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Three everyday percentage problems in one place: "20% of 200" for discounts and tips, "50 is what % of 200" for shares and grades, and "% change from 100 to 120" for growth, inflation and price moves.
X% of Y — multiply: 20% of 200 = 40. X is what % of Y — divide: 50 ÷ 200 = 25%. % change — (new − old) ÷ old: 100 → 120 is a 20% increase.
Percent change is asymmetric: up 50% then down 50% does not return to start (100 → 150 → 75). Always note what the percent is of.
Subtract old from new, divide by old, multiply by 100. 100 → 120 is (20/100) × 100 = 20%.
"% of" is a slice of a whole; "% change" compares two values over time. They answer different questions.
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