1. **State the problem:** Add the fractions $\frac{1}{8}$ and $\frac{3}{4}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum is given by $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$. 3. **Find a common denominator:** The denominators are 8 and 4. The least common denominator (LCD) is 8. 4. **Convert fractions:** $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$. 5. **Add the fractions:** $\frac{1}{8} + \frac{6}{8} = \frac{1+6}{8} = \frac{7}{8}$. 6. **Final answer:** The sum is $\frac{7}{8}$.