Percent of a number, percentage change, and part of a whole.
| Task | Working | Answer |
|---|---|---|
| 15% of 200 | 200 × 0.15 | 30 |
| 30 out of 120 | 30 ÷ 120 × 100 | 25% |
| 80 rises to 100 | 20 ÷ 80 × 100 | +25% |
| Add 18% | 500 × 1.18 | 590 |
| Remove 18% | 590 ÷ 1.18 | 500 |
Multiply 200 by 0.15, which gives 30.
The second percentage applies to a smaller base. $100 losing 50% leaves $50; a 50% gain on $50 returns only $75. You need a 100% gain to recover a 50% loss.
Divide by 1 plus the rate. To strip 20% from $120: 120 ÷ 1.20 = $100. Subtracting 20% gives $96, which is wrong.
A percentage point is the plain arithmetic gap between two percentages; a percentage change is relative. A rate moving from 4% to 6% is a 2 percentage point rise, but a 50% increase — since 2 is half of 4.
Divide by 100 — 45% becomes 0.45, 8% becomes 0.08. To go back, multiply the decimal by 100 and add a percent sign.
Yes — it just means the amount exceeds the original whole. $150 is 150% of $100. That’s normal for growth, markups and price comparisons; it only breaks down for things that must sum to a fixed total, like a pie chart.