Converting percentages to fractions is an essential skill in everyday math, especially in areas like finance, statistics, and general problem-solving. The process is straightforward and involves a few basic steps. This guide will explain how to convert any percentage into a fraction, simplify it, and provide examples for better understanding.
Basic Steps to Convert a Percent to a Fraction
Step 1: Write the Percentage as a Fraction Over 100
Since “percent” means “per hundred,” any percentage can be written as a fraction with 100 as the denominator.
For example, for 75%, you start by writing:
Step 2: Simplify the Fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.
For 75/100, the GCD of 75 and 100 is 25. Divide both the numerator and the denominator by 25:
So, 75% as a fraction is 3/4.
Step 3: Simplify Further if Possible
If the fraction can be simplified further, continue to do so until you reach the fraction’s simplest form. In the above example, 3/4 is already in its simplest form.
Example Conversions
1. Convert 50% to a Fraction
- Write as a fraction: 50/100.
- Simplify: The GCD of 50 and 100 is 50:
So, 50% as a fraction is 1/2.
2. Convert 25% to a Fraction
- Write as a fraction: 25/100.
- Simplify: The GCD of 25 and 100 is 25:
So, 25% as a fraction is 1/4.
3. Convert 125% to a Fraction
- Write as a fraction: 125/100.
- Simplify: The GCD of 125 and 100 is 25:
So, 125% as a fraction is 5/4.
Example Table for Quick Reference
Here’s a table with some common percentages and their fractional equivalents:
| Percentage | Fraction | Simplified Fraction |
|---|---|---|
| 10% | 10/100 | 1/10 |
| 20% | 20/100 | 1/5 |
| 25% | 25/100 | 1/4 |
| 40% | 40/100 | 2/5 |
| 50% | 50/100 | 1/2 |
| 60% | 60/100 | 3/5 |
| 75% | 75/100 | 3/4 |
| 80% | 80/100 | 4/5 |
| 90% | 90/100 | 9/10 |
| 100% | 100/100 | 1 |
| 125% | 125/100 | 5/4 |
| 150% | 150/100 | 3/2 |
| 200% | 200/100 | 2 |
Converting Percentages Greater Than 100%
When the percentage is greater than 100%, you will end up with an improper fraction (where the numerator is larger than the denominator). Simplify it as usual.
Example: Convert 150% to a Fraction
- Write as a fraction: 150/100
- Simplify: The GCD of 150 and 100 is 50:
So, 150% as a fraction is 3/2.
Quick Tips for Conversion
- Always Use 100 as the Denominator: Since “percent” means “per 100,” always start with 100 as the denominator.
- Simplify: Always simplify the resulting fraction by finding the greatest common divisor (GCD) to reduce it to its lowest terms.
- Mixed Numbers: If the percentage is greater than 100% and simplifies to an improper fraction, you can also express it as a mixed number. For example, 125% simplifies to 5/4 or 1 x 1/4.
Practice Problems
- Convert 65% to a fraction.
- Write as a fraction: 65/100.
- Simplify: Divide both by the GCD of 5: 13/20.
- Convert 80% to a fraction.
- Write as a fraction: 80/100.
- Simplify: Divide both by the GCD of 20: 4/5.
- Convert 12.5% to a fraction.
- Write as a fraction: 12.5/100.
- Multiply to remove the decimal: 125/1000.
- Simplify: Divide both by the GCD of 125: 1/8.
The key steps are writing the percentage as a fraction over 100, simplifying the fraction, and expressing it in its simplest form. This skill is not only useful in mathematics but also in daily life when you need to compare values or perform quick mental calculations.