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Teacher Guide: Finding Percent of a Number

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

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All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Percentages. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Convert percentages to decimals and fractions
  • Calculate any percent of a given number
  • Apply percent calculations to real-world situations
  • Use mental math shortcuts for common percentages
Prerequisites
  • • Understanding of what percent means (per hundred)
  • • Decimal multiplication
  • • Converting between fractions and decimals
Discussion Starters
  • 1. When was the last time you saw a percentage in real life? What was it?
  • 2. Why do stores advertise '50% off' instead of 'half price'?
  • 3. If a test has 25 questions and you got 80%, how many did you get right?
  • 4. Which is a better deal: 25% off a 100 euro item, or 30% off an 80 euro item?
Common Misconceptions

Thinking that a bigger percent always means a bigger amount

Remediation: Show that 50% of 10 (= 5) is less than 10% of 100 (= 10). The base number matters too!

Believing that you can add percentages from different bases

Remediation: Demonstrate: 50% of 100 + 50% of 50 is not 100% of 150. Calculate each separately: 50 + 25 = 75.

Differentiation Ideas

For Struggling Students:

  • • Start with 10%, 50%, and 25% only (easy mental math)
  • • Use grid paper to visualize 100 squares
  • • Provide a percent-to-decimal conversion chart

For On-Level Students:

  • • Calculate various percentages including single-digit percents
  • • Solve two-step problems (discount then tax)
  • • Compare different percentage scenarios

For Advanced Students:

  • • Work with percentages greater than 100%
  • • Calculate successive percentages (20% off, then additional 10% off)
  • • Reverse percentage problems (the answer is 30, which is 15% of what?)
Standards Alignment
  • 6.RP.A.3c (CCSS.MATH.CONTENT.6.RP.A.3.C)

    Find a percent of a quantity as a rate per 100

  • 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)

    Use proportional relationships to solve multistep ratio and percent problems

Lesson Resources
  • visualPercent Bar Model

    Visual representation showing percent as part of a whole

  • activityShopping Simulation

    Calculate discounts on fictional store items

  • worksheetTip Calculator Practice

    Calculate tips for various meal amounts

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

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

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 the wrong direction (writing 20% as 2.0 instead of 0.20)

Why it's wrong: To convert percent to decimal, move the decimal point two places LEFT (divide by 100).

Correct: 20%=0.2020\% = 0.20 (decimal moves LEFT two places)

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.

Why It Matters

Calculating percentages is one of the most practical math skills you'll ever learn:
  • Shopping: Calculate discounts - "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: Batting averages, free throw 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:

A 80 euro jacket is 25% off. Savings: 80×0.25=2080 \times 0.25 = 20 euros. Sale price: 80−20=6080 - 20 = 60 euros.

1Try It Yourself

A video game normally costs 50 euros. 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 euro meal, a 15% tip is 40×0.15=640 \times 0.15 = 6 euros.

2Try It Yourself

Your restaurant bill is 65 euros. 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

What is the fastest way to find 10% of any number?

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.

How do I find 15% quickly?

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.

Is finding 25% of a number the same as dividing by 4?

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

Convert percent to decimal and multiply

Fraction Method

Part=Whole×p100\text{Part} = \text{Whole} \times \frac{p}{100}

Use the percent as a fraction over 100

More in This Topic

Introduction to Percentages

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Percent Increase and Decrease

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Percent Proportion

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Percent Equation

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