Fraction Simplifier Calculator
Simplify any fraction to its lowest terms.
Enter a numerator and denominator to find the greatest common divisor and reduced fraction.
Simplifying a fraction (also called “reducing to lowest terms”) means dividing both the numerator and denominator by their Greatest Common Divisor (GCD) until they share no common factor other than 1.
Formula:
Simplified Fraction = (Numerator / GCD) / (Denominator / GCD)
Where:
- Numerator = the top number of the fraction
- Denominator = the bottom number of the fraction
- GCD = the largest number that divides evenly into both the numerator and denominator
Finding the GCD (Euclidean Algorithm): This ancient algorithm, described by the Greek mathematician Euclid around 300 BC, efficiently finds the GCD:
- Divide the larger number by the smaller number
- Note the remainder
- Replace the larger number with the smaller, and the smaller with the remainder
- Repeat until the remainder is 0
- The last non-zero remainder is the GCD
Practical Example: Simplify 48/64 First, find GCD of 48 and 64:
- 64 / 48 = 1 remainder 16
- 48 / 16 = 3 remainder 0
- GCD = 16 Then divide both parts: 48/16 = 3, 64/16 = 4 Result: 48/64 = 3/4 As a decimal: 0.75. As a percentage: 75%.
When to use this calculator: Use it whenever you need to express a fraction in its simplest form — for homework, recipe conversions, measurement calculations, or any time you want the cleanest representation of a ratio. It also shows the decimal and percentage equivalents.
A fraction is fully simplified when the GCD of the numerator and denominator is 1. For example, 3/4 cannot be reduced further because 3 and 4 share no common factor.
Tips:
- Negative fractions are handled automatically — the calculator places the negative sign on the numerator
- If the result has a denominator of 1, the fraction is actually a whole number
- Common fractions to memorize: 1/4 = 0.25, 1/3 = 0.333, 1/2 = 0.50, 2/3 = 0.667, 3/4 = 0.75