To solve \( \frac{7}{8} \div \frac{3}{4} \), you can multiply by the reciprocal of the second fraction:
\[ \frac{7}{8} \div \frac{3}{4} = \frac{7}{8} \times \frac{4}{3} \]
Now, perform the multiplication:
\[ = \frac{7 \times 4}{8 \times 3} = \frac{28}{24} \]
Now, simplify \( \frac{28}{24} \):
\[ = \frac{28 \div 4}{24 \div 4} = \frac{7}{6} \]
Therefore, the answer is:
\(\frac{7}{6}\)