Fraction Calculator (Add, Subtract, Multiply, Divide)
Add, subtract, multiply, and divide fractions. Shows simplified result and decimal equivalent. Handles mixed numbers.
What this calculates
Fractions trip up everyone occasionally — especially when adding or subtracting with different denominators. This calculator handles the four operations on any two fractions, simplifies the result to its lowest terms, and shows the decimal equivalent.
Formula & how it works
Add/subtract: find a common denominator, combine numerators, simplify. (a/b ± c/d) = (a·d ± b·c) / (b·d). Multiply: (a/b) × (c/d) = (a·c) / (b·d). Divide: (a/b) ÷ (c/d) = (a·d) / (b·c). Simplify by dividing numerator and denominator by their greatest common divisor (GCD), found with Euclid's algorithm.
Worked example
3/4 + 1/6. Common denominator = 12. = 9/12 + 2/12 = 11/12. Already simplified (GCD(11,12) = 1). Decimal = 0.91667. Another: 2/3 × 3/4 = 6/12 = simplified 1/2 = 0.5.
Frequently asked questions
What if the result is improper?
Improper fractions like 7/4 are mathematically fine. We also show the mixed-number form (1 3/4) when applicable.
How do I enter a mixed number?
Convert manually first: 2 1/3 = 7/3. We accept improper fractions directly. Mixed-number input might come in a future version.
Does this handle negative fractions?
Yes — enter a negative numerator. The sign tracks through all four operations correctly.
Why simplify?
Same value, more readable. 6/12 and 1/2 are equal, but 1/2 is the canonical form and easier to compare with other simplified fractions.