Operations with Fractions
Fraction Operations: A Simple Guide
Addition
When adding fractions, you must first find a common denominator. For example, to add
$$\frac{1}{2} + \frac{1}{3} = \frac{1\times3}{2\times3} + \frac{1\times2}{3\times2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$
Subtraction
Subtracting fractions also requires a common denominator. For instance:
$$\frac{3}{4} - \frac{1}{6} = \frac{3\times3}{4\times3} - \frac{1\times2}{6\times2} = \frac{9}{12} - \frac{2}{12} = \frac{7}{12}$$
Multiplication
Multiplying fractions is straightforward: multiply the numerators together and the denominators together. For example:
$$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$
No common denominator is required.
Division
Dividing fractions means multiplying by the reciprocal. For example, note that the reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\); thus:
$$\frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1} = \frac{28}{8} = \frac{7}{2}$$
