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Fraction Simplifier & Calculator

Perform arithmetic on fractions and automatically reduce results to the lowest terms. Supports addition, subtraction, multiplication, and division with GCD visualization.

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Category Math & Algebra
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About

Fractions represent rational numbers as a ratio of two integers: the numerator and the denominator. Operations on fractions differ significantly from integer arithmetic because they require finding common denominators for addition and subtraction, or reciprocal multiplication for division. In professional and academic contexts, presenting the final result in its simplest form (lowest terms) is a mandatory standard.

This calculator handles the four basic arithmetic operations on two fractions. It includes a built-in Euclidean algorithm to calculate the Greatest Common Divisor (GCD), ensuring that outputs are mathematically irreducible. It also detects improper fractions and converts them into mixed number notation for better readability.

fractions math rational numbers gcd calculator

Formulas

Simplification utilizes the Greatest Common Divisor (GCD) of the numerator and denominator:

Simplified = numerator ÷ GCDdenominator ÷ GCD

Reference Data

OperationFormulaConstraint
Additionab + cd = ad + bcbdb, d ≠ 0
Subtractionab − cd = ad − bcbdb, d ≠ 0
Multiplicationab × cd = acbdb, d ≠ 0
Divisionab ÷ cd = adbcb, c, d ≠ 0

Frequently Asked Questions

Division by zero is undefined in mathematics. The tool will return an error or "NaN" (Not a Number) if a denominator of 0 is entered.
It calculates the Greatest Common Divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both numbers by this value.
Yes. Negative signs are typically floated to the numerator in standard notation (e.g., 1/-2 becomes -1/2). The logic respects arithmetic rules for signed integers.