➗ Exact Rational Arithmetic
Fraction Calculator & Reducer
Add, subtract, multiply, and divide fractions with step-by-step GCD reductions and mixed number outputs.
Sample Fractions:
3/4 + 1/2
5/8 × 2/3
7/3 − 5/6
9/4 ÷ 3/2
Exact Solution
5/4 = 1 ¼
Equivalent Representations:
Simplified Fraction
5/4
Mixed Number
1 ¼
Decimal Value
1.25
Percentage
125%
Rules of Rational Fraction Arithmetic
A fraction $\frac{a}{b}$ represents the exact quotient of two integers (where $b \neq 0$).
- Addition & Subtraction: Requires a common denominator: $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$.
- Multiplication: Multiply numerators and denominators straight across: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$.
- Division: Multiply by the inverted divisor reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$.