Percent to Fraction Converter
Convert percentages to fractions easily and accurately.
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Table of Contents
Comprehensive Guide to Percent to Fraction Conversion
Understanding Percentages
A percent (%) represents a value out of 100. The term "percent" literally means "per hundred." When we write 45%, we're expressing 45 out of 100, or 45 parts per hundred.
The Fundamental Approach
The mathematical foundation for converting percentages to fractions is straightforward:
- Write the percentage as a fraction over 100 (remove the % symbol)
- Simplify the fraction to its lowest terms
- Express as a proper or improper fraction as needed
Conversion Formulas
Basic Formula: Percent value ÷ 100 = Fraction
Example: 75% = 75/100 = 3/4
Different Types of Percentage Conversions
1. Simple Percentages
These are whole number percentages like 25%, 50%, or 75% that often simplify to common fractions.
- 25% = 25/100 = 1/4
- 50% = 50/100 = 1/2
- 75% = 75/100 = 3/4
2. Decimal Percentages
Percentages with decimal values require additional steps:
Example: 12.5%
Step 1: 12.5% = 12.5/100
Step 2: Multiply both numerator and denominator to eliminate the decimal:
12.5/100 = (12.5 × 10)/(100 × 10) = 125/1000
Step 3: Simplify by dividing by the greatest common divisor (GCD):
125/1000 = (125 ÷ 125)/(1000 ÷ 125) = 1/8
3. Percentages Greater than 100%
These convert to improper fractions or mixed numbers:
Example: 150%
Step 1: 150% = 150/100
Step 2: Simplify: 150/100 = 3/2 (improper fraction)
Step 3: Convert to mixed number if desired: 3/2 = 1 1/2
Common Conversions Reference Table
| Percentage | Fraction (Simplified) | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 10% | 1/10 | 0.1 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33.33% | 1/3 | 0.3333... |
| 50% | 1/2 | 0.5 |
| 66.67% | 2/3 | 0.6666... |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.8 |
| 100% | 1/1 or 1 | 1.0 |
| 125% | 5/4 or 1 1/4 | 1.25 |
| 150% | 3/2 or 1 1/2 | 1.5 |
| 200% | 2/1 or 2 | 2.0 |
Special Cases and Considerations
1. Repeating Decimals
Some percentages convert to fractions with repeating decimals:
Example: 33.33% (repeating)
This is exactly 1/3 in fraction form.
Similarly, 66.67% (repeating) = 2/3
2. Simplification Techniques
The key to simplifying fractions is finding the greatest common divisor (GCD) of the numerator and denominator. This can be done by:
- Finding prime factors of both numbers
- Using the Euclidean algorithm
- Using a step-by-step division process
Real-World Applications
Understanding percent-to-fraction conversions is useful in many areas:
- Finance: Interest rates, discounts, and tax calculations
- Cooking: Converting recipe measurements
- Construction: Calculating material requirements
- Statistics: Interpreting data and probabilities
- Education: Grading scales and academic assessments
Practical Tips for Quick Conversions
- Memorize common conversions (25% = 1/4, 50% = 1/2, 75% = 3/4)
- For percentages that are multiples of 5, look for factors of 5 and 2 to simplify
- For decimal percentages, multiply both numerator and denominator to eliminate decimals
- Use the GCD to ensure fractions are in their simplest form
- Check your work: The simplified fraction converted back to a percentage should equal the original percentage
Pro Tip:
When working with complex percentages, consider converting to a decimal first, then to a fraction. For example, 87.5% → 0.875 → 7/8.
How to Convert Percent to Fraction
To convert a percentage to a fraction, follow these steps:
-
1Write down the percentage divided by 100
-
2Simplify the fraction to its lowest terms
75% = 75/100 = 3/4
50% = 50/100 = 1/2
25% = 25/100 = 1/4
Common Examples
Example 1 100%
100% = 100/100 = 1
Example 2 75%
75% = 75/100 = 3/4
Example 3 50%
50% = 50/100 = 1/2
Example 4 25%
25% = 25/100 = 1/4