Operations with Fractions and Mixed Numbers
To add or subtract fractions, ensure they have a common denominator. For example, to add (\frac{1}{4} + \frac{1}{2}), convert (\frac{1}{2}) to (\frac{2}{4}) so that both fractions have the same denominator. Thus, (\frac{1}{4} + \frac{2}{4} = \frac{3}{4}).
When multiplying fractions, simply multiply the numerators and the denominators. For example, (\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}) in simplest form.
For division, multiply by the reciprocal. For example, (\frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \frac{3}{2} = \frac{9}{8}), which can be expressed as the mixed number (1 \frac{1}{8}).
Always simplify your answers to their lowest terms.
Key points to remember
- Find a common denominator for addition and subtraction.
- Multiply numerators and denominators for multiplication.
- Use the reciprocal for division of fractions.
- Express answers in simplest form.
- Convert improper fractions to mixed numbers when necessary.
Worked example
Add: (\frac{3}{5} + \frac{1}{10})
Convert (\frac{3}{5}) to (\frac{6}{10}): (\frac{6}{10} + \frac{1}{10} = \frac{7}{10}).