The rule
percentage = part ÷ total × 100
Why it works
A percentage is a fraction with 100 as the denominator. Dividing the part by the total gives the fraction; multiplying by 100 rewrites it in the form everyone reads without thinking.
How to do it by hand
- Divide the part by the total
- Multiply the result by 100
- The answer is the percentage
- Simplifying the fraction often shows the relationship more plainly
What is worth knowing
The word itself is the definition: per cent means per hundred, from the Latin. That is why 15 % and 15/100 and 0.15 are three ways of writing the same thing, and why converting between them is just moving a decimal point. The fraction form is often the more revealing one: 45 out of 300 simplifies to 3/20, which tells you at a glance that it is a bit under a fifth. Percentages became standard in commerce because they make different-sized quantities comparable, and that remains their whole purpose.