Introduction to Percentages
Learn what percentages are and how they relate to fractions and decimals.
Definition
- (the whole thing)
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Worked Examples
Write as a fraction in lowest terms.
Write as a fraction over 100
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Find the GCD of 75 and 100
Factors of 75: 1, 3, 5, 15, 25, 75\nFactors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100\nGCD = 25 → GCD = 25
Divide both by GCD
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Answer:
Common Mistakes
Confusing with
Why it's wrong: When converting, students sometimes forget to multiply by 100. , not .
Correct: To convert decimal to percent, multiply by 100:
Forgetting that means the whole thing
Why it's wrong: Students sometimes think percentages can't reach 100 or go beyond.
Correct: (all of it). You can even have more than : means 1.5 times the original.
Moving the decimal the wrong direction
Why it's wrong: Confusion about which way to move when converting between decimals and percents.
Correct: Percent to decimal: divide by 100 (move left 2 places). Decimal to percent: multiply by 100 (move right 2 places).
Interactive Visual
Pie Chart
Ratio Tape Diagram
Adjust the ratio parts using + and - buttons.
Click on the bar to change the fraction
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
18 problemsWhat does 50% mean?
Why It Matters
- Shopping: Sales and discounts ("25% off")
- School: Test scores ("85% correct")
- Sports: Statistics ("Made 70% of free throws")
- News: Statistics and polls ("60% of voters agree")
- Health: Nutrition labels ("15% of daily calcium")
Real World Applications
Shopping Discounts
Stores use percentages to advertise sales and help customers calculate savings.
Example:
A 25% discount on a 40 dollar item saves you 10 dollars.
You're buying a video game that normally costs 80 dollars. The store has a 15% off sale.
How much will you pay after the discount?
Step 1: Write the mathematical expression
First find 15% of 80, then subtract:
Test Scores
Teachers use percentages to show how well you performed on tests and assignments.
Example:
Getting 17 out of 20 questions correct means you scored .
You answered 42 questions correctly out of 50 on a math test.
What is your percentage score?
Step 1: Write the mathematical expression
Divide correct by total, then multiply by 100:
Nutrition Labels
Food packages show the percent of daily nutrients in each serving.
Example:
If a snack provides 20% of your daily fiber, eating 5 servings would give you 100% of your daily fiber needs.
A glass of milk provides 30% of your daily calcium. You drink 2 glasses.
What percentage of your daily calcium did you get?
Step 1: Write the mathematical expression
Multiply the percent by the number of servings:
Key Takeaways
- 1Percent means "per hundred" - the symbol % represents this relationship
- 2To convert percent to decimal: divide by 100 ()
- 3To convert decimal to percent: multiply by 100 ()
- 4To convert percent to fraction: write over 100 and simplify ()
- 5To find a percent of a number: convert to decimal and multiply ( of )
Frequently Asked Questions
Glossary
- Percent
- A ratio expressed as a fraction of 100, using the symbol %
- Percentage
- Another word for percent; a proportion expressed out of 100
- Percent of a number
- A fraction of a quantity found by converting the percent to a decimal and multiplying
- Discount
- A reduction in price, often expressed as a percentage off the original price
Formula Card
Percent to Decimal
Divide the percent by 100 to convert it to a decimal
Decimal to Percent
Multiply the decimal by 100 to convert it to a percent
Percent of a Number
Convert the percent to a decimal, then multiply by the whole