Solving Percent Problems
Learn how to find a percent of a number, find what percent one number is of another, and find the whole when you know a part and a percent.
Reading is good — doing is better. Practice Solving Percent Problems as an interactive lesson.
Try the lessonDefinition
A percent is a way of showing a part out of 100. Solving percent problems means figuring out the missing piece — the part, the percent, or the whole — when you know the other two pieces.
Remember the rule
Use the formula: Part = Percent × Whole. Rearrange it to find any missing piece: Percent = Part ÷ Whole, or Whole = Part ÷ Percent. Always convert the percent to a decimal first by dividing by 100.
Key words
- Percent
- A number out of 100. The word means 'per hundred.' The symbol is %.
- Part
- The piece or portion you are talking about — a smaller amount taken from the whole.
- Whole
- The total amount, or the full group you are comparing to.
- Rate
- The percent itself — the number with the % sign that tells you how big the part is compared to the whole.
- Proportion
- An equation that says two ratios (fractions) are equal to each other.
- Decimal
- A number written with a dot (like 0.25) that can be used instead of a fraction or percent in calculations.
- Is/Of
- In percent word problems, 'is' usually means equals (=) and 'of' usually means multiply (×).
- Equation
- A math sentence with an equals sign that shows two things have the same value.
Worked examples
What is 30% of 200?
→ Convert 30% to a decimal: 30 ÷ 100 = 0.30. Then multiply: 0.30 × 200 = 60. The answer is 60. · You are finding the Part, so use Part = Percent × Whole.
What percent of 50 is 12?
→ Use Percent = Part ÷ Whole. Divide: 12 ÷ 50 = 0.24. Convert to a percent: 0.24 × 100 = 24%. The answer is 24%. · Dividing the part by the whole always gives you the percent as a decimal first.
18 is 45% of what number?
→ Use Whole = Part ÷ Percent. Convert 45% to a decimal: 45 ÷ 100 = 0.45. Divide: 18 ÷ 0.45 = 40. The answer is 40. · You are finding the Whole, so divide the part by the decimal form of the percent.
A store has 80 apples. 15% are green. How many apples are green?
→ Part = 0.15 × 80 = 12. There are 12 green apples. · Real-life problems use the same formula — identify the part, percent, and whole first.
A student got 36 out of 40 questions correct. What percent did she get right?
→ Percent = 36 ÷ 40 = 0.90. Multiply by 100: 0.90 × 100 = 90%. She got 90% correct. · Divide the part (correct answers) by the whole (total questions) then multiply by 100.
A shirt costs $12, which is 20% of the original price. What was the original price?
→ Whole = Part ÷ Percent = 12 ÷ 0.20 = $60. The original price was $60. · When you know the part and the percent, divide to find the whole.
Common mistakes
- Forgetting to convert the percent to a decimal before multiplying — for example, using 30 instead of 0.30, which gives an answer 100 times too big.
- Mixing up the part and the whole — always ask yourself 'what is the total?' to identify the whole correctly.
- Dividing in the wrong order when finding a percent — you must divide the part BY the whole, not the whole by the part.
- Leaving the answer as a decimal when the question asks for a percent — remember to multiply by 100 and add the % symbol.
- Setting up the proportion or equation for the wrong unknown — read the problem carefully to decide if you are missing the part, the percent, or the whole.
FAQs
Do I always have to convert percent to a decimal?
Yes, when you multiply or divide. Divide the percent by 100 to get the decimal. For example, 75% becomes 0.75. You can also use a fraction like 75/100, but the decimal method is usually fastest.
How do I know which number is the 'whole' in a word problem?
The whole usually comes after the word 'of.' In '30% of 200,' the 200 is the whole. It is also the total or starting amount before any part is taken out.
Can I use a proportion to solve percent problems instead of the formula?
Yes! Set up: Part/Whole = Percent/100. Cross-multiply to solve. For example, to find 30% of 200: x/200 = 30/100, so x = 60. Both methods work — use whichever makes more sense to you.
What if the percent is more than 100?
That just means the part is bigger than the whole. For example, 150% of 40 = 0.150 × 40 = 60. The formula still works the same way.
Why do we multiply by 100 at the end when finding a percent?
Because percent means 'out of 100.' When you divide part by whole you get a decimal. Multiplying that decimal by 100 tells you how many out of 100 that equals, which is the percent.
How can I check my answer?
Plug your answer back into Part = Percent × Whole. If both sides of the equation match, your answer is correct. For example, if you found the part is 60: does 0.30 × 200 = 60? Yes, so 60 is right.
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