The coefficient of proportionality and the cross-product

The coefficient of proportionality

In a table of proportionality, we move from one row to the next by multiplying by a fixed number: the coefficient of proportionality. If y = k × x, then k is this coefficient.

Example: a recipe for 4 people uses 200 g of flour. For 6 people, we work out the coefficient: 6/4 = 1.5. We therefore multiply 200 g by 1.5, giving 300 g of flour.

The cross-product

When we know three values from a table of proportions and one is missing, we use the cross-product.

People	4	6
Flour (g)	200	x

We write the ratio equation: 200/4 = x/6.

Cross-multiplication: x = (200 × 6) / 4 = 1200 / 4 = 300 g.

Pitfall to avoid

Do not confuse multiplicative reasoning (we multiply) with additive reasoning (we add). If 4 people = 200 g, this does not mean 6 people = 200 + 6 = 206 g! In a proportionality problem, you must always multiply by the coefficient; never add.

Tip for checking your answer: work out the coefficient both ways (200/4 = 50 and 300/6 = 50). If they are the same, your calculation is correct.