Fraction Calculation Formulas

Mathematics & Education Formula • Published on September 01, 2026 • Last updated September 01, 2026

Mathematical Equation

$$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}, \quad \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}, \quad \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$$

Variable Definitions

a, c

Numerators of input fractions

b, d

Denominators of input fractions (b, d ≠ 0)

Detailed Explanation

In-Depth Guide

Fraction arithmetic rules govern addition, subtraction, multiplication, and division of rational numbers by finding common denominators or multiplying numerators and denominators directly.

How to Calculate: Step-by-Step

1. Addition/Subtraction: Cross-multiply numerators with opposite denominators and combine over the product of denominators. 2. Multiplication: Multiply top numbers together and bottom numbers together. 3. Division: Multiply the first fraction by the reciprocal (flip) of the second fraction.

Worked Calculation Example

Add 1/2 and 2/3: - (1×3 + 2×2) / (2×3) = (3 + 4) / 6 = 7/6 = 1 1/6.

Common Use Cases

Algebraic simplification
Cooking recipe scaling
Construction measurements

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