How to Solve Percent Problems? (+FREE Worksheet!)

Percent problems appear everywhere — in sales discounts, test scores, tax calculations, and data analysis. Every percent problem falls into one of three types: finding the part, finding the percent, or finding the whole. Once you learn the percent equation, you can solve all three types with the same approach.

What Is a Percent Problem?

A percent means “per hundred.” The key relationship is:

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

Rearranging this gives the three problem types. The percent must be written as a decimal (divide by 100) before multiplying.

The Three Types of Percent Problems

Type 1: Find the Part

“What is 30% of 150?”
Part is unknown. Convert: \(\color{blue}{30\% = 0.30}\). Multiply: \(\color{blue}{0.30 \times 150 = 45}\).

Type 2: Find the Percent

“45 is what percent of 180?”
Percent is unknown. Rearrange: \(\color{blue}{\text{ Percent } = \text{ Part } \div \text{ Whole }}\). Calculate: \(\color{blue}{45 \div 180 = 0.25 = 25\%}\).

Type 3: Find the Whole

“25 is 20% of what number?”
Whole is unknown. Rearrange: \(\color{blue}{\text{ Whole } = \text{ Part } \div \text{ Percent }}\). Calculate: \(\color{blue}{25 \div 0.20 = 125}\).

Step-by-Step Summary

1. Identify which quantity is unknown: the part, the percent, or the whole.
2. Write the percent equation: \(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\).
3. Convert the percent to a decimal by dividing by 100.
4. Substitute the known values and solve for the unknown.
5. If the answer is a percent, multiply by 100 to express it as a percentage.

Watch: Finding a Percent of a Number

Math Antics explains how to find the percent of a number using simple multiplication:

Percent Problems – Worked Examples

Example 1: What is 30% of 150?

Convert: \(\color{blue}{30\% = 0.30}\). Multiply: \(\color{blue}{0.30 \times 150 = 45}\).

Example 2: 45 is what percent of 180?

\(\color{blue}{\text{ Percent } = \text{ Part } \div \text{ Whole }}\): \(\color{blue}{45 \div 180 = 0.25}\). Multiply by 100: \(\color{blue}{25\%}\).

Example 3: 25 is 20% of what number?

\(\color{blue}{\text{ Whole } = \text{ Part } \div \text{ Percent }}\): \(\color{blue}{25 \div 0.20 = 125}\).

Example 4: What is 15% of 80?

Convert: \(\color{blue}{15\% = 0.15}\). Multiply: \(\color{blue}{0.15 \times 80 = 12}\).

More Practice: Using the Percent Equation

Math with Mr. J works through all three types of percent problems using the percent equation:

Exercises for Percent Problems

Solve each problem using the percent equation.

1. What is 15% of 80?
2. 12 is what percent of 48?
3. 36 is 90% of what number?
4. What is 40% of 250?
5. 7 is what percent of 35?
6. 18 is 60% of what number?

Answers

1. \(\color{blue}{12}\)
2. \(\color{blue}{25\%}\)
3. \(\color{blue}{40}\)
4. \(\color{blue}{100}\)
5. \(\color{blue}{20\%}\)
6. \(\color{blue}{30}\)

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Frequently Asked Questions

How do I convert a percent to a decimal?

Divide the percent by 100. For example, \(\color{blue}{35\% = 35 \div 100 = 0.35}\). Equivalently, move the decimal point two places to the left.

What is the percent equation?

The percent equation is \(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\). You can rearrange it to find any of the three quantities: \(\color{blue}{\text{ Percent } = \text{ Part } \div \text{ Whole }}\) or \(\color{blue}{\text{ Whole } = \text{ Part } \div \text{ Percent }}\).

Can I use a proportion instead of the percent equation?

Yes. The proportion method is \(\color{blue}{\frac{\text{ part }}{\text{ whole }} = \frac{\text{ percent }}{100}}\). Cross-multiply to solve. Both methods give the same answer.

Related Topics

• Percent of Increase and Decrease
• Discount, Tax, and Tip
• Simple Interest
• Proportional Ratios
• Similarity and Ratios