Ratio
and
Proportion
Ratio
A ratio compares the sizes of parts or quantities to each other.
What is the ratio of red counters to blue
counters?
red : blue
=9:3
=3:1
For every three red counters there is one blue counter.
Ratio
What is the ratio of red counters
to yellow counters to blue
counters?
red : yellow : blue
= 12 :
4
: 8
= 3 :
1
: 2
For every three red counters there is one yellow counter and two blue counters.
Simplifying ratios
Ratios can be simplified like fractions by dividing each part by the highest common
factor.
21 : 35
÷7
÷7
=3:5
For a three-part ratio all three parts must be divided by the same number.
6 : 12 : 9
÷3
÷3
=2:4:3
Dividing in a given ratio
Divide £40 in the ratio 2 : 3.
A ratio is made up of parts.
We can write the ratio 2 : 3 as:
2 parts : 3 parts
The total number of parts is:
2 parts + 3 parts = 5 parts
We need to divide £40 by the total number of parts.
£40 ÷ 5 = £8
Proportion
Proportion compares the size of a part to the size of a whole.
There are many ways to express a proportion.
What proportion of these counters
are red?
We can express this proportion as:
12 out of 16
3 in every 4
3
4
0.75
or
75%
Direct proportion problems
3 packets of crisps weigh 90 g.
How much do 6 packets weigh?
3 packets weigh 90 g.
×2
×2
6 packets weigh
180 g.
If we double the number of packets then we double the weight.
The number of packets and the weights are in direct proportion.
Now try these:
Divide:
Answers:
1. 6:4
6. 16:12
11. 35:15
16. 8:8:4
20. 15:9:3
24. 35:28:21
28. 6:8:10
2. 16:4
7. 10:6
12. 33:44
17. 6:4:2
21. 42:21:7
25. 60:24:24
29. 60:150:210
3. 10:4
8. 50:20
13. 6:15
18. 25:20:5
22. 56:24:16
26. £80, £60
30. 2.5:10:12.5
4. 18:6
5. 15:3
9. 35:10
10. 50:40
14. 16:24
15. 36:3
19. 15:10:5
23. 60:36:24
27. 6:9:12