1. **State the problem:** 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 $$\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ 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. **Rewrite each fraction with the LCD:** $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$ 5. **Add the numerators:** $$\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}$$ 6. **Simplify if possible:** $\frac{7}{12}$ is already in simplest form. **Final answer:** $$\boxed{\frac{7}{12}}$$