To add the fractions \( \frac{1}{4} \) and \( \frac{1}{6} \), we need to find a common denominator. The least common multiple (LCM) of 4 and 6 is 12.
Next, we convert each fraction to have the common denominator of 12:
\[ \frac{1}{4} = \frac{3}{12} \quad \text{(because } 1 \times 3 = 3 \text{ and } 4 \times 3 = 12\text{)} \]
\[ \frac{1}{6} = \frac{2}{12} \quad \text{(because } 1 \times 2 = 2 \text{ and } 6 \times 2 = 12\text{)} \]
Now, we can add the two fractions:
\[ \frac{3}{12} + \frac{2}{12} = \frac{3 + 2}{12} = \frac{5}{12} \]
Thus, \( \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \).