Fraction Simplifier Calculator

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:

1. Divide the larger number by the smaller number
2. Note the remainder
3. Replace the larger number with the smaller, and the smaller with the remainder
4. Repeat until the remainder is 0
5. 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