Fraction Calculator
Simplify any fraction and calculate its decimal and percentage equivalents.
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Enter your values and click Calculate
How It Works
The Euclidean algorithm finds the Greatest Common Divisor (GCD) of the numerator and denominator: repeatedly divide the larger by the smaller and take the remainder until the remainder is zero; the last non-zero remainder is the GCD. Both numerator and denominator are then divided by the GCD to produce the simplified fraction. The decimal is computed as Numerator ÷ Denominator. The percentage is Decimal × 100. When the simplified denominator is 1, the output is displayed as a whole number rather than a fraction with denominator 1.
Examples
Common reduction
Simplifying 8 over 24.
Result: The fraction simplifies to 1/3, which is 0.333333 or 33.3333%.
Improper fraction
A top-heavy fraction like 50/20.
Result: Simplifies to 5/2, a decimal of 2.5, and 250%.
Already simplified
Entering a fraction like 3/7.
Result: Remains 3/7, converts to 0.428571 or 42.8571%.
Frequently Asked Questions
What is a numerator and denominator?
The numerator is the top number of a fraction representing the parts you have. The denominator is the bottom number representing the total parts in a whole.
Why does the calculator return a whole number sometimes?
If the numerator is perfectly divisible by the denominator (like 10/2), the simplified fraction is just the whole number (5).
Can a fraction be negative?
Yes. If either the numerator or denominator is negative, the entire fraction's value is negative.
What is the Greatest Common Divisor (GCD)?
The GCD is the largest positive integer that divides both the numerator and the denominator without leaving a remainder. It is the key to simplifying fractions.