UNIT TWELVE

RATIOS

Produced by Frank Pettitt

at Woolwich College

OBJECTIVES OF UNIT XII.

When you have completed this unit you should be able to:

- Understand the concept of a ratio and proportional parts.

- solve simple problems involving ratios

RATIOS

A scale is a means of comparing the size of a model with the size of a real thing and this comparison is by means of a ratio. For example a real plane may be 96 times bigger than a model of that plane. This difference is expressed by the ratio 1:96.

A ratio should be expressed in its simplest form. E.g. 3:2 instead of 6:4.

A ratio has no units. (I.e. it is not expressed as pounds, feet etc.)

EXAMPLES

A. We want to divide £20 between Jane and Sue in the ratio 2:3.

i) 2 + 3 = 5

ii) 20 / 5 = 4

iii) 2 X 4 = 8 (Jane gets œ8)

iv) 3 X 4 = 12 (Sue gets œ12)

(CHECK: 8 + 12 = 20)

B. We want to divide £750 between Jane, Steve and Sue in the ratio 3:4:8

i) 3 + 4 + 8 = 15

ii) 750 / 15 = 50

iii) 3 X 50 = 150 (Jane gets œ150)

iv) 4 X 50 = 200 (Steve gets œ200)

v) 8 X 50 = 400 (Sue gets œ400)

(CHECK: 150 + 200 + 400 = 750)

EXERCISES.

1. £60 is divided between John and Karen in the ratio 5:7. How much money does each get?

2. £200 is divided between John and Karen in the ratio 3:7. How much money does each get?

3. £ 150 is divided between John and Karen in the ratio 3:2. How much money does each get?

4. £ 900 is divided between John and Karen in the ratio 4:5. How much money does each get?

5. £ 250 is divided between John and Karen in the ratio 1:1. How much money does each get?

6. £ 250 is divided between John and Karen in the ratio 1:5. How much money does each get?

7. £600 is divided between John and Karen in the ratio 3:2. How much money does each get?

8. £1000 is divided between John and Karen in the ratio 4:1. How much money does each get?

9. £300 is divided between John and Karen in the ratio 3:1. How much money does each get?

10. £400 is divided between John and Karen in the ratio 3:1. How much money does each get?

11. £600 is divided between John, Jean and Karen in the ratio 3:2:1. How much money does each get?

12. £800 is divided between John, Jean and Karen in the ratio 4:3:1. How much money does each get?

13. £150 is divided between John, Jean and Karen in the ratio 1:1:1. How much money does each get?

14. £900 is divided between John, Jean and Karen in the ratio 1:1:5. How much money does each get?

15. £250 is divided between John, Jean and Karen in the ratio 3:1:1. How much money does each get?

16. £250 is divided between John, Jean and Karen in the ratio 1:1:23. How much money does each get?

17. £600 is divided between John, Jean and Karen in the ratio 3:2:1 How much money does each get?

18. £1000 is divided between John, Jean and Karen in the ratio 5:4:1. How much money does each get?

19. £300 is divided between John, Jean and Karen in the ratio 2:2:1. How much money does each get?

20. £400 is divided between John, Jean and Karen in the ratio 2:1:1. How much money does each get?

EXAMPLES

A. Express the following ratio as simply as possible: £1,200 to £640.

1200 120 15

640 64 8

---- = --- = -- i.e. 15:8

B. Express the following ratio as simply as possible: A school contains 360 girls and 240 boys. Find the ratio of

i) The number of girls to the number of boys.

360 36 3

240 24 2

--- = -- = - i.e. 3:2

i.e. For every 3 girls there are 2 boys in the school

ii) The number of boys to the total number of pupils in the school

240 240 2

--- = --- - i.e. 2:5

360+240 600 5

Out of every 5 pupils in the school 2 are boys.

EXERCISES

Express each of the following ratios as simply as possible:

21. £1200 to £640

22. 35 minutes to 2 1/4 hours

23. 1.5 to 2

24. £1200 to £600

25. 300 boys to 200 girls

26. 600 pupils to 20 teachers

27. 6 children to 2 adults

28. £12000 to £640

29. 450 boys to 150 girls

30. 4500 boys to 1500 girls