Percents

"Per cent" literally means per hundred. So $\frac{\text{part}}{\text{whole}}$ and $\frac{\text{percent}}{100}$ are two names for the same ratio:

$\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}$

Every percent problem just hides one of those three pieces. Find the part ("what is $30\%$ of $60$?"), the percent ("$12$ is what percent of $48$?"), or the whole ("$20\%$ of what is $30$?") — it's the same proportion each time, solved by the cross-multiplication you already know.

Finding the part. $30\%$ of $60$: that's $\frac{30}{100} \times 60$.

$\frac{30}{100} \times 60 = 0.30 \times 60 = 18$

Finding the percent. Is $12$ what percent of $48$? Put it over the whole and scale to $100$:

$\frac{12}{48} = \frac{1}{4} = \frac{25}{100} = 25\%$

Everyday percents are the same setup. A $80 jacket at $25\%$ off: the discount is $25\%$ of 80 = \20$, so the sale price is$80 - 20 = $60$. Tax and tips work the same way — find the percent of the amount, then add it on.

For a discount, find the percent of the price first, then subtract. Predict before you check.