The rule of three is a fundamental mathematical concept used to solve proportion problems. It's one of the most practical mathematical tools you'll use in everyday life, from cooking and shopping to business calculations and scientific applications.

What is the Rule of Three?

The rule of three helps you find an unknown value when you know three related values. It's based on the principle that if two ratios are equal, you can find the missing value through cross multiplication.

Types of Rule of Three

Simple Direct Rule of Three: When quantities increase or decrease proportionally
Simple Inverse Rule of Three: When one quantity increases as the other decreases
Compound Rule of Three: Involving more than three quantities

Real-World Applications

Cooking: Scaling recipes up or down
Shopping: Comparing unit prices and bulk discounts
Currency Exchange: Converting between different currencies
Speed and Distance: Calculating travel times
Business: Calculating costs, profits, and productivity
Construction: Scaling blueprints and material calculations

Step-by-Step Solution Method

Identify the three known values and the unknown value
Set up the proportion: A : B = C : X
Cross multiply: A × X = B × C
Solve for X: X = (B × C) ÷ A
Check your answer by substituting back into the original proportion

Common Examples

Example 1 - Recipe Scaling:
If 2 cups of flour make 12 cookies, how much flour is needed for 18 cookies?
Solution: 2 : 12 = X : 18 → X = (2 × 18) ÷ 12 = 3 cups

Example 2 - Unit Price:
If 3 items cost $15, how much do 7 items cost?
Solution: 3 : $15 = 7 : X → X = ($15 × 7) ÷ 3 = $35

Example 3 - Time and Work:
If 4 workers complete a job in 6 hours, how long will it take 3 workers?
Solution: 4 workers : 6 hours = 3 workers : X → X = (4 × 6) ÷ 3 = 8 hours

Tips for Success

Always check that your units are consistent
Make sure the ratios make logical sense
Double-check your calculation by working backwards
Practice with real-world scenarios to build intuition

Rule of Three Calculator

Proportion Formula