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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

 

 

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