Finding Percent of a Number

Learn how to calculate any percentage of a number using multiplication and conversion techniques.

Intermediate25 min18 problems
Practice Problems

Definition

To find a percent of a number, convert the percent to a decimal (or fraction) and multiply.
The Formula:
Percent of a Number=Number×Percent100\text{Percent of a Number} = \text{Number} \times \frac{\text{Percent}}{100}
Quick Method (Decimal):
  1. 1.Convert percent to decimal: divide by 100
  2. 2.Multiply by the number
Example: Find 25% of 80
25% of 80=80×0.25=2025\% \text{ of } 80 = 80 \times 0.25 = 20

Try it now

What is 10% of 50?

Worked Examples

Find 20% of 150.
1

Convert percent to decimal

20%=20÷100=0.2020\% = 20 \div 100 = 0.20
2

Multiply by the number

150×0.20150 \times 0.20 → 30
3

State the answer

20%20\% of 150150 equals 3030

Common Mistakes

Forgetting to convert percent to decimal (calculating 20×150=300020 \times 150 = 3000 instead of 0.20×150=300.20 \times 150 = 30)

Why it's wrong: The percent symbol means 'per hundred'. 20% is 20 per 100, which equals 0.20, not 20.

Correct: Always divide the percent by 100 first: 20%=0.2020\% = 0.20, then multiply.

Moving the decimal point only one place (writing 5% as 0.5 instead of 0.05)

Why it's wrong: Percent means 'divide by 100', so the decimal point moves two places LEFT, not one. 0.5 would be 50%.

Correct: 5%=0.055\% = 0.05 and 20%=0.2020\% = 0.20 (the decimal point moves two places LEFT)

Confusing 'percent of' with 'percent off'

Why it's wrong: '20% of 100' means find 20 (the answer). '20% off 100' means subtract 20 to get 80 (the final price).

Correct: For discounts, first find the percent, then subtract from the original.

Interactive Visual

20% and 80% of a number

20%
30
= 30
80%
30
30
30
30
= 120
100%
= 5 (150)
If total is:
20% value:30
80% value:120

Bar Chart

20% of 150(12%)
20% of 45(4%)
75% of 240(73%)
8% of 350(11%)

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

18 problems
Problem 1 of 18
Easy
What is 10% of 50?

Why It Matters

Calculating percentages is one of the most practical math skills you'll ever learn:
  • Shopping: Calculate discounts, like "This 60 dollar jacket is 30% off"
  • Tipping: Figure out a 15% or 20% tip at a restaurant
  • Taxes: Understand sales tax added to purchases
  • Grades: Know what score you need on a test
  • Sports: Free throw and shooting percentages
  • Finance: Interest rates, savings goals
Every time you see a % sign, you're ready to calculate!

Real World Applications

Shopping Discounts

Stores use percentages to show how much you save during sales.

Example:

An 80 dollar jacket is 25% off. Savings: 80×0.25=2080 \times 0.25 = 20 dollars. Sale price: 80−20=6080 - 20 = 60 dollars.

1Try It Yourself

A video game normally costs 50 dollars. It is on sale for 40% off.

How much do you save, and what is the sale price?

Step 1: Write the mathematical expression

Calculate the savings: 50×0.4050 \times 0.40

Restaurant Tips

Calculating tips is a common use of percentages.

Example:

On a 40 dollar meal, a 15% tip is 40×0.15=640 \times 0.15 = 6 dollars.

2Try It Yourself

Your restaurant bill is 65 dollars. You want to leave a 20% tip.

How much should you tip?

Step 1: Write the mathematical expression

Calculate: 65×0.2065 \times 0.20

Test Scores

Teachers often tell you what percent you scored on a test.

Example:

If a test has 40 questions and you need 80% to pass, you need 40×0.80=3240 \times 0.80 = 32 correct answers.

3Try It Yourself

A test has 50 questions. You need to score at least 70% to pass.

How many questions must you answer correctly?

Step 1: Write the mathematical expression

Calculate: 50×0.7050 \times 0.70

Key Takeaways

  • 1To find a percent of a number, convert the percent to a decimal and multiply
  • 2Convert percent to decimal by dividing by 100 (move decimal 2 places left)
  • 3Formula: Number×Percent100\text{Number} \times \frac{\text{Percent}}{100}
  • 4Useful shortcuts: 10% = divide by 10, 50% = divide by 2, 25% = divide by 4

Frequently Asked Questions

Just move the decimal point one place to the left! 10% of 250 = 25.0 = 25. This works because dividing by 10 moves the decimal left.
Just move the decimal point one place to the left! 10% of 250 = 25.0 = 25. This works because dividing by 10 moves the decimal left.
Find 10% (divide by 10), then find 5% (half of 10%), and add them together. For 15% of 80: 10% = 8, 5% = 4, so 15% = 12.
Yes! 25% = 25/100 = 1/4. So 25% of 80 = 80/4 = 20.

Glossary

Percent
A ratio that compares a number to 100. The symbol % means 'per hundred'.
Decimal equivalent
The percent divided by 100. For example, 25% = 0.25.
Whole (or Base)
The total number you are finding a percent of.
Part
The result when you calculate a percent of a whole.

Formula Card

Decimal Method

Part=Whole×decimal\text{Part} = \text{Whole} \times \text{decimal}

Convert percent to decimal and multiply

Fraction Method

Part=Whole×Percent100\text{Part} = \text{Whole} \times \frac{\text{Percent}}{100}

Use the percent as a fraction over 100

Today's challengeOne problem, three tries

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