Relation of a part to the whole (usually expressed as a fraction or percentage). In mathematics two variable quantities x and y are proportional if, for all values of x, y = kx, where k is a constant. This means that if x increases, y increases in a linear fashion.
Direct proportion If A and B are in direct proportion, then as one grows bigger the other also grows bigger by the same proportion (or ratio). For example, if B doubles then A doubles. This can be written as A ∝ B or A = kB (where k is a constant multiplier). For example, when costing a number of pens:
For every extra pen bought, the cost goes up by the same amount (30p). So the cost of the pens will be proportional to the number bought.
If A is proportional to B there are two things that are true:
the multiplier rule – if A is multiplied by a value then B must be multiplied by the same value.
the graph of A against B is always a straight line through (0,0) and the gradient of the graph is the same as the ratio of A:B.
Inverse proportion If A is inversely proportional to B, then as B gets bigger A gets smaller by the same factor. For example, if B is increased by a factor of 2 (B doubles) then A decreases by a factor of 2 (A is halved). This can be written as:
A ∝ 1/B or A = k/B
For example, a group of people want to hire a minibus at a charge of £60 a day. If only 1 person uses the minibus it will cost them £60, for 2 people the cost will be £30 each, and for 3 people the cost will be £20 each. A table and graph showing the number of people and cost can be completed:
cost per person ∝ 1/peoplecost per person = k/people
k = the hire of the bus (£60), so cost per person = 60/people
The shape of the graph is typical of an inversely proportional relationship.
Many laws of science relate quantities that are proportional (for example, Boyle's law).
Calculating with proportion
Proportional Representation – Using Proportion in Paper Sizes
The Hole in the Ground – Using Inverse Proportion
Maths for Morons Like Us
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