Percent Word Problems
Master the three types of percent problems: finding the part, finding the whole, and finding the percent.
Definition
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Worked Examples
A jacket costs 80 dollars. The store offers a 25% discount. How much money do you save?
Identify the problem type
We need to find 25% OF 80 dollars → Type 1: Finding the Part
Convert percent to decimal
→
Multiply to find the part
→
Write the answer with units
The discount is 20 dollars → You save 20 dollars
Answer: You save 20 dollars on the jacket.
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: , 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: .
Interactive Visual
Ratio Tape Diagram
Adjust the ratio parts using + and - buttons.
Pie Chart
Interactive Sandbox
Expression Calculator
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Practice Problems
16 problemsWhat is 20% of 50?
Why It Matters
- 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
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 dollars, so you pay dollars.
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 dollars.
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:
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 .
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., )
- 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
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.