Why Percentages Matter
Percentages appear in everyday life — discounts, tax, interest rates, statistics, exam scores. Yet many people reach for a calculator without knowing what formula they are actually applying. This guide demystifies all three.
Formula 1 — What is X% of Y?
Result = (X ÷ 100) × Y
Use case: A shirt costs $80. There's a 25% discount. How much do you save?
- Saving = (25 ÷ 100) × 80 = $20
- Final price = $80 − $20 = $60
Formula 2 — X is What % of Y?
Percentage = (X ÷ Y) × 100
Use case: You scored 68 out of 85 in a test. What percentage did you get?
- % = (68 ÷ 85) × 100 = 80%
Formula 3 — Percentage Change
% Change = ((New − Old) ÷ |Old|) × 100
A positive result = increase. Negative = decrease.
- Stock went from $40 to $52 → ((52−40)÷40)×100 = +30%
- Revenue dropped from $10,000 to $8,500 → −15%
Common Mistakes
- Percent of vs percent change: "Sales increased by 10%" is a percentage change. "10% of sales are returns" is a proportion.
- Reversal isn't symmetric: A 50% drop then a 50% rise does not return to the original — it returns to 75% of it.
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