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. 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?
    1 + 4 + 5 = 10 ∴ the fractional parts are as follows: William, 110 × 140 = 14; Anna, 410 × 140 = 56; Terry, 510 × 140 = 70
  2. What are the fractional parts of the ratio 2:3:4?
    2 + 3 + 4 = 9 which becomes the denominator in the fractional parts
  3. 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?
    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
  4. 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?
    1 + 4 + 5 = 10 ∴ the fractional parts are as follows: Dave, 110 × £600 = £60; Harry, 410 × £600 = £240; Mary, 510 × £600 = £300
  5. How else can the ratio 0.125:1.25:2.125 be written?
    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
  6. 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
  7. How else can the ratio 7:1.5 be written?
    7:1.5 = 14:3 (multiply by 2)
  8. 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?
    A:B:C: = 260:340:400 = 26:34:40 (dividing by 10) = 13:17:20 (dividing by 2)
  9. What are the fractional parts of the ratio 2:9?
    2 + 9 = 11 which becomes the denominator in the fractional parts
  10. How else can the ratio 5:1.25:3 be written?
    5:1.25:3 = 20:5:12 (multiply by 4)

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