To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
So, to solve \( \frac{5}{6} \div \frac{6}{7} \):
- Take the reciprocal of \( \frac{6}{7} \), which is \( \frac{7}{6} \).
- Multiply \( \frac{5}{6} \) by \( \frac{7}{6} \):
\[ \frac{5}{6} \times \frac{7}{6} = \frac{5 \times 7}{6 \times 6} = \frac{35}{36} \]
Therefore, \( \frac{5}{6} \div \frac{6}{7} = \frac{35}{36} \).