Fractions Calculator

The Fractions Calculator performs the four core arithmetic operations on fractions: addition, subtraction, multiplication, and division. You enter two fractions as numerator-over-denominator pairs, choose an operation, and the tool returns an exact rational result rather than a rounded decimal. Because it keeps numbers in fractional form throughout the calculation, it preserves precision that floating-point decimals would lose, which matters for recipes, woodworking measurements, and math homework.

Under the hood, addition and subtraction require a common denominator. The calculator finds the denominators' least common multiple, rescales both numerators accordingly, combines them, and then reduces the answer to lowest terms by dividing the numerator and denominator by their greatest common factor. Multiplication simply multiplies numerators and denominators straight across, while division multiplies the first fraction by the reciprocal of the second (flipping the divisor). The final reduction step is what turns 6/8 into the cleaner 3/4.

Common use cases include scaling cooking recipes up or down, splitting measurements in construction and sewing, and checking school answers where fractional form is required. It is also handy when working with ratios or probabilities that need to stay exact. If you ever need the result as a decimal instead, pair it with a Decimal to Fraction conversion in reverse, and for the reduction math itself the GCF & LCM Calculator shows the same factors this tool uses internally.

A practical tip: always note whether your result is improper (numerator larger than denominator) versus a mixed number, since both are correct but contexts differ — recipes usually want mixed numbers like 1 1/2, while algebra often prefers improper fractions like 3/2. Watch out for a zero denominator, which is undefined, and remember that dividing by a fraction is the same as multiplying by its flip, a rule that trips many people up.