To add and simplify the fractions \( \frac{3}{4} + \frac{2}{3} + \frac{1}{8} \), you need a common denominator. The least common denominator for 4, 3, and 8 is 24.
\[ \frac{3}{4} \times \frac{6}{6} + \frac{2}{3} \times \frac{8}{8} + \frac{1}{8} \times \frac{3}{3} \]
This gives you:
\[ \frac{18}{24} + \frac{16}{24} + \frac{3}{24} \]
Combine the numerators:
\[ \frac{18 + 16 + 3}{24} \]
Simplify the numerator:
\[ \frac{37}{24} \]
So, \( \frac{3}{4} + \frac{2}{3} + \frac{1}{8} \) simplifies to \( \frac{37}{24} \).