Percentages - Definition, Examples, Quiz, FAQ, Trivia
Learn to work with percentages through simple explanations, examples, and activities
What is Percentage?
Percentage (or percent) means "per hundred" and is represented by the symbol %. It's a way to express how much of something there is compared to a whole, where the whole is always considered as 100 equal parts.
Think of percentage as a special fraction where the denominator (bottom number) is always 100. For example:
- 25% means 25 out of 100
- 50% means 50 out of 100 (which is the same as 1/2)
- 100% means all 100 parts (the whole thing)
We use percentages everywhere in daily life - when we see discounts in stores ("50% off"), when we look at test scores ("85% correct"), or when we check the battery on our devices ("75% charged").
Key Concept
Percent means "per hundred". 1% = 1/100 = 0.01. 100% = 100/100 = 1 (the whole).
Converting Percentages
Converting percentages to decimals and fractions is an important math skill. Here's how to do it:
Conversion Formulas
To convert a percentage to a decimal, simply divide by 100 or move the decimal point two places to the left.
Examples:
- 25% → 25 ÷ 100 = 0.25
- 8% → 8 ÷ 100 = 0.08
- 150% → 150 ÷ 100 = 1.50
Converting Percent to Fraction:
Write the percentage as a fraction with a denominator of 100, then simplify if possible.
Examples:
- 25% = 25/100 = 1/4
- 75% = 75/100 = 3/4
- 10% = 10/100 = 1/10
Remember
Moving the decimal point two places to the left converts percent to decimal. Moving it two places to the right converts decimal to percent.
Calculating Percentages
Calculating percentages involves finding a part of a whole. There are two main methods:
Method 1: Using the Formula
Percentage Formula
Solution: (15 ÷ 20) × 100 = 0.75 × 100 = 75%
Method 2: Finding Percentage of a Quantity
To find a percentage of a quantity, convert the percentage to a decimal and multiply.
Example: What is 20% of 80 apples?
Solution: 20% = 0.20 → 0.20 × 80 = 16 apples
You can also use fractions:
20% = 1/5 → (1/5) × 80 = 16 apples
Common Percentages Chart
| Percentage | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.10 |
| 20% | 1/5 | 0.20 |
| 25% | 1/4 | 0.25 |
| 50% | 1/2 | 0.50 |
| 75% | 3/4 | 0.75 |
| 100% | 1 | 1.00 |
Percentage Tricks
Here are some helpful tricks to calculate percentages quickly:
1. Finding 10%: Move the decimal point one place to the left.
Example: 10% of 250 = 25.0
2. Finding 50%: Half of the number.
Example: 50% of 80 = 40
3. Finding 25%: Quarter of the number (half of half).
Example: 25% of 60 = 15
4. Finding 20%: Find 10% and double it.
Example: 20% of 150 = (10% of 150) × 2 = 15 × 2 = 30
5. Finding 5%: Find 10% and divide by 2.
Example: 5% of 200 = (10% of 200) ÷ 2 = 20 ÷ 2 = 10
6. Finding 1%: Move the decimal point two places to the left.
Example: 1% of 500 = 5.00
With these tricks, you can calculate many percentages without a calculator!
Quick Tip
To calculate 15%, find 10% and add half of that amount. For 30%, find 10% and multiply by 3.
Real-World Examples
Let's practice percentage calculations with real-world examples:
Example 1: Discounts
A shirt costs $40 and is 25% off. What is the sale price?
Solution: 25% of $40 = 0.25 × 40 = $10 discount
Sale price: $40 - $10 = $30
Example 2: Test Scores
Sarah got 18 questions right out of 20. What percentage is this?
Solution: (18 ÷ 20) × 100 = 0.90 × 100 = 90%
Example 3: Tips
You want to leave a 15% tip on a $50 restaurant bill. How much is the tip?
Solution: 15% of $50 = 0.15 × 50 = $7.50
Example 4: Sales Tax
An item costs $80 with 8% sales tax. What is the total cost?
Solution: 8% of $80 = 0.08 × 80 = $6.40 tax
Total: $80 + $6.40 = $86.40
Look for percentages around you - in stores, on your devices, and in the news!
Percentage Practice Quiz
Test your percentage knowledge with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about percentages:
Math Trivia
Discover interesting facts about percentages and mathematics:
Origin of the Percent Sign
The percent sign (%) evolved from the Italian phrase "per cento" meaning "for a hundred". The symbol was created by gradually combining the letters "p" and "c" with a line between them.
Percentages in Nature
About 60% of the human body is water. Similarly, 71% of Earth's surface is covered in water. Percentages help us understand proportions in the natural world.
Percentages in Space
Only about 5% of the universe is made up of normal matter that we can see. The rest is dark matter (27%) and dark energy (68%) - concepts scientists are still trying to understand.
Percentage World Record
The largest percentage discount ever offered was 100% off - meaning completely free! Many businesses occasionally offer products for free as promotions.