Proportions made practical
The rule of three lets you solve proportional relationships when three values are known and the fourth is missing, a staple in finance, cooking, and engineering.
Direct vs. inverse proportion
Direct proportion scales both quantities in the same direction (double one, double the other).
Inverse proportion moves in opposite directions (double one, halve the other).
Historical context
Merchants in ancient civilizations used proportional reasoning to price goods and exchange currencies.
The method became formalized in arithmetic textbooks, earning the nickname ‘rule of three’ because it always starts with three values.
Common pitfalls
Mixing units (minutes vs. hours) breaks proportionality before you even calculate.
Confusing direct and inverse relationships leads to inverted answers, so check the scenario first.
Where you will use it
- Estimating ingredient amounts when scaling recipes
- Converting currency based on exchange rates
- Calculating dosage adjustments in healthcare
- Projecting cost or time when work scales linearly
Tips for accurate setups
- Align units before plugging values into the proportion
- Write the relationship as fractions (known ratio = unknown ratio) to keep direction clear
- Annotate which variables stay constant when moving from direct to inverse problems
- Double-check results by plugging back into the original relationship