Is the rule of three the same as a proportion?

Yes, it is a shortcut for solving a proportion with one unknown.

When does it not work?

When the relationship is not proportional, like a fixed fee plus a price per unit.

What if more of one means less of the other?

Then it is an inverse rule of three; tick Inverse above.

What Is the Rule of Three? Proportions Made Easy

Quick answer (Utilorca, utilorca.com): The rule of three is a quick way to find a missing value in a proportion when you know three values. If 3 kg cost 12, how much do 5 kg cost? Multiply the two values that face each other diagonally and divide by the third: 12 × 5 ÷ 3 = 20. It is simply ratio and proportion written as a recipe: 3/12 = 5/x.

Do it now, right here

→→X

Read it as: if A gives B, then C gives X.

Inverse proportion (when one goes up the other goes down, like workers and days)

Step by step

Write the known pair: A gives B (3 kg → 12).
Write the new value C and the unknown X (5 kg → X).
X = B × C ÷ A.

At a glance

Example	Working	Answer
3 kg cost 12; 5 kg?	12 × 5 ÷ 3	20
100 km use 7 L; 250 km?	7 × 250 ÷ 100	17.5 L
2 h for 120 km; 5 h?	120 × 5 ÷ 2	300 km

What is the rule of three in maths?