Fraction Calculator

Working with fractional quantities is a frequent necessity in architectural drafting, culinary ingredient scaling, residential construction framing, and algebraic problem-solving across technical disciplines in classroom and workshop environments. Typical inputs consist of integer pairs representing the numerator and denominator for each rational term, along with the desired arithmetic operator. When combining fractions with unequal denominators, manual computation requires identifying a shared common denominator, cross-multiplying numerators, and executing the chosen operation while preserving exact mathematical proportionality.

The resulting output provides the fully simplified fraction reduced to its lowest common terms, any equivalent mixed number representation, and the corresponding decimal value. Reviewing both fractional and decimal formats helps bridge theoretical textbook solutions with physical measuring instruments such as tape measures or graduated cylinders in practical carpentry or chemistry workflows. Note that a denominator must never equal zero, as division by zero represents an undefined mathematical operation that halts any valid calculation.

Addition and subtraction align fractions across a shared denominator via cross-multiplication before combining numerators. Multiplication takes the direct product of both numerators over the product of both denominators, whereas division multiplies the first fraction by the reciprocal of the second. The resulting rational expression is subsequently simplified by dividing by the greatest common divisor.