Addition
\(\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\) - Find common denominator, then add numerators
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Fraction Calculator
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Fraction Operations
Fraction operations follow specific rules for each mathematical operation.
Key Points:
- Always simplify fractions to lowest terms
- Denominators cannot be zero
- For division, the second fraction cannot have zero numerator
- Find common denominators for addition and subtraction
\(\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}\)
Worked Examples
Subtraction
\(\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}\) - Find common denominator, then subtract numerators
Multiplication
\(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\) - Multiply numerators and denominators
Division
\(\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}\) - Multiply by the reciprocal of the second fraction
Example: 1/4 + 1/3
\(\frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}\)
Example: 2/3 × 3/4
\(\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}\)