A percentage expresses a quantity per hundred of a specified base. The calculation is usually simple once that base is clear. Many errors come from choosing the wrong reference amount rather than multiplying incorrectly.
Find a percentage of an amount
To find 15% of 240, calculate 0.15 × 240 = 36. You can check it mentally: 10% is 24 and 5% is 12, totaling 36.
Breaking a percentage into familiar pieces can be useful in timed reasoning. It also provides an independent check on the decimal calculation.
Work backward from a percentage
Suppose 18 is 30% of an unknown total. The equation is 0.30 × total = 18, so total = 18 ÷ 0.30 = 60.
Multiplying 18 by 30% would answer a different question: 30% of 18. When the percentage amount is already given, you need to recover the base.
Percentage points are different
A success rate rises from 40% to 50%. The increase is 10 percentage points. Relative to the original 40%, the percentage increase is 10 ÷ 40 = 25%.
Both descriptions are correct, but they use different units. Write the requested one explicitly so that a reader does not have to infer which comparison you mean.
Try a combined example
A class has 80 students. Sixty percent choose option A, and one-quarter of those students also choose option B. How many choose both?
First find the A group: 0.60 × 80 = 48. Then take one-quarter of that group: 48 ÷ 4 = 12. The second percentage or fraction applies to the subgroup, not directly to the full class.
A useful question before every calculation
Ask percent of what? State the answer in words, then calculate. This habit helps with surveys, discounts, domain accuracy and almost any numerical reasoning problem involving percentages.