What Is a Percentage?
Taught in US schools
Key Takeaways
- A percentage is a ratio out of 100 - 50% means 50 out of every 100, which equals 1/2 or 0.5.
- You can convert between fractions, decimals, and percentages using division and multiplication by 100.
- Benchmark percentages (25%, 50%, 75%, 100%) make mental math with percents much faster.
What Is a Percentage?
A percentage is a special kind of ratio that compares any number to 100. The word comes from the Latin per centum, meaning "per hundred." We write percentages using the percent sign: %.
Example: 75% means 75 out of every 100. If you got 75 out of 100 questions right on a test, you scored 75%.
The Percent, Fraction, and Decimal Connection
Percentages, fractions, and decimals all represent the same idea - parts of a whole - just in different forms.
100%: 1 (the whole) - 1.0
75%: 3/4 - 0.75
50%: 1/2 - 0.5
25%: 1/4 - 0.25
10%: 1/10 - 0.1
1%: 1/100 - 0.01
Knowing these benchmarks by heart makes percent problems much faster.
Converting Between Forms
Fraction → Percent: Divide numerator by denominator, then multiply by 100.
3/5 → 3 ÷ 5 = 0.6 → 0.6 × 100 = 60%
Percent → Decimal: Divide by 100 (move the decimal point two places left).
45% → 45 ÷ 100 = 0.45
Decimal → Percent: Multiply by 100 (move the decimal point two places right).
0.08 → 0.08 × 100 = 8%
Finding a Percent of a Number
To find a percent of a number, convert the percent to a decimal and multiply.
20% of 60: 20% = 0.20, and 0.20 × 60 = 12
50% of 84: 50% = 0.5, and 0.5 × 84 = 42
A shortcut: 10% of any number is just that number divided by 10. Then you can build other percentages from it.
- 10% of 80 = 8
- 20% of 80 = 16 (double 10%)
- 5% of 80 = 4 (half of 10%)
Percentages in Real Life
Percentages appear constantly in the real world:
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Test scores: A score of 92 out of 100 = 92%
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Sales and discounts: A shirt originally $40 is 25% off - savings of $10
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Sales tax: A $20 item with 5% tax costs $20 + $1 = $21
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Survey results: 68% of students chose pizza as their favorite lunch
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Sports statistics: A basketball player made 80% of her free throws
Practice Activities
- Use a 100-square grid and shade different percentages to visualize what 25%, 50%, and 75% look like.
- Convert a set of fractions and decimals to percentages and sort them from least to greatest.
- Calculate a 10% tip on a pretend restaurant bill, then extend to 15% and 20%.
- Find sale prices by calculating a given percent off a list of items from a store flyer.
- Create a class survey on a favorite topic, then report the results as percentages.
Frequently Asked Questions
What does percent mean?
The word percent comes from the Latin per centum, meaning per hundred. So 40% literally means 40 per 100, or 40 out of every 100 parts.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/4 = 0.75, and 0.75 x 100 = 75%.
How do I find a percentage of a number?
Convert the percent to a decimal by dividing by 100, then multiply. For example, 20% of 60 = 0.20 x 60 = 12.
Free Percentage Worksheets
Curriculum-aligned printable worksheets for 5th Grade. Download free.
