Why Percentages Don't Always Add Up

Fractions, decimals and percentages are just three ways of describing the same idea—a part of a whole. Yet in everyday life, we treat them like totally different beasts. Take sales: two 50% discounts often leave you paying more than zero dollars. Why? In this post, we’ll explore how these number forms connect, where they came from, and a common trap that catches many shoppers (and students) off guard.

Where did this come from?

The word "percent" comes from the Latin per centum, meaning "by the hundred." Italian merchants in the 15th century used per cento in their ledgers when calculating taxes and interest. Before that, Ancient Greeks like Euclid studied fractions—especially unit fractions like 1/2 or 1/3—in geometry and measurement, laying the groundwork for all the ways we slice up a whole.

Where you'll see this in real life

In retail sales, if you take 50% off then another 20% off, you don’t get 70% off total—you pay 50% of the price, then 20% of that reduced price. Compound interest in bank accounts or loans relies on percentages applied to growing (or shrinking) balances. Recipes often ask you to increase or decrease ingredient amounts by a percentage to feed more or fewer people. Economists report inflation and population growth as yearly percentage changes.

A common misconception

Many people think that percentage changes can be added directly—20% increase plus 10% increase equals 30% total—but that only works when each change starts from the original whole. In reality, a 20% boost followed by a 10% boost applies the second percentage to an already larger number, giving you 32% overall. The key is remembering that each percentage is a fraction of whatever you have at that moment, not always the original amount.