Percent to Fraction Calculator

Understanding Percentages and Fractions

A percentage represents a value out of 100. The word "percent" itself means "per hundred," indicating that when we see a percentage, we're looking at a part of a whole divided into 100 equal parts. Converting percentages to fractions is a fundamental mathematical skill that helps in simplifying calculations and understanding proportional relationships.

The Mathematical Relationship

Mathematically, percentages and fractions are just different ways to express the same proportional relationship. Here's how they connect:

• A percentage is written with the % symbol (e.g., 75%)
• The same value as a fraction would be written over 100 (e.g., 75/100)
• When simplified, the fraction gives us the cleanest representation (e.g., 3/4)

Step-by-Step Conversion Process

1. Remove the percent symbol and divide by 100

   To convert a percentage to a fraction, start by removing the percent symbol and dividing by 100. This gives you the initial fraction with 100 as the denominator.

   For example: 25% = 25/100

2. Handle decimal percentages

   If the percentage contains a decimal, multiply both numerator and denominator by an appropriate power of 10 to eliminate the decimal.

   For example: 12.5% = 12.5/100 = 125/1000

3. Simplify the fraction

   Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by this value to get the simplified fraction.

   For 25/100, GCD = 25, so: 25/100 = (25÷25)/(100÷25) = 1/4

Special Cases and Considerations

Percentages Greater Than 100%

Percentages greater than 100% convert to improper fractions (where the numerator is larger than the denominator) or mixed numbers.

Very Small Percentages

When dealing with very small percentages (like 0.001%), be careful with decimal placement when converting to ensure accuracy.

Repeating Decimals

Some percentages may convert to fractions with repeating decimals, which require special handling.

Common Percentage to Fraction Conversions

Practical Applications

Converting percentages to fractions is useful in many real-life situations:

• Cooking and recipes - When scaling ingredients that are given as percentages
• Financial calculations - For understanding interest rates, discounts, and taxes
• Construction and manufacturing - When working with measurements and specifications
• Academic grading - Converting percentage scores to GPA or other grading systems
• Statistical analysis - Representing proportions and probability as fractions

Common Mistakes to Avoid

• Forgetting to remove the percent symbol before performing calculations
• Not handling decimals correctly when converting to fractions
• Failing to simplify the fraction to its lowest terms
• Misinterpreting percentages greater than 100% or very small percentages

A fraction represents a part of a whole number. It consists of a numerator (top number) and a denominator (bottom number). For example:

To convert a percentage to a fraction:

1. 1
   Write the percentage as a fraction with 100 as the denominator
2. 2
   Simplify the fraction by finding the greatest common divisor (GCD)
3. 3
   Divide both numerator and denominator by the GCD

For example, to convert 75% to a fraction: