To divide fractions, you multiply by the reciprocal of the divisor. So to divide \( \frac{5}{8} \) by \( \frac{3}{4} \), you can rewrite it as follows:
\[ \frac{5}{8} \div \frac{3}{4} = \frac{5}{8} \times \frac{4}{3} \]
Now, multiply the numerators and the denominators:
\[ = \frac{5 \times 4}{8 \times 3} = \frac{20}{24} \]
Next, simplify \( \frac{20}{24} \). Both the numerator and the denominator can be divided by 4:
\[ \frac{20 \div 4}{24 \div 4} = \frac{5}{6} \]
So, \( \frac{5}{8} \div \frac{3}{4} = \frac{5}{6} \).