1. **State the problem:** We need to solve the division of the mixed number $2 \frac{1}{7}$ by the fraction $\frac{5}{6}$. 2. **Convert the mixed number to an improper fraction:** $2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{15}{7}$ 3. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{15}{7} \div \frac{5}{6} = \frac{15}{7} \times \frac{6}{5}$$ 4. **Multiply the fractions:** $$\frac{15}{7} \times \frac{6}{5} = \frac{15 \times 6}{7 \times 5} = \frac{90}{35}$$ 5. **Simplify the fraction:** Both numerator and denominator can be divided by 5: $$\frac{90 \div 5}{35 \div 5} = \frac{18}{7}$$ 6. **Convert back to a mixed number:** $$\frac{18}{7} = 2 \frac{4}{7}$$ **Final answer:** $$2 \frac{4}{7}$$