In more detail
Three questions cover almost every case: the part (15% of 80 is 0.15 × 80 = 12), the rate (18 is 18 / 72 = 25% of 72) and the whole (if 12 is 15%, the whole is 12 / 0.15 = 80). Percent change is (new − old) / old × 100, measured against the starting value: 80 to 100 is a 25% increase, while 100 back to 80 is a 20% decrease. See the Percentage Formulas Cheat Sheet.
Why it matters
Percentages of percentages mislead. A rate rising from 4% to 5% has gone up 1 percentage point but 25% in relative terms, and headlines often mix the two. Successive changes multiply rather than add: +10% followed by −10% leaves 1.1 × 0.9 = 0.99, a 1% loss. Removing a percentage means dividing, not subtracting: a price of 120 that includes 20% tax was 120 / 1.2 = 100 before tax, not 120 × 0.8 = 96.
Example
15% of 80 0.15 × 80 = 12
18 as a % of 72 18 / 72 × 100 = 25%
80 → 100 20 / 80 × 100 = +25%
100 → 80 −20 / 100 × 100 = −20%
+10% then −10% 1.10 × 0.90 = 0.99 (−1%)
120 including 20% tax 120 / 1.20 = 100