1. What is Proportion?
Proportion is a relationship between two quantities such that a change in one quantity relates to change in another quantity.
1.1 Direct Proportions:
Two variables are said to be directly proportional to each other if increment of one quantity leads to increment in the second quantity similarly decrement of one quantity leads to decrement in the second quantity.
Represented as X ∝ Y, read as ‘X is directly proportional to Y’
X = k X, where k is proportionality constant.
For Example
Ciara put a 2p coin in her piggy bank daily so she will have 14p in her piggy bank by the week. Here the amount of savings is directly proportional to the number of days.
Golden rule to solve direct proportions: Divide for One then Times for All
Example:
If Mr. John earns £160 per day working 8 hours a day, How much will he earn by working 30 hours?
1.2 Indirect Proportions:
When two quantities are related to each other in a way that increment in one quantity leads to decrement in another quantity and vice versa, we say they are inversely proportional.
Represented as X ∝ 1⁄y, read as ‘X is indirectly proportional to Y’.
X =k 1⁄y, where k is proportionality constant.
For Example:
Gia takes 30 minutes to reach school from her home on bicycle. If she doubles her speed she would reach school in 15 minutes. Here we can see the speed is inversely proportional to the time taken to complete the journey.
Golden Rule to solve indirect proportions: Times for One then Divide for All
Example:
5 workers take 3 days to paint a wall. How long will only one worker take to paint the same wall?
