The Fraction Calculator evaluates arithmetic expressions between two fractions, detailing common denominator steps, greatest common divisor (GCD) simplification, and mixed number conversions.

### Operational Arithmetic Formulas The solver evaluates two input fractions, $a/b$ and $c/d$: - **Addition ($+$)**: $$\frac{a}{b} + \frac{c}{d} = \frac{(a \times d) + (c \times b)}{b \times d}$$ - **Subtraction ($-$)**: $$\frac{a}{b} - \frac{c}{d} = \frac{(a \times d) - (c \times b)}{b \times d}$$ - **Multiplication ($\times$)**: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ - **Division ($\div$)**: $$\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}$$ - **Euclidean GCD Simplification**: Both raw numerator and denominator are divided by their greatest common divisor $\text{GCD}(\text{num}, \text{den})$ to yield lowest irreducible terms.

### Worked Step-by-Step Example Adding $3/4$ and $2/5$: - **Cross-Multiplication for Common Denominator**: $$\text{Raw Numerator} = (3 \times 5) + (2 \times 4) = 15 + 8 = 23$$ $$\text{Raw Denominator} = 4 \times 5 = 20$$ $$\text{Unsimplified Fraction} = \frac{23}{20}$$ - **Reduction**: $\text{GCD}(23, 20) = 1$, meaning $23/20$ is already in lowest irreducible terms. - **Mixed Number Form**: $23 \div 20 = 1$ with a remainder of $3$, yielding $1 \frac{3}{20}$. - **Decimal Representation**: $23 / 20 = 1.15$.

### In-Browser Processing & Privacy Note All arithmetic calculations, greatest common divisor loops, and step-by-step formatting run locally in client-side JavaScript. No math problems or input values are transmitted across external networks.