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Ratio (Difficult)
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Ratio (Difficult)

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 23 are boys, and 13 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.

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1.
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, 110 × £600 = £60; Harry, 410 × £600 = £240; Mary, 510 × £600 = £300
2.
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, 110 × 140 = 14; Anna, 410 × 140 = 56; Terry, 510 × 140 = 70
3.
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)
4.
What are the fractional parts of 12:4:8?
312, 112 and 212
36, 16 and 26
33, 13 and 23
32, 12 and 22
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.
What are the fractional parts of the ratio 2:3:4?
22, 32 and 42
29, 39 and 49
23, 33 and 43
25, 35 and 45
2 + 3 + 4 = 9 which becomes the denominator in the fractional parts
6.
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)
7.
What are the fractional parts of the ratio 2:9?
27 and 97
911 and 29
211 and 911
29 and 119
2 + 9 = 11 which becomes the denominator in the fractional parts
8.
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
9.
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, 211 × 1,100 = 200; B, 611 × 1,100 = 600; C, 311 × 1,100 = 300
10.
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)
Author:  Frank Evans

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