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Ratio. Objectives Understand how to use ratios to find specific quantities Simplify ratios by identifying common factors Demonstrate a medium level of.

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Presentation on theme: "Ratio. Objectives Understand how to use ratios to find specific quantities Simplify ratios by identifying common factors Demonstrate a medium level of."— Presentation transcript:

1 Ratio

2 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

3 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.

4 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.

5 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.

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

7 Simplify- 4:10 Q1 End

8 Q2 Simplify- 6:12 End

9 Q3 Simplify- 9:12 End

10 Q4 Simplify- 15:25 End

11 Q5 Simplify- 6:18 End

12 Q6 Simplify- 50:70 End

13 Q7 Simplify- 27:30 End

14 Q8 Simplify- 36:48 End

15 Q9 Simplify- 4:10:12 End

16 Q10 Simplify- 6:12:21 End

17 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

18 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

19 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?

20 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?

21 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?

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

23 £5 £4 £3 £1 A)B) C)D) £20 is shared in the ratio 1:3 How much is 1 share worth? End

24 £6 £1£5 £2 A)B) C)D) £30 is shared in the ratio 2:3 How much is 1 share worth? End

25 £6£3 £18£2 A)B) C)D) £18 is shared in the ratio 1:2 How much is 1 share worth? End

26 £5£9 £4£6 A)B) C)D) £45 is shared in the ratio 4:5 How much is 1 share worth? End

27 £15 £16£12 £3 A)B) C)D) £20 is shared in the ratio 1:3 How much is 3 shares worth? End

28 £18£12 £15£20 A)B) C)D) £30 is shared in the ratio 2:3 How much is 3 shares worth? End

29 £12£6 £18£3 A)B) C)D) £18 is shared in the ratio 1:2 How much is 2 share worth? End

30 £25 £18 £20 £15 A)B) C)D) £45 is shared in the ratio 4:5 How much is 5 shares worth? End

31 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

32 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

33 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?

34 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

35 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?

36 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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