1. **State the problem:** Calculate the sum of $\frac{1}{2}$ and $\frac{1}{3}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ is given by: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ 3. **Find the common denominator:** The denominators are 2 and 3. The least common denominator (LCD) is 6. 4. **Convert fractions:** $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$ $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$ 5. **Add the fractions:** $$\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}$$ 6. **Final answer:** $$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$$