What is a proportional situation?

Two quantities that vary together

Two quantities are said to be proportional when converting from one to the other always involves multiplying by the same number, known as the coefficient of proportionality.

Example: at the market, 1 kg of apples costs 2 euros. The price is proportional to the mass purchased.

Mass (kg)	1	2	3	5
Price (euros)	2	4	6	10

We always multiply the mass by 2 to obtain the price: 1 × 2 = 2, 2 × 2 = 4, 3 × 2 = 6, 5 × 2 = 10. The coefficient of proportionality is therefore 2.

How do you check that a table is proportional?

You calculate the quotients (ratios) column by column: price / mass. If they are all equal, the table is proportional.

2/1 = 2, 4/2 = 2, 6/3 = 2, 10/5 = 2 -> they are all equal, so it is indeed proportional.

A common pitfall

Note: not all situations where two quantities increase together are proportional! For example, a child’s age and height both increase, but one cannot be converted into the other by a constant multiplication. Similarly, a pricing structure with a fixed fee (for example, 5 euros + 1 euro per entry) is not proportional, because for a quantity of zero, the price would not be zero.

A simple rule to remember: in a proportional relationship, if the initial value is 0, the final value is also 0.