Percentages • Topic 1 of 5

Percent Basics & Conversions

Percent means "per hundred", so x% = x/100. The fastest GRE test-takers never compute the slow way — they know the fraction–percent table cold (1/2 = 50%, 1/3 ≈ 33.3%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.7%, 1/8 = 12.5%, 1/10 = 10%, 1/20 = 5%) and read questions in fractions. "37.5% of 64" is just (3/8) × 64 = 24 in one step, no calculator needed. To find what percent one quantity is of another, divide and multiply by 100. Converting a decimal to a percent shifts the point two places right (0.45 → 45%); a percent to a decimal shifts it two places left (7% → 0.07). Watch units: a "percent of a percent" and a "percentage-point" difference are not the same thing — going from 5% to 7% is a 2 percentage-point rise but a 40% relative increase.

✅ Solved examples

1. Find 62.5% of 240.
62.5% = 5/8. (5/8) × 240 = 5 × 30 = 150.
2. What percent of 1.5 kg is 90 g?
1.5 kg = 1500 g. (90/1500) × 100 = 6%.
3. Convert 7/40 to a percent.
(7/40) × 100 = 700/40 = 17.5%.
4. A tax rate rises from 5% to 6%. By what percent did the rate increase?
This is a change of 1 on a base of 5: (1/5) × 100 = 20% (a 1 percentage-point, but 20% relative, rise).

✏️ Practice — try these, take hints as needed

1. Find 87.5% of 96.
87.5% = 7/8.
(7/8) × 96.
7 × 12.
84
2. What percent of 2 hours is 24 minutes?
Use the same unit.
2 h = 120 min.
(24/120) × 100.
20%
3. Express 0.375 as a percent and as a fraction.
Decimal → percent: shift two places.
0.375 = 37.5%.
= 3/8.
37.5% = 3/8
4. A score of 45 out of 60 is what percent?
(45/60) × 100.
45/60 = 3/4.
3/4 = 75%.
75%
5. An unemployment rate goes from 4% to 5%. Percentage-point rise, and percent (relative) rise?
Point rise = 5 − 4.
Relative = change / base.
(1/4) × 100.
1 point; 25% relative

📝 Topic test — 8 questions

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