1. The problem involves finding the sum of two fractions: $\frac{1}{2}$ and $\frac{1}{3}$.\n\n2. To add fractions, we need a common denominator. The denominators are 2 and 3, so the least common denominator (LCD) is 6.\n\n3. Convert each fraction to an equivalent fraction with denominator 6:\n$$\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}$$\n\n4. Now add the numerators while keeping the denominator the same:\n$$\frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}$$\n\n5. The final answer is $\frac{5}{6}$.\n\nThis shows how to add fractions by finding a common denominator and summing the numerators.