Complex Fraction Calculator with Parentheses

Precise calculation of rational expressions is fundamental in fields ranging from carpentry to structural engineering. Errors often arise not from the arithmetic itself but from the incorrect application of operator precedence when mixing fractional values with integers and grouping symbols. A standard calculator forces decimal conversion which introduces rounding errors. This tool maintains values in their rational form throughout the computation.

The calculator utilizes a parsing algorithm to respect the strict hierarchy of mathematical operations. It processes parentheses first, followed by exponents, multiplication and division from left to right, and finally addition and subtraction. This ensures that an expression like 12 ÷ 14 returns 2 rather than 0.125. It supports mixed numbers and improper fractions simultaneously.

The core logic relies on finding the Least Common Multiple (LCM) for addition and subtraction of unlike denominators. For any two fractions ab and cd, the sum is calculated as:

Division is handled by multiplying the first fraction by the reciprocal of the second: