Fraction Calculator
Add, subtract, multiply, and divide fractions with instant simplification using GCD.
Fraction A
/
Operation
Fraction B
/
1/2 + 1/3
5 / 6
≈ 0.8333
Result
Fraction
5 / 6
Decimal
0.8333
Operation
1/2 + 1/3
Simplified Form
5/6
Input: 1/2 + 1/3
Raw: 5/6
Simplified: 5/6
How to use the fraction calculator?
Enter the numerator and denominator for both fractions, then choose an operation (add, subtract, multiply, or divide). The calculator instantly shows the result as both a simplified fraction and a decimal value. The result is reduced to its lowest terms using the greatest common divisor (GCD).
Formula
a/b + c/d = (a×d + b×c) / (b×d)
a/b − c/d = (a×d − b×c) / (b×d)
a/b × c/d = (a×c) / (b×d)
a/b ÷ c/d = (a×d) / (b×c)
a/b − c/d = (a×d − b×c) / (b×d)
a/b × c/d = (a×c) / (b×d)
a/b ÷ c/d = (a×d) / (b×c)
Example
Add 1/2 and 1/3: the result is (1×3 + 1×2) / (2×3) = 5/6. As a decimal, that equals approximately 0.8333. Multiplying 1/2 × 1/3 gives 1/6 (≈ 0.1667).
FAQs
- What does "simplified form" mean? The fraction is reduced so that the numerator and denominator share no common factor other than 1 — for example, 4/8 becomes 1/2.
- What happens if the denominator is zero? Division by zero is mathematically undefined. The calculator will show a result of 0 for the division case if the denominator becomes zero.
- Can I enter negative fractions? Yes — enter a negative sign in the numerator field (e.g., −3/4). The simplification step handles signs automatically.
Common Use Cases
- Adding or subtracting recipe measurements expressed in fractions.
- Resolving homework problems involving fraction arithmetic.
- Converting mixed fraction operations into a single simplified result.