Fraction Calculator: Add, Subtract, Multiply and Divide Fractions
This calculator adds, subtracts, multiplies and divides fractions and returns the answer in lowest terms, along with the decimal equivalent. Each operation follows a different rule, and knowing which rule applies is most of the work.
The four rules
- Addition and subtraction: convert to a common denominator first, then combine numerators.
- Multiplication: multiply numerators together and denominators together — no common denominator needed.
- Division: multiply by the reciprocal, so a/b ÷ c/d = a/b × d/c.
- Simplify: divide numerator and denominator by their greatest common divisor.
Worked example
To add 3/4 and 5/6, the least common denominator of 4 and 6 is 12. That gives 9/12 + 10/12 = 19/12, which as a mixed number is 1 7/12, or 1.5833 as a decimal. Multiplying the same two fractions is simpler: 3 × 5 over 4 × 6 is 15/24, which reduces to 5/8.
Where fractions beat decimals
Fractions are exact. One third is 0.333… as a decimal and rounding it introduces error that compounds through a calculation. Recipes, timber cuts, drill sizes, music timing and algebra all stay in fractions for that reason — and imperial measurements are fraction-based by design.
Key takeaways — Fraction Calculator
- Only addition and subtraction need a common denominator.
- Dividing by a fraction is multiplying by its reciprocal.
- Always reduce the answer by the greatest common divisor.