Working Through Real Percentage Problems Step by Step
Most everyday percentage problems fall into one of three types — finding a percentage of a number, finding what percent one number is of another, or finding percentage change — and matching the problem to the right formula, rather than guessing, is what actually prevents mistakes.
Seeing each percentage type applied to a real, concrete problem makes it much easier to recognize which formula a new problem actually needs.
Problem 1: a discount (percentage of a number)
A $85 jacket is 30% off — what's the discount amount, and the final price? (30 ÷ 100) × 85 = $25.50 discount, so the final price is 85 − 25.50 = $59.50. This is a straight "percentage of a number" problem, formula: (percentage ÷ 100) × number.
Problem 2: a test score (what percent is one number of another)
Scoring 42 out of 50 on a test — what percentage is that? 42 ÷ 50 × 100 = 84%. This is a "what percent is X of Y" problem, formula: (part ÷ whole) × 100 — note the part (42) is divided by the whole (50), not the other way around.
Problem 3: a price increase (percentage change)
A subscription went from $12/month to $15/month — what's the percentage increase? (15 − 12) ÷ 12 × 100 = 25%. This is a percentage-change problem, formula: ((new − old) ÷ old) × 100 — critically dividing by the original $12, not the new $15.