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Result
Method
Addition and subtraction use a common denominator: a/b ± c/d = (ad ± bc)/bd. Multiplication uses ac/bd, and division uses ad/bc. Every result is reduced by the Euclidean greatest-common-divisor algorithm and its denominator is positive.
Worked example
1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6. Also, 2/3 × 9/10 reduces from 18/30 to 3/5.
Limits and assumptions
Numerators and denominators must be signed integers of at most 5,000 digits. Denominators and a division divisor cannot be zero. Decimal input belongs in Decimal to Fraction; simplifying one existing fraction belongs in Fraction Simplifier.
Exactness and privacy
Supported integer calculations use BigInt and validated text, not floating-point Number conversion. Results are rendered as inert text. This educational calculator does not send calculation values to a server or make professional decisions for you.