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