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Teacher Guide: Percent Word Problems

Master the three types of percent problems: finding the part, finding the whole, and finding the percent.

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

Worksheet Answer key

Class quiz

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

For Teachers

Learning Objectives
  • Identify the three types of percent word problems
  • Convert between percents and decimals fluently
  • Apply the formula Part = Percent × Whole appropriately
  • Solve real-world problems involving discounts, tips, and taxes
  • Check solutions for reasonableness
Prerequisites
  • • Understanding of percent as parts per hundred
  • • Converting between fractions, decimals, and percents
  • • Basic multiplication and division with decimals
  • • Solving one-step equations
Discussion Starters
  • 1. When shopping, how do you quickly estimate a 20% discount in your head?
  • 2. Why do you think restaurants suggest tip amounts on receipts?
  • 3. If a store offers '50% more free,' how is that different from '50% off'?
  • 4. A test has 25 questions. How many do you need to get right for an 80%?
Common Misconceptions

Percent of a number is always smaller than the number

Remediation: Show examples with percents greater than 100%. '150% of 40 is 60' - larger than the original!

Adding percents: 20% off + 10% off = 30% off

Remediation: Demonstrate with numbers: 100 dollars → 20% off = 80 dollars → 10% off = 72 dollars. That's only 28% off total, not 30%!

The order of discount and tax doesn't matter

Remediation: Show that discount first, then tax gives a different result than tax first, then discount. Always follow the store's actual order.

Differentiation Ideas

For Struggling Students:

  • • Use only multiples of 10 for percents (10%, 20%, 50%)
  • • Provide a flowchart for identifying problem types
  • • Use visual tape diagrams for every problem

For On-Level Students:

  • • Include percents like 15%, 25%, 33%
  • • Multi-step problems with discount and tax
  • • Percent increase and decrease applications

For Advanced Students:

  • • Successive percent changes (compound interest preview)
  • • Reverse percent problems (original price from discounted)
  • • Create their own word problems for classmates
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; solve problems involving finding the whole, given a part and the percent

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

    Use proportional relationships to solve multistep ratio and percent problems

Lesson Resources
  • visualTape Diagram Explorer

    Visualize percent relationships with interactive bar models

  • activityShopping Simulation

    Calculate discounts and final prices for various items

  • worksheetThree Types Practice

    Mixed practice identifying and solving each problem type

Lesson Content

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

Definition

Percent word problems come in three main types, each asking you to find a different piece of information:
Type 1: Finding the Part
Part=Percent×Whole\text{Part} = \text{Percent} \times \text{Whole}
*"What is 25% of 80?"*
Type 2: Finding the Whole
Whole=PartPercent\text{Whole} = \frac{\text{Part}}{\text{Percent}}
*"15 is 30% of what number?"*
Type 3: Finding the Percent
Percent=PartWhole×100\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100
*"What percent of 50 is 12?"*
The key to solving percent problems is identifying which type you're dealing with, then applying the correct formula.

Worked Examples

A jacket costs 80 dollars. The store offers a 25% discount. How much money do you save?
1

Identify the problem type

We need to find 25% OF 80 dollars → Type 1: Finding the Part
2

Convert percent to decimal

25%=25÷100=0.2525\% = 25 \div 100 = 0.25
3

Multiply to find the part

0.25×80=200.25 \times 80 = 20
4

Write the answer with units

The discount is 20 dollars → You save 20 dollars

Common Mistakes

Forgetting to convert percent to decimal before multiplying

Why it's wrong: 25% means 25 per hundred, not 25. Using 25 instead of 0.25 gives an answer 100 times too large.

Correct: Always divide the percent by 100 first: 25%=0.2525\% = 0.25, then multiply.

Dividing when you should multiply (or vice versa)

Why it's wrong: Confusing "finding the part" with "finding the whole" leads to inverse operations.

Correct: Ask yourself: Am I looking for a PIECE of something (multiply) or the TOTAL (divide)?

Calculating percent increase/decrease incorrectly

Why it's wrong: Applying the percent to the wrong number or forgetting to add/subtract from the original.

Correct: For increase: Original × (1 + percent). For decrease: Original × (1 - percent).

Mixing up the part and the whole

Why it's wrong: In "15 is what percent of 60?", students sometimes put 60 in the numerator.

Correct: The part (smaller value, 15) always goes in the numerator: 1560=25%\frac{15}{60} = 25\%.

Why It Matters

Percent problems appear constantly in everyday life:
  • Shopping: Calculating discounts ("30% off") and sales tax
  • Dining: Figuring out tips at restaurants (15%, 18%, 20%)
  • Finance: Understanding interest rates, loans, and investments
  • School: Converting test scores to percentages
  • Health: Reading nutrition labels ("25% of daily value")
  • Sports: Analyzing shooting percentages, win rates, and statistics
Mastering these three problem types gives you a powerful toolkit for handling real-world math!

Real World Applications

Shopping and Discounts

Calculating sale prices requires finding the part (discount amount) and subtracting from the original.

Example:

A 50 dollar shirt is 30% off. The discount is 0.30×50=150.30 \times 50 = 15 dollars, so you pay 50−15=3550 - 15 = 35 dollars.

1Try It Yourself

A pair of sneakers originally costs 120 dollars. They're on sale for 25% off.

How much do you pay for the sneakers?

Step 1: Write the mathematical expression

First find 25% of 120, then subtract:

Restaurant Tips

Tips are calculated as a percent of the bill before tax.

Example:

On a 60 dollar bill, a 20% tip is 0.20×60=120.20 \times 60 = 12 dollars.

2Try It Yourself

Your family's dinner bill is 85 dollars. You want to leave an 18% tip.

How much should you tip?

Step 1: Write the mathematical expression

Calculate: 85×0.1885 \times 0.18

Test Scores and Grades

Converting scores to percentages helps compare performance across different tests.

Example:

If you got 42 out of 50 questions right, your percent is 4250×100=84%\frac{42}{50} \times 100 = 84\%.

3Try It Yourself

You scored 54 points on a test. Your score was 90% of the total possible points.

How many points was the test worth?

Step 1: Write the mathematical expression

If 54 = 90% of total, then total = 54 ÷ 0.90:

Key Takeaways

  • 1Three types: Finding the Part (multiply), Finding the Whole (divide), Finding the Percent (divide then multiply by 100)
  • 2Always convert percent to decimal first by dividing by 100 (e.g., 25%=0.2525\% = 0.25)
  • 3Part = Percent × Whole is the fundamental relationship
  • 4Identify key words: "of" usually means multiply, "is" means equals
  • 5Check your answer by plugging it back into the original problem

Frequently Asked Questions

How do I know which type of percent problem I'm solving?

Look at what's missing: If you know the percent AND the whole, find the part (multiply). If you know the part AND the percent, find the whole (divide). If you know the part AND the whole, find the percent (divide then × 100).

Why do I divide by the percent to find the whole?

If Part = Percent × Whole, then Whole = Part ÷ Percent. Think of it like this: if 30 is 50% of something, that something must be bigger than 30. Dividing 30 by 0.50 gives 60.

What's the difference between percent increase and percent of?

"20% of 100" is just 20. "20% increase on 100" means 100 + 20 = 120. Percent increase adds to the original; percent of is just multiplication.

Glossary

Percent
A ratio that compares a number to 100. The symbol % means "per hundred."
Part
The portion or piece of the whole that corresponds to the given percent.
Whole
The total or complete amount that represents 100%.
Discount
A reduction in price, usually expressed as a percent of the original price.
Sales tax
An additional percent added to the purchase price, collected by the government.

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