Fraction Calculator
Add, subtract, multiply, and divide fractions and mixed numbers with step-by-step GCD simplification and decimal conversion.
How to Use the Fraction Calculator
Enter the numerator and denominator for both fractions, select your mathematical operator (+, -, ×, ÷), and get the exact simplified fraction, mixed number, and decimal representation.
Formula & Calculation Method
Add: (a/b) + (c/d) = (ad + bc)/bd | Multiply: (a/b) × (c/d) = (ac)/(bd)Uses exact integer cross-multiplication and Euclidean Greatest Common Divisor (GCD) reduction to eliminate floating-point approximation inaccuracies.
Calculation Examples
Addition of Unlike Denominators
Cross multiplied: (1×3 + 1×2) / 6 = 5/6
Subtraction
(4/6) - (1/6) = 3/6, simplified to 1/2
Multiplication
6/20 reduced by GCD 2 to 3/10
Division
Multiplied by reciprocal: 1/2 × 4/3 = 4/6 = 2/3
Frequently Asked Questions
Does this calculator simplify fractions automatically?
Yes. All calculation outputs are automatically reduced to their simplest canonical form using the Euclidean GCD algorithm.
Can this tool handle negative fractions and improper fractions?
Yes. Negative numerators and denominators are normalized cleanly, and improper fractions (where numerator > denominator) also show their mixed number equivalent.
What happens if a denominator is set to zero?
Division by zero is mathematically undefined. The calculator alerts you immediately to correct zero denominators.