1. **Problem 1:** Calculate $2 \frac{3}{4} \div \left(\frac{6}{8} - \frac{1}{4}\right) + 1 - 2$. 2. Convert mixed number to improper fraction: $2 \frac{3}{4} = \frac{11}{4}$. 3. Simplify inside parentheses: $\frac{6}{8} - \frac{1}{4} = \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$. 4. Division of fractions: $\frac{11}{4} \div \frac{1}{2} = \frac{11}{4} \times \frac{2}{1} = \frac{22}{4} = \frac{11}{2}$. 5. Add and subtract: $\frac{11}{2} + 1 - 2 = \frac{11}{2} + \frac{2}{2} - \frac{4}{2} = \frac{11 + 2 - 4}{2} = \frac{9}{2} = 4 \frac{1}{2}$. 6. **Problem 2:** Calculate $1 \frac{1}{2} \div \left(\frac{1}{3} + \frac{5}{6}\right) + 2$. 7. Convert mixed number: $1 \frac{1}{2} = \frac{3}{2}$. 8. Simplify inside parentheses: $\frac{1}{3} + \frac{5}{6} = \frac{2}{6} + \frac{5}{6} = \frac{7}{6}$. 9. Division of fractions: $\frac{3}{2} \div \frac{7}{6} = \frac{3}{2} \times \frac{6}{7} = \frac{18}{14} = \frac{9}{7}$. 10. Add 2: $\frac{9}{7} + 2 = \frac{9}{7} + \frac{14}{7} = \frac{23}{7} = 3 \frac{2}{7}$. 11. **Problem 3:** Calculate $\frac{1}{5} + \left(\frac{2}{2} \times \frac{2}{2}\right) \div 5$. 12. Simplify multiplication inside parentheses: $\frac{2}{2} \times \frac{2}{2} = 1 \times 1 = 1$. 13. Division: $1 \div 5 = \frac{1}{5}$. 14. Add: $\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$. **Final answers:** - Problem 1: $4 \frac{1}{2}$ - Problem 2: $3 \frac{2}{7}$ - Problem 3: $\frac{2}{5}$