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 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.

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

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

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

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

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

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

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

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

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

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

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

18. 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?

19. 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

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. 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

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

23. £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)

24. £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)

25. £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)

26. £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)

27. £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)

28. £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)

29. £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)

30. £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)

31. Tom and Ellie share £15 in the ratio 1:212 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)

32. Libby and Grant share £42 in the ratio 3:412 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)

33. 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

34. 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

35. 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?

36. 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