Fraction Calculator
This calculator performs arithmetic on two fractions and returns the result in three forms: simplified fraction, mixed number, and decimal. All simplification is done using the Greatest Common Divisor (GCD) via Euclid's algorithm.
Fraction Operations
Subtraction: a/b − c/d = (ad − bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / bc
Simplification
After computing the raw result, the calculator finds the GCD of the numerator and denominator and divides both by it to give the fully reduced fraction. For example, 6/8 becomes 3/4 because GCD(6,8) = 2.
Mixed Numbers
If the result is an improper fraction (numerator ≥ denominator), it is also expressed as a mixed number. For example, 7/4 = 1 3/4. If the result is a whole number or a proper fraction, the mixed number form is not shown.
Frequently Asked Questions
Can I enter negative fractions?
Yes. Enter a negative sign in the numerator field — e.g., −3 over 4 gives you −3/4. The calculator handles negative values correctly in all four operations.
What happens if I enter 0 as a denominator?
Division by zero is undefined. The calculator will show an error. Similarly, for division, if the second fraction's numerator is zero, the calculator will reject the input.
How do I enter a whole number?
Enter the whole number as the numerator and 1 as the denominator — e.g., 5/1 represents the number 5.