PROPORTION
Proportion is another name for ratio or fraction and it is important that the same units are used. It is sometimes more useful to represent a proportion as a percentage.Example
In a manufacturing process, light bulbs are being made. 150 bulbs are rejected in a batch of 30,000. What proportion of bulbs in the batch are satisfactory?
Solution
The number of bulbs accepted = 30,000 - 150 = 29,850
The proportion of bulbs accepted = 29,850/30,000 = 199/200
Percentage o bulbs accepted = 199/200 × 100 = 99.5%
DIRECT PROPORTION
If two quantities vary but remain in the same ratio, they are said to be in direct proportion. They increase or decrease at the same rate. Thus if one quantity is doubled, then the other is doubled too. If one quantity is halved, then the other is halved too and so on....To solve some direct proportion problems you may have to find the 'amount' for 1 unit of a quantity first. This is sometimes called the unitary method.
Examples
If a car uses 2 hours to consume 10 litres of petrol, how many litres of petrol is consumed in i) 5 hours ii) 30 minutes
Solution
i ) if 2 hrs = 10 litres
then 5 hrs = 5 hrs/ 2 hrs × 10 litres = 25 litres
ii ) the 30 minutes must be changed to hours i.e 30/60 hrs = 1/2 hrs
If 2 hrs = 10 litres
then 1/2 hrs = 1/2/2 × 10 litres
= 10/4 litres = 2.5 litres
ASSIGNMENT
Three boys can weed a pier o land in 4 hours. How long would it take 18 boys to weed the piece o land, if they weed at the same rate?
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