Fraction Calculator
Enter two fractions and pick an operation to get the result, automatically simplified to lowest terms, along with its decimal equivalent.
How the Fraction formula works
The four fraction operations:
Add: a/b + c/d = (a×d + c×b) / (b×d) Subtract: a/b − c/d = (a×d − c×b) / (b×d) Multiply: a/b × c/d = (a×c) / (b×d) Divide: a/b ÷ c/d = (a×d) / (b×c)
Every result is then reduced by dividing numerator and denominator by their greatest common divisor (GCD).
Step-by-step calculation
- Apply the formula matching your chosen operation to get an unsimplified result.
- Find the greatest common divisor (GCD) of the resulting numerator and denominator.
- Divide both by the GCD to reduce the fraction to lowest terms.
- Divide numerator by denominator to also show the decimal equivalent.
Worked example
2/3 + 1/4 = (2×4 + 1×3) / (3×4) = (8+3)/12 = 11/12. Since 11 and 12 share no common factors, 11/12 is already in lowest terms — as a decimal, that's approximately 0.9167.
Frequently asked questions
How is a fraction simplified to lowest terms?
By dividing both the numerator and denominator by their greatest common divisor (GCD) — the largest number that evenly divides both — until no common factor larger than 1 remains.
Can I use negative numbers or mixed numbers?
Negative whole numbers work in the numerator or denominator. For mixed numbers (like 1½), convert to an improper fraction first (1½ becomes 3/2) before entering it.
What happens if the denominator is zero?
Division by zero is undefined, so a fraction with a zero denominator has no valid value — the calculator will flag this as an invalid input.