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Percentages for the PSAT/NMSQT: Complete Study Guide + Free Practice Problems
Everything the PSAT/NMSQT tests about percentages in one place: converting between percents, decimals, and fractions, finding a percent of a number, percent increase and decrease, reverse percentage problems, and successive percent changes — with step-by-step examples, worked problems, and 2 free practice quizzes.
Practice these quizzes
Free · No signupWhat is a percentage?
A percentage is a way of expressing a number as a fraction of 100. "40%" literally means 40 out of every 100. Percentages let you compare quantities on a common scale, even when the totals they're drawn from are completely different sizes.
Percentages show up across nearly every PSAT topic, not just as standalone questions — they're embedded inside data analysis, word problems, and even geometry. Getting comfortable converting quickly between forms pays off across the whole test.
Percent, decimal & fraction conversions
| Convert | Method | Example |
|---|---|---|
| Percent → decimal | Divide by 100 (move decimal 2 places left) | 40% = 0.40 |
| Decimal → percent | Multiply by 100 (move decimal 2 places right) | 0.09 = 9% |
| Percent → fraction | Put over 100, then simplify | 60% = 60/100 = 3/5 |
| Fraction → percent | Divide numerator by denominator, multiply by 100 | 5/8 = 0.625 = 62.5% |
A common decimal-point slip: multiplying by 0.40 when the problem meant 40%, versus multiplying by 40 when it meant 0.40. Always double-check which form you're plugging into a calculation.
Finding a percentage of a number
What is 24% of 350?
Percent increase & decrease
A backpack originally costs $50. The price increases by 12%. What is the new price?
Using a single growth or decay factor (1.12 or 0.88) is faster and less error-prone than calculating the percent amount separately and then adding or subtracting it in a second step.
Reverse percentage problems
A reverse percentage problem gives you the result after a percent change and asks for the original value.
After a 25% discount, a jacket costs $60. What was the original price?
Do not simply add 25% of $60 back to $60 to "undo" the discount — that finds 25% of the wrong (discounted) base. Divide by the decay factor instead, since the discount was applied to the unknown original price.
Successive percent changes
When a quantity changes by one percentage, then changes again by a different percentage, the two changes do not combine by simple addition. Each change applies to the new value left over from the previous step.
A ticket price increases by 20%, then decreases by 10%. What is the overall percent change from the original price?
A 20% increase followed by a 10% decrease does not equal a flat 10% increase — always multiply the successive growth/decay factors together rather than adding or subtracting the percentages directly.
Common PSAT traps
- Percent of the wrong base: always check what the percentage is "of" — the original amount or the new amount.
- Adding percentages instead of multiplying factors: successive percent changes require multiplying growth/decay factors.
- Percentage points vs. percent change: going from 20% to 25% is a 5 percentage point increase, but a 25% relative increase in the rate itself.
- Forgetting to convert before calculating: plugging a percent directly into a formula meant for a decimal produces answers off by a factor of 100.
Test day strategy for percentages
| Question signal | Fastest approach |
|---|---|
| "What percent of ___ is ___" | Set up part/whole = percent/100, or divide directly |
| "Increased/decreased by ___%" | Multiply by a single growth or decay factor (1 ± rate) |
| Given the result, asked for the original | Divide by the growth/decay factor — don't just add/subtract the percent |
| Two or more percent changes in sequence | Multiply each factor together in order; never add the percentages |
| "Percentage points" language | Treat as a straight subtraction of the two percentages, not a percent change |
Now put it to work
Two quiz sets, each building on the last — start with Quiz 1 and work through in order, or jump straight to the topic you need.
Percentages 1
Conversions, finding a percent of a number, percent increase/decrease.
Start quiz → Quiz 2Percentages 2
Reverse percentage problems and successive percent changes.
Start quiz →