Complete course on the rule of three

Direct, inverse, tables, cross product method, traps and quizzes.

5chapters0%progression

1) Understanding the rule of three

Proportionality and finding a missing value.

direct

inverse

units

When to use it?

We use it when two quantities are proportional (directly or inversely).
We know 3 values and are looking for the 4th (missing value).
Before calculating, put all values in consistent units.

Quick test

Direct: if A doubles, B doubles (constant ratio).
Inverse: if A doubles, B is divided by 2 (constant product).

Mini-quiz

The rule of three is suitable if:

Use case

Solve an exercise '3 known values, 1 unknown'Put the values in a table and quickly find the 4th value (direct or inverse).
Calculate a price, a quantity, or a dosagePrice per kilo, recipe for more/less people, dilution, dosage, consumption... with consistent units.
Understand and verify a proportionalityKnow how to test if it is indeed proportional (constant ratio) or if it is the inverse (constant product) before calculating.
Use a proportionality tableFind the coefficient k, complete a table, and check the consistency of the results.
Revise for a test/examRemember the methods (unit conversion, cross multiplication), useful formulas, and classic pitfalls.
Practice with corrected quizzesMCQs and numerical exercises to automate the right reflex (direct vs inverse + units).

What you get

A clear and progressive course: definition of proportionality, quick test (direct/inverse), then step-by-step calculation methods.

The two main methods: unit conversion (intuitive) and cross multiplication (fast and standard), with tables and examples.

A chapter 'proportionality table' to easily complete via the coefficient k.

A section 'inverse proportionality' (constant product) with typical cases and mini-consistency tests.

Corrected quizzes to check that you know how to choose the right relationship, manage units, and apply the right formula.

Limits and points of attention

The rule of three only applies if there is proportionality (direct or inverse). If the relationship is not proportional, the result will be wrong even if the calculation is 'well done'.
Units must be consistent (minutes/hours, grams/kilos, €/kg...). An overlooked conversion is one of the number one causes of error.
Be careful with the direction (direct vs inverse): if you get the relationship wrong, you will get a 'possible' result but inconsistent with the logic of the problem.
With numbers that have many decimals, keep sufficient precision during the calculation (rounding too early can distort the final result).

Frequently asked questions

How to know if it is a direct or inverse proportionality?

Direct: if A increases, B increases (constant ratio). Inverse: if A increases, B decreases (constant product A×B). A mini-mental test before calculating avoids most errors.

Does cross multiplication always work?

Yes, if (and only if) the relationship is proportional and the table is correctly constructed (same quantities in the same column) with consistent units.

Which method to choose: unit conversion or cross multiplication?

Unit conversion is very intuitive when the numbers are simple. Cross multiplication is faster and standard (especially in tests), provided the values are placed correctly.

What to do if I don't have exactly '3 values and 1 unknown'?

You can often simplify: convert units, bring to an equivalent situation (per unit, per person...), or break down into several successive rules of three.

Tip

Before calculating, do the "sense check": if the starting quantity increases, should the result increase or decrease? If your calculation gives the opposite, you have reversed direct/inverse or filled out the table incorrectly.