Rule of three calculator
Solve proportions in a second: if A corresponds to B, what corresponds to C? Available in direct form (more, more) and inverse form (more, less).
Direct: more A, more B (price per unit, recipe ingredients…).
X = B × C ÷ A
Direct proportion: when everything grows together
The rule of three solves a very specific kind of problem: you know three related figures and you're after the fourth. It's direct when the two quantities grow together. If 3 kg of oranges cost £4.50, how much do 5 kg cost? More kilos, more money: you cross-multiply, 5 × 4.50 ÷ 3 = £7.50. The pattern is always "if A is to B, then C is to X", with X = C × B ÷ A.
Inverse proportion: when one goes up and the other goes down
Some relationships work the other way: one quantity rises while the other falls, and there the maths changes. The classic example: if 4 workers take 6 days to build a wall, how long do 8 workers take? More workers, fewer days. Here you don't cross-multiply, you multiply straight across: 4 × 6 ÷ 8 = 3 days. Confusing direct with inverse is the number-one error, so before calculating it's worth asking: if this goes up, does the other go up or down?
Where you use it without realising
The rule of three sits behind countless everyday sums: scaling a recipe up for more guests, working out how much paint you need for a bigger wall, turning a map scale into real distances, splitting a cost in proportion or finding a percentage (a percentage is nothing more than a rule of three out of 100). It's probably the most useful piece of everyday maths there is.
A trick to avoid mistakes
Always put figures of the same kind in the same column (kilos with kilos, pounds with pounds) and check the answer makes sense: if you asked for more and a direct rule gives you a smaller number, you've crossed something over. That final sanity check catches most errors.