How to Solve Word Problems Involving the Percentage of a Number?

How to solve word problems involving the percentage of a number, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Free tool: try the problems from this lesson in our Percentage Calculator.

Finding the percentage of a number is one of the most practical math skills you can have. Whether you are calculating a tip at a restaurant, figuring out how much you save during a sale, or computing a tax amount, the process is always the same: convert the percent to a decimal and multiply. Let’s master it step by step.

What Does “Percentage of a Number” Mean?

When a problem says “find 40% of 75,” it is asking: if you take 40 out of every 100 equal parts of 75, what do you get? The formula is:

\(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\)

Convert the percent to a decimal first, then multiply by the whole.

How to Solve Percentage-of-a-Number Word Problems

Step 1, Identify the percent and the whole

Read the problem. Find the percent (the number with the % symbol) and the whole (the total or reference amount).

Step 2, Convert the percent to a decimal

Divide the percent by 100: \(\color{blue}{40\% \rightarrow 0.40}\).

Step 3, Multiply

\(\color{blue}{\text{ Part } = \text{ decimal } \times \text{ whole }}\)

Step 4, Interpret the result

Make sure the answer makes sense in context and attach the correct unit (dollars, pounds, students, etc.).

Step-by-Step Summary

1. Identify the percent and the whole number in the problem.
2. Convert percent to a decimal (divide by 100).
3. Multiply: \(\color{blue}{\text{ decimal } \times \text{ whole } = \text{ part }}\).
4. For discount problems: sale \(\color{blue}{\text{ price } = \text{ whole } – \text{ part }}\).
5. For increase problems: new \(\color{blue}{\text{ amount } = \text{ whole } + \text{ part }}\).

Watch: How to Find a Percent of a Number (Video Lesson)

Math with Mr. J demonstrates finding a percent of a number with clear examples:

Worked Examples

Example 1: Find 40% of 75.

Convert: \(\color{blue}{40\% = 0.40}\). Multiply: \(\color{blue}{0.40 \times 75 = 30}\).
Answer: 30

Example 2: A $120 jacket is on sale for 25% off. What is the sale price?

Discount: \(\color{blue}{0.25 \times 120 = $30}\). Sale price: \(\color{blue}{$120 – $30 = $90}\).
Answer: $90

Example 3: A restaurant bill is $60. You want to leave a 15% tip. How much is the tip?

Tip: \(\color{blue}{0.15 \times 60 = $9}\).
Answer: $9

Example 4: A school has 850 students. 60% ride the bus. How many students ride the bus?

Bus riders: \(\color{blue}{0.60 \times 850 = 510}\).
Answer: 510 students

More Practice: Math Antics, Finding A Percent Of A Number

Math Antics reinforces the same method with additional examples and a visual approach:

Exercises

1. Find 35% of 200.
2. A $80 pair of shoes is 20% off. What is the sale price?
3. A class has 40 students. 75% passed the exam. How many students passed?
4. Sales tax is 8% on a $55 item. What is the total cost including tax?
5. A 12% tip on a $45 dinner. How much is the tip?
6. Find 5% of 360.

Answers

1. \(\color{blue}{70}\)
2. \(\color{blue}{$64}\)
3. \(\color{blue}{30 \text{ students }}\)
4. \(\color{blue}{$59.40}\)
5. \(\color{blue}{$5.40}\)
6. \(\color{blue}{18}\)

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Frequently Asked Questions

How do you find the percent of a number?

Change the percent to a decimal by dividing by 100, then multiply by the number. To find 40% of 75, write 40% as 0.40 and multiply: 0.40 × 75 = 30. In a word problem, add the unit to your answer, such as 30 students or 30 dollars, and check that it makes sense.

What is the percent of a number formula?

The formula is Part = Percent × Whole, with the percent written as a decimal. If a jacket costs $60 and the sales tax is 8%, the tax is 0.08 × 60 = $4.80. You can rearrange the same formula to find the whole or the percent when one of those is the missing piece.

What is 10 percent of a number?

Ten percent of a number is one tenth of it, so you can just divide by 10 or move the decimal point one place to the left. For example, 10% of 230 is 23, and 10% of 45.50 is 4.55. This is a handy shortcut for tips and discounts, since 20% is double that and 5% is half.

What is 25 percent of a number?

Twenty-five percent of a number is one quarter of it, so divide the number by 4. For example, 25% of 84 is 84 ÷ 4 = 21. If a $36 shirt is 25% off, the discount is $9 and the sale price is 36 − 9 = $27.

What does percent of a number mean?

It means a part of the number out of every 100 equal parts. “Percent” means per hundred, so 15% of 200 means 15 for every 100, which is 30. The word “of” tells you to multiply, which is why the steps are always to change the percent to a decimal and multiply by the number.

How do you find what percent one number is of another?

Divide the part by the whole, then multiply by 100. If 18 out of 24 students passed a quiz, divide 18 ÷ 24 = 0.75 and multiply by 100 to get 75%. This is the reverse of finding a percent of a number, so it is a good way to check your answers.

Related Topics

• Representing Percentage
• Solving Percentage Word Problems
• Using Grid Models to Solve Percentage Problems
• Fractional and Decimal Percentages
• Word Problems Involving Comparing Percent and Fractions