Question: Show and solve $\frac{1}{2} + \frac{1}{3}$
1. **State the problem:** We want to find the sum of the fractions $\frac{1}{2}$ 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 each fraction:**
$$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$
$$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$
5. **Add the fractions:**
$$\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}$$
6. **Simplify if possible:** $\frac{5}{6}$ is already in simplest form.
**Final answer:** $$\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$$