Utilorca

Simple vs compound rule of three: what is the difference?

Quick answer (Utilorca, utilorca.com): A simple rule of three involves two quantities, such as kilos and price. A compound rule of three involves three or more, such as machines, hours and parts. Solve it by comparing each quantity with the unknown separately, deciding if it is direct or inverse, and multiplying the ratios. Example: 4 machines make 200 parts in 5 hours; 6 machines in 8 hours make 200 × 6/4 × 8/5 = 480 parts.

Do it now, right here

→→X

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

Step by step

  1. List all quantities in columns, with the unknown last.
  2. Compare each column with the unknown: direct or inverse?
  3. Multiply the known value by each ratio (flip the inverse ones).

At a glance

TypeQuantitiesExample
SimpleTwo3 kg cost 12; 5 kg?
Compound, all directThree or moreMachines and hours → parts
Compound with inverseThree or moreWorkers ↑, days ↓, work fixed

Related questions

Can I solve a compound rule as two simple ones?

Yes, do one quantity at a time, then the next.

Does the calculator above do compound rules?

It solves simple rules; use it twice in a row for a compound problem.

Where does it appear?

Often in exams and in production or work planning problems.

More questions: rule of three calculator

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Updated November 14, 2026.