direct proportion

In mathematics, term used to describe quantities that increase in the same ratio. For example, if 5 kg of potatoes cost £1.35, the cost of 12 kg of the potatoes will be in direct proportion to the quantities bought. The ratio of the quantities = 12:5, so the ratio of the prices = 12:5. The cost of 12 kg, therefore, is 12 ÷ 5 × £1.35 = £3.24.

The symbol ∝ is read as ‘is proportional to’. For example, the statement ‘price is proportional to quantity’ could be written as p ∝ q, where p stands for price and q stands for quantity.

a ∝ b means a = kb where k is a positive number describing the relationship between a and b. If one pair of values for a and b is known, k can be found.

For example, y is proportional to x and when x is 20, y is 30. Since y ∝ x, then

y = kx and 30 = k × 20; therefore, k = 30 ÷ 20 = 1.5

The relationship between x and y is, therefore, y = 1.5x.