1. Evaluate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$. - First, calculate $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$. - Then sum inside parentheses: $\frac{8}{5} + \frac{9}{2} = \frac{16}{10} + \frac{45}{10} = \frac{61}{10}$. - Finally, $12 - \frac{61}{10} = \frac{120}{10} - \frac{61}{10} = \frac{59}{10} = 5.9$. 2. Evaluate $\left(\frac{9}{2} + \frac{5}{2}\right) \div \frac{11}{2} \div \frac{1}{5}$. - Sum numerator: $\frac{9}{2} + \frac{5}{2} = \frac{14}{2} = 7$. - Division: $7 \div \frac{11}{2} = 7 \times \frac{2}{11} = \frac{14}{11}$. - Then divide by $\frac{1}{5}$: $\frac{14}{11} \div \frac{1}{5} = \frac{14}{11} \times 5 = \frac{70}{11} \approx 6.3636$. 3. Evaluate $5^{\frac{2}{3} + 1 + \frac{1}{3}}$. - Sum exponents: $\frac{2}{3} + 1 + \frac{1}{3} = \frac{2}{3} + \frac{3}{3} + \frac{1}{3} = 2$. - So, $5^2 = 25$. 6. Evaluate $\frac{11}{2} + \frac{9}{2} - (3 - 2)$. - Sum fractions: $\frac{11}{2} + \frac{9}{2} = \frac{20}{2} = 10$. - Parentheses: $3 - 2 = 1$. - Result: $10 - 1 = 9$. 7. Evaluate $10 + 4 - \frac{3}{2} - \frac{9}{2}$. - Sum integers: $10 + 4 = 14$. - Sum fractions: $\frac{3}{2} + \frac{9}{2} = \frac{12}{2} = 6$. - Result: $14 - 6 = 8$. 8. Evaluate $4^{\frac{2}{3}} \times 5 \times 1$. - $4^{\frac{2}{3}} = \left(4^{\frac{1}{3}}\right)^2 = (\sqrt[3]{4})^2$. - Approximate $\sqrt[3]{4} \approx 1.5874$, so $1.5874^2 \approx 2.52$. - Multiply: $2.52 \times 5 \times 1 = 12.6$. 11. Evaluate $4 - \frac{4}{3} \times \frac{5}{4} + \frac{11}{6}$. - Multiply: $\frac{4}{3} \times \frac{5}{4} = \frac{20}{12} = \frac{5}{3}$. - Expression: $4 - \frac{5}{3} + \frac{11}{6}$. - Convert to common denominator 6: $4 = \frac{24}{6}$, $\frac{5}{3} = \frac{10}{6}$. - Sum: $\frac{24}{6} - \frac{10}{6} + \frac{11}{6} = \frac{25}{6} \approx 4.1667$. 12. Evaluate $\left(\frac{11}{3} - \frac{7}{3} + 2\right) \div \frac{2}{5}$. - Inside parentheses: $\frac{11}{3} - \frac{7}{3} = \frac{4}{3}$. - Add 2: $\frac{4}{3} + 2 = \frac{4}{3} + \frac{6}{3} = \frac{10}{3}$. - Divide by $\frac{2}{5}$: $\frac{10}{3} \times \frac{5}{2} = \frac{50}{6} = \frac{25}{3} \approx 8.3333$. 13. Evaluate $1 - 1 + 8 - \frac{2}{5}$. - Simplify: $1 - 1 = 0$. - Expression: $0 + 8 - \frac{2}{5} = 8 - \frac{2}{5} = \frac{40}{5} - \frac{2}{5} = \frac{38}{5} = 7.6$. Final answers: 1. $\frac{59}{10}$ or 5.9 2. $\frac{70}{11}$ or approx. 6.3636 3. 25 6. 9 7. 8 8. approx. 12.6 11. $\frac{25}{6}$ or approx. 4.1667 12. $\frac{25}{3}$ or approx. 8.3333 13. $\frac{38}{5}$ or 7.6