How fraction calculations work
Fractions represent parts of a whole. Adding, subtracting, multiplying, and dividing fractions follow standard rules:
- **Addition/Subtraction:** Find a common denominator, convert both numerators, perform addition or subtraction, and reduce the output. E.g. \(\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}\).
- **Multiplication:** Multiply both numerators and multiply both denominators. E.g. \(\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\).
- **Division:** Multiply the first fraction by the reciprocal (flip) of the second fraction. E.g. \(\frac{1}{2} \div \frac{1}{3} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2}\).