Percent as a Proportion

A percent is a ratio out of 100: per cent means per hundred. So the question what percent of 30 is 18? is a proportion with a missing number: $\frac{n}{100} = \frac{18}{30}$, where n is the percent.

30 does not turn into 100 by multiplying by a whole number, so simplify first. $\frac{18}{30}$ divides by 6 to give $\frac{3}{5}$. Now 5 times 20 is 100, so scale the top by 20 as well: 3 times 20 is 60. 18 is 60 percent of 30.

Why is simplifying allowed? $\frac{18}{30}$ and $\frac{3}{5}$ are the same ratio, so they share the same percent. Simplify until the bottom is a number that divides 100 (2, 4, 5, 10, 20, 25 and 50 do), then use the scale factor exactly as in any proportion. When no simplifying gets there, as with $\frac{1}{3}$, divide the top by the bottom and multiply by 100 instead.