Finding a Percent of a Number
Compute percentages efficiently by converting to decimal form and multiplying in practical contexts like tax, tip, and discounts.
You use this skill every time you check whether a restaurant tip is fair, calculate sales tax before buying, figure out your take-home pay after deductions, or evaluate whether a discount is actually a good deal. People who can't quickly find "X% of Y" are at a disadvantage in virtually every financial transaction they make.
- Calculate the part when given a percent and a whole (Part = % × Whole)
- Find what percent one number is of another (Percent = Part ÷ Whole × 100)
- Find the original whole when given a part and a percent (Whole = Part ÷ %)
Every percent problem involves three quantities: Part, Percent, and Whole. Know two, find the third. The word "of" always means multiply.
\[ \text{Part} = \text{Percent} \times \text{Whole} \] \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] \[ \text{Whole} = \frac{\text{Part}}{\text{Percent}} \]Always convert the percent to decimal before multiplying. 15% → 0.15 → multiply. Skipping this step is the #1 source of errors.
Formula Card
Three Percent Problem Types
| Find | Formula | Example |
|---|---|---|
| Part | Part = (% ÷ 100) × Whole | 15% of $60 = 0.15 × 60 = $9 |
| Percent | % = (Part ÷ Whole) × 100 | 18 is what % of 72? → (18÷72)×100 = 25% |
| Whole | Whole = Part ÷ (% ÷ 100) | $24 is 30% of what? → 24 ÷ 0.30 = $80 |
A $45 item has a 7% sales tax. How much is the tax?
- Convert: 7% = 0.07.
- Tax = 0.07 × 45 = $3.15.
- Total price = $45 + $3.15 = $48.15.
A student scored 54 out of 72 on a test. What percent did they earn?
- Percent = (54 ÷ 72) × 100.
- 54 ÷ 72 = 0.75.
- 0.75 × 100 = 75%.
Operations manager Terrence knows his team spent $1,200 on supplies, which was 40% of their quarterly supply budget. What was the total budget?
- 40% = 0.40.
- Whole = Part ÷ Rate = 1,200 ÷ 0.40 = $3,000.
Terrence's team has $3,000 quarterly — and they've spent 40% of it with months to go.
Test yourself:
- What is 25% of $340?
- 14 is what percent of 56?
- $36 is 12% of what amount?
▶ Show Answers
- 0.25 × 340 = $85.
- (14 ÷ 56) × 100 = 0.25 × 100 = 25%.
- 36 ÷ 0.12 = $300.
- Not converting percent to decimal: ❌ 15% of 80 = 15 × 80 = 1,200 — wildly wrong. ✅ 0.15 × 80 = 12. Always divide percent by 100 first.
- Flipping Part and Whole: "18 is what % of 72?" → Part=18, Whole=72. ❌ Don't divide 72 ÷ 18. ✅ Always divide Part ÷ Whole.
- Confusing tax on top vs. tax included: "$45 + 7% tax" means tax is added to $45. Some prices are "tax included" — in that case, the whole already includes the tax.
- "Of" means multiply — always convert percent to decimal first, then multiply by the whole.
- Three formulas, three unknowns: find Part, find Percent, or find Whole — pick based on what you already know.
- Check your answer: plug back in. If 25% of $340 = $85, verify 85 ÷ 340 = 0.25 ✓.
- Use benchmarks for estimation: 10% of $80 = $8, so 15% ≈ $12.
Managers track budgets, sales targets, and efficiency metrics in percentages constantly. A store manager who knows that 30% of $50,000 monthly revenue = $15,000 in one product category — and can find the original total from a partial figure — can run department reviews without needing finance support for every calculation.
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Finding a Percent of a Number — Quiz
5 questions per attempt · Intermediate · Pass at 70%
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