1. **State the problem:** We need to add the fractions $\frac{1}{3}$ and $\frac{1}{4}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula is: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers and $b, d \neq 0$. 3. **Find the common denominator:** The denominators are 3 and 4. The least common denominator (LCD) is 12. 4. **Convert each fraction:** $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ 5. **Add the fractions:** $$\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}$$ 6. **Final answer:** The sum of $\frac{1}{3}$ and $\frac{1}{4}$ is $\frac{7}{12}$.