½ Fraction Calculator
Add, subtract, multiply, or divide two fractions. Results are automatically simplified and shown as a decimal too.
Enter Fractions
Result
How Fraction Math Works
This calculator performs the four basic operations on fractions and automatically simplifies the result using the greatest common divisor (GCD).
Formulas
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c)
The result is then simplified by dividing both numerator and denominator by their greatest common divisor (GCD), found using the Euclidean algorithm.
Worked Example
The calculator loads with 1/2 + 1/3. Using the addition formula: (1×3 + 1×2) / (2×3) = (3 + 2) / 6 = 5/6. Since the GCD of 5 and 6 is 1, the fraction is already in its simplest form, with a decimal equivalent of 0.8333.
Frequently Asked Questions
How is a fraction simplified?
The numerator and denominator are both divided by their greatest common divisor (GCD), which reduces the fraction to its lowest terms.
What happens if I divide by a fraction with a zero numerator?
Dividing by a fraction equal to zero is undefined (equivalent to division by zero), so the calculator will show an error note.
Can I enter negative fractions?
Yes, numerators can be negative. A denominator of zero is invalid and will trigger a validation message.