Percentage Word Problems: A Method That Always Works
Most people who say they "can't do percentages" can actually do the arithmetic perfectly well. What trips them up is translation: deciding which number in a sentence is the part, which is the whole, and which is the rate. This guide gives you a four-step method that handles every standard percentage question type, then twelve graded practice problems — with solutions you reveal only when you want them.
Label three slots: part, whole and rate, then fit them into Part = Rate × Whole. The word "of" almost always points at the whole; "is" points at the part. Whichever slot is missing is what you solve for — divide when the part or the whole is missing, multiply when the part is.
The four-step method
- Underline the three numbers (one may be missing — that is your unknown).
- Label them: rate is the one with a % sign; whole is the number after "of"; part is what remains.
- Write Part = Rate × Whole with the decimal form of the rate (18% → 0.18).
- Solve, then sanity-check: a rate under 100% must give a part smaller than the whole.
Word signals to look for
| Phrase in the question | What it marks |
|---|---|
| "…% of 240" | 240 is the whole |
| "…is 45" | 45 is the part |
| "out of", "per" | The number after it is the whole |
| "increased to", "after" | A reverse-percentage problem |
| "by how much more" | Percentage change, not percentage of |
The five question types
- Find the part — "What is 22% of 350?" → 0.22 × 350.
- Find the rate — "45 out of 60 is what percent?" → 45 ÷ 60 × 100. Use the What Percentage Calculator.
- Find the whole — "18 is 12% of what?" → 18 ÷ 0.12.
- Find the change — "Price went from 40 to 52" → (52 − 40) ÷ 40 × 100.
- Undo a change — "Costs $69 after 25% off" → 69 ÷ 0.75. See Reverse Percentage.
Practice: foundation
1. A class of 25 students has 15 girls. What percentage are girls?
2. A phone costs $480. Sales tax is 8%. How much tax?
3. Maya scored 34 out of 40. What percent is that?
4. 30% of a 2.5-litre bottle has been drunk. How much is left?
Practice: intermediate
5. A rent of $1,150 rises by 6%. What is the new rent?
6. 42 is 15% of what number?
7. Site visits fell from 8,400 to 7,140. What is the percentage decrease?
8. A bill is $86 and you leave a $15.48 tip. What tip percentage is that?
Practice: challenge
9. A laptop costs $918 including 8% sales tax. What was the pre-tax price?
10. A salary rises 4% one year and 3% the next. Total increase?
11. A jacket is reduced 20%, then a further 25% at the till, ending at $102. Original price?
12. A town's unemployment rate moves from 8% to 6%. Describe the change two ways.
The four common errors
- Dividing by the wrong number. Percentage change always divides by the original value, never the new one.
- Adding a percentage back to undo it. Adding 25% to a price that had 25% removed does not return the original — divide instead.
- Adding successive percentages. Two changes multiply: +4% then +3% is +7.12%.
- Confusing points with percent. A rate moving 8% → 6% is 2 points and 25%; see Percent vs Percentage.
Need the formulas behind each type? See The Percentage Formula. Want more drilling? Work through 50 Percentage Examples or speed up with mental-math tricks.
Sources and method: problem types follow standard curriculum coverage of percentages at lower and upper secondary level. Written and reviewed by The Snap PercentCalc Team; every solution was cross-checked against the site's calculators.
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