About

Intermediate algebra often introduces multi-step equations where order of operations becomes the primary source of error. This tool bridges the gap between simple binary calculations and complex algebraic systems. It solves operations involving four distinct rational numbers (fractions), adhering strictly to the PEMDAS hierarchy (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

Accuracy in fractional arithmetic is critical in fields ranging from carpentry (combining measurements) to chemistry (stoichiometry ratios). A miscalculation in the denominator during an intermediate step can cascade into a significantly incorrect final value. This calculator utilizes BigInt logic to prevent integer overflow during the determination of the Least Common Denominator (LCD) and provides a visual breakdown of the reduction process.

Formulas

The core logic follows the standard arithmetic definition of a rational number Q, where any number can be expressed as pq with q ≠ 0. When combining four terms, the precedence is:

Result = F₁ op₁ F₂ op₂ F₃ op₃ F₄

If multiplication (×) or division (÷) operators are present, they are evaluated before addition (+) or subtraction (−), effectively grouping terms into intermediate results.

Reference Data

Operation	Rule	Visual Formula
Addition	Find LCD, add numerators	ab + cd = ad + bcbd
Subtraction	Find LCD, subtract numerators	ab − cd = ad − bcbd
Multiplication	Multiply across	ab × cd = acbd
Division	Multiply by reciprocal	ab ÷ cd = adbc

Frequently Asked Questions

The calculator adheres to the Order of Operations (PEMDAS). If you entered "1/2 + 1/3 * 1/4", the tool calculates "1/3 * 1/4" first because multiplication has higher precedence than addition. The steps reflect this prioritization to ensure mathematical correctness.

Yes. Negative signs are normalized to the numerator automatically. For example, "1/-2" is treated as "-1/2". This standard form simplifies the internal logic for finding common denominators.

This tool uses JavaScript BigInt primitives, allowing for integer precision well beyond the standard 64-bit float limit (2^53). You can safely calculate with numerators and denominators containing dozens of digits.

The final result is calculated by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). This ensures the output is always in its simplest form (lowest terms).