How to Find a Percentage
Percentage questions come in exactly three shapes, and confusing them is where the marks go. Once you can name which of the three you are looking at, each one is a single line of arithmetic.
The three shapes
- Percent of a number: what is 15% of 240? Multiply by the decimal.
- One number as a percent of another: 18 is what percent of 45? Divide, then multiply by 100.
- Percentage change: it went from 80 to 92, by what percent did it rise? Divide the change by the original.
Turning a percent into a decimal
Percent means per hundred, so 15% is 15/100 = 0.15. Move the decimal point two places left. This is the step that makes the first shape a single multiplication.
The original always goes on the bottom
For percentage change, the denominator is where you started, not where you ended. A rise from 80 to 92 is a 15% rise, but a fall from 92 back to 80 is a 13.04% fall. The same gap, different percentages, because the starting point changed.
Worked examples
Example 1
Question
What is 15% of 240?
Answer
36
Steps
- 1Convert the percent to a decimal: 15% = 0.15.
- 2Multiply: 0.15 x 240.
- 30.15 x 240 = 36.
- 4Mental check: 10% of 240 is 24, and 5% is half of that, 12. 24 + 12 = 36.
The 10% plus 5% trick works without a calculator for any multiple of 5 percent.
Example 2
Question
18 is what percent of 45?
Answer
40%
Steps
- 1Divide the part by the whole: 18 / 45.
- 218 / 45 = 0.4.
- 3Multiply by 100 to make it a percent: 40%.
- 4Check: 40% of 45 is 0.4 x 45 = 18. Correct.
Example 3
Question
A price rises from 80 to 92. What is the percentage increase?
Answer
15%
Steps
- 1Find the change: 92 - 80 = 12.
- 2Divide by the original value, not the new one: 12 / 80.
- 312 / 80 = 0.15.
- 4Multiply by 100: a 15% increase.
Dividing by 92 instead of 80 gives 13.04%, which is the answer to a different question: what percent of the new price the rise represents.
Common mistakes
Multiplying by 15 instead of 0.15 and getting 3600.
Convert to a decimal first. If the answer is wildly bigger than the original, you skipped this step.
Using the new value as the denominator in percentage change.
The original value always goes on the bottom. Change over original, every time.
Assuming a 20% fall undoes a 20% rise.
It does not. 100 rises to 120, then a 20% fall takes it to 96, because the second percentage is of a bigger number.
Adding percentages of different totals, like 30% of one group and 40% of another.
Percentages of different bases cannot be added. Convert both to actual counts first.
Practice it
Work these out first, then open the answer. Stuck halfway? Select the problem and ask Solvecoon for the step you are missing.
1. What is 12% of 350?
Show answer
42. Multiply 0.12 x 350.
2. 27 is what percent of 60?
Show answer
45%. Divide 27 / 60 = 0.45, then multiply by 100.
3. A price falls from 50 to 38. What is the percentage decrease?
Show answer
24%. The change is 12, and 12 / 50 = 0.24.
Questions people ask
- How do I find a percentage without a calculator?
- Build it from 10%, which is just moving the decimal one place. 5% is half of that, 1% is a tenth of it, and most percentages are a short sum of those pieces.
- What is the difference between percent and percentage points?
- Going from 5% to 7% is a rise of 2 percentage points, but a 40% increase. News stories mix these up constantly, and exams test the difference.
- How do I reverse a percentage?
- If a price after a 20% rise is 120, divide by 1.2 to get back to 100. Subtracting 20% instead gives 96, which is wrong.
- Is percentage change ever negative?
- Yes, and that is exactly what a decrease is. Keep the sign rather than describing it in words if the question asks for a value.
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