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.

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:

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(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

What is the formula for finding a percent of a number?

(color{blue}{text{ Part } = text{ Percent }}) (color{blue}{(text{ as a decimal }) times text{ Whole }}). Always convert the percent to a decimal by dividing by 100 before multiplying.

How do I find the sale price after a percent discount?

Find the discount amount first: (color{blue}{text{ discount } = text{ percent } times text{ original price }}). Then subtract: (color{blue}{text{ sale price } = text{ original price } – text{ discount }}). Or shortcut: (color{blue}{text{ sale price } = (1 – text{ percent decimal }) times text{ original price }}).

What if the percent is more than 100?

The math works the same way. For example, 150% of (color{blue}{60 = 1.50 times 60 = 90}), which is 1.5 times the original number.

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