**A ratio is a way of showing how two or more quantities are related.** For example, if there are double the number of boys in a class compared with the number of girls, then we can show this by writing 2:1. This would be read as: 'the ratio of boys to girls is two to one'. Two parts of the class are boys and one part is girls, but: what is 'part(s) of' as a fraction? It's easy: 2 + 1 = 3, so ^{2}⁄_{3} are boys, and ^{1}⁄_{3} is girls. You would deal with other ratios in a similar way.

Be warned: if you reverse the order of the numbers in a ratio, the ratio changes. 2:1 is NOT the same as 1:2. The order in which you write your ratio is important. Finally, ratios can be simplified by dividing/multiplying the ratio by another number, e.g. 4:8 can be written as 1:2 by dividing both numbers in the ratio by 4.

Play this 11-plus Maths quiz and see how well you do.

1.

What are the fractional parts of the ratio 2:3:4?

2 + 3 + 4 = 9 which becomes the denominator in the fractional parts

2.

The workload has to be shared out between three workers, A, B and C in the ratio 2:6:3 respectively. If the work consists of 1,100 units, how many units will each of the workers have to do?

A 600, B 200 and C 300

A 300, B 600 and C 200

A 200, B 600 and C 300

A 300, B 200 and C 600

2 + 6 + 3 = 11 ∴ the fractional parts are as follows: A, ^{2}⁄_{11} × 1,100 = 200; B, ^{6}⁄_{11} × 1,100 = 600; C, ^{3}⁄_{11} × 1,100 = 300

3.

What are the fractional parts of the ratio 2:9?

2 + 9 = 11 which becomes the denominator in the fractional parts

4.

What are the fractional parts of 12:4:8?

12:4:8 = 3:1:2 (dividing by 4). 3 + 1 + 2 = 6 which becomes the denominator in the fractional parts. Always try and simplify your ratios BEFORE you work out the fractional parts

5.

If 1,000 toy soldiers are divided into three parts, Alan gets 260, Brian gets 340 and Charles gets 400, what is this as the ratio A:B:C in its lowest form?

13:17:20

17:13:20

17:20:13

20:17:13

A:B:C: = 260:340:400 = 26:34:40 (dividing by 10) = 13:17:20 (dividing by 2)

6.

How else can the ratio 5:1.25:3 be written?

5:20:12

20:5:12

20:12:5

12:5:20

5:1.25:3 = 20:5:12 (multiply by 4)

7.

How else can the ratio 7:1.5 be written?

3:14

7:3

14:3

14:1.5

7:1.5 = 14:3 (multiply by 2)

8.

William, Anna and Terry all have their birthdays on the same day. If their ages are in the ratio 1:4:5 respectively, and their combined age is 140, how old are they?

William 70, Anna 56, and Terry 14

William 14, Anna 70, and Terry 56

William 56, Anna 14, and Terry 70

William 14, Anna 56, and Terry 70

1 + 4 + 5 = 10 ∴ the fractional parts are as follows: William, ^{1}⁄_{10} × 140 = 14; Anna, ^{4}⁄_{10} × 140 = 56; Terry, ^{5}⁄_{10} × 140 = 70

9.

Granny gave Dave, Harry and Mary £600. If the money was shared out in the ratio 1:4:5 respectively, how much did each person get?

Dave £60, Harry £240 and Mary £300

Dave £240, Harry £60 and Mary £300

Dave £300, Harry £240 and Mary £60

Dave £240, Harry £300 and Mary £60

1 + 4 + 5 = 10 ∴ the fractional parts are as follows: Dave, ^{1}⁄_{10} × £600 = £60; Harry, ^{4}⁄_{10} × £600 = £240; Mary, ^{5}⁄_{10} × £600 = £300

10.

How else can the ratio 0.125:1.25:2.125 be written?

10:1:17

17:10:1

17:1:10

1:10:17

0.125:1.25:2.125 = 1:10:17 (multiplying by 8). This example should show you why it is important to be able to simplify ratios