Compute $\frac{1}{2} + \frac{1}{3}$.

How we read your problem

Exact arithmetic with fractions (results kept in lowest terms).

Step-by-step solution

1. 1

   Rewrite both fractions with the least common denominator

   The LCD of 2 and 3 is 6.

   $$\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6}$$
2. 2

   Add the numerators and keep the denominator

   $$\frac{3 + 2}{6} = \frac{5}{6}$$
3. 3

   Final answer in lowest terms

   $$\frac{5}{6}$$

Formulas used

• Addition

  $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

• Multiplication

  $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$

• Division

  $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$

Fractions are combined over a common denominator for addition and subtraction, multiplied straight across, and divided by multiplying by the reciprocal. The result is reduced by the greatest common factor.

Verification

• Decimal check: 5/6 ≈ 0.8333333333