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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 can be written as 3:2 and is said to be 3 to 2. **

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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Q1 Simplify- 4:10 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q2 Simplify- 6:12 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q3 Simplify- 9:12 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q4 Simplify- 15:25 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q5 Simplify- 6:18 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q6 Simplify- 50:70 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q7 Simplify- 27:30 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q8 Simplify- 36:48 10 9 11 13 15 14 8 12 6 1 End 2 3 5 4 7

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Q9 10 9 11 12 15 14 13 8 6 1 End 2 3 5 4 7 Simplify- 4:10:12

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Q10 10 9 11 12 15 14 13 8 6 1 End 2 3 5 4 7 Simplify- 6:12:21

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

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**Ratios and finding quantities**

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?

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**How do you split 300g in the ratio 2:1?**

Ask yourself 3 questions: How many parts are there? 3 (2 of cement, 1 of sand) How much is 1 share worth? 300g ÷ 3 = 100g How much of each is needed? 2 parts cement = 2 x 100g = 200g 1 part sand = 1 x 100g = 100g

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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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**How do you split £600 in the ratio 1:2:3?**

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

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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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**£20 is shared in the ratio 1:3**

How much is 1 share worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £4 £1 A) B) £5 £3 C) D)

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**£30 is shared in the ratio 2:3**

How much is 1 share worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £1 £5 A) B) £2 £6 C) D)

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**£18 is shared in the ratio 1:2**

How much is 1 share worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £3 £6 A) B) £2 £18 C) D)

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**£45 is shared in the ratio 4:5**

How much is 1 share worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 3 4 £5 £9 A) B) £6 £4 C) D)

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**£20 is shared in the ratio 1:3**

How much is 3 shares worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £16 £12 A) B) £3 £15 C) D)

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**£30 is shared in the ratio 2:3**

How much is 3 shares worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £12 £18 A) B) £20 £15 C) D)

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**£18 is shared in the ratio 1:2**

How much is 2 share worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £6 £12 A) B) £3 £18 C) D)

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**£45 is shared in the ratio 4:5**

How much is 5 shares worth? 12 13 10 8 9 11 14 19 20 18 17 15 16 7 5 1 6 2 End 4 3 £18 £15 A) B) £25 £20 C) D)

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**Tom and Ellie share £15 in the ratio 1:2**

12 13 11 9 7 8 10 14 19 20 18 17 15 16 6 5 1 2 3 4 End How much do they get each? Tom- £5 Ellie- £10 Tom- £10 Ellie- £5 A) B) Tom- £3 Ellie- £6 Tom- £1 Ellie- £2 C) D)

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**Libby and Grant share £42 in the ratio 3:4**

12 13 11 9 7 8 10 14 19 20 18 17 15 16 6 5 1 2 3 4 End How much do they each get Libby- £20 Grant- £22 Libby- £24 Grant- £18 A) B) Libby- £21 Grant- £28 Libby- £18 Grant- £24 C) D)

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**Questions £30 is shared in the ratio 1:2**

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

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

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Extension Ben and Jerry share some money in the ratio of 3:4, Ben gets £21, how much does Jerry get? Jon and Ade share some socks in the ratio 2:7 Jon gets 18 socks, how many does Ade get 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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Extension 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. z y x

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Bellwork Write each rational number as a fraction in simplest form.

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