To divide fractions, you multiply by the reciprocal of the second fraction.
So, \( \frac{5}{6} \div \frac{6}{7} \) can be rewritten as:
\[ \frac{5}{6} \times \frac{7}{6} \]
Now, multiply the numerators and the denominators:
\[ \frac{5 \times 7}{6 \times 6} = \frac{35}{36} \]
Thus, \( \frac{5}{6} \div \frac{6}{7} = \frac{35}{36} \).