £10 Tom- £10 Ellie- £5 Tom- £1 Ellie- £2 Tom- £3 Ellie- £6 A)B) C)D) Tom and Ellie share £15 in the ratio 1:2 How much do they get each? End

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Libby- £18 Grant- £24 Libby- £20 Grant- £22 Libby- £24 Grant- £18 Libby- £21 Grant- £28 A)B) C)D) Libby and Grant share £42 in the ratio 3:4 How much do they each get End

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Questions 1)£30 is shared in the ratio 1:2 a)How many shares are there? b)How much is one share worth? c)How much does each person get? 2) £40 is shared in the ratio 1:3 a)How many shares are there? b)How much is one share worth? c)How much does each person get? 3) £50 is shared in the ratio 2:3 a)How many shares are there? b)How much is one share worth? c)How much does each person get? 4)£42 is shared in the ratio 2:5 a)How many shares are there? b)How much is one share worth? c)How much does each person get? 5)£56 is shared in the ratio 1:2:4 a)How many shares are there? b)How much is one share worth? c)How much does each person get?

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Questions 1)Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do they each get if they have: a)10 toysb) 30 toys c) 45 toys 2)Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share: a)20 sweets b) 30 sweets c)55 sweets 3)Sue and Linda share some money in the ratio 3:7, how many do they each get if they share: a)£30b)£60c)£90 4)Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do they each get if they share: a)60 pieces b) 72 pieces c) 300 pieces

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Extension 1.Ben and Jerry share some money in the ratio of 3:4, Ben gets £21, how much does Jerry get? 2.Jon and Ade share some socks in the ratio 2:7 Jon gets 18 socks, how many does Ade get 3.Nora, Ben and Jon share some Easter eggs in the ratio 2:5:7, Ben gets 60, how many do Jon and Nora get?

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x y z Firstly, do you remember what the angles in a triangle add up to??? The angles in this triangle (x, y and z) are in the ratio 5:1:3 - find the size of the angles. Extension

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