1. **State the problem:** Add the fractions $\frac{1}{8}$ and $\frac{1}{16}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum is given by $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$. 3. **Find the common denominator:** The denominators are 8 and 16. The least common denominator (LCD) is 16. 4. **Convert fractions:** Convert $\frac{1}{8}$ to have denominator 16: $$\frac{1}{8} = \frac{1 \times 2}{8 \times 2} = \frac{2}{16}$$ 5. **Add the fractions:** $$\frac{2}{16} + \frac{1}{16} = \frac{2 + 1}{16} = \frac{3}{16}$$ 6. **Final answer:** The sum of $\frac{1}{8}$ and $\frac{1}{16}$ is $\frac{3}{16}$.