1. **Ordering numbers from greatest to least:** The numbers are $2$, $-5$, $|-3|$, $1$, and $-2$. 2. Calculate the absolute value: $|-3| = 3$. 3. Now the list is $2$, $-5$, $3$, $1$, $-2$. 4. Order from greatest to least: $3$, $2$, $1$, $-2$, $-5$. --- 5. **Calculate** $\frac{1}{2} + \left(-1 - \left(\frac{2}{3} - \frac{1}{2}\right)\right)$. 6. Simplify inside the parentheses: $\frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6} = \frac{1}{6}$. 7. Then: $-1 - \frac{1}{6} = -\frac{6}{6} - \frac{1}{6} = -\frac{7}{6}$. 8. Finally: $\frac{1}{2} + \left(-\frac{7}{6}\right) = \frac{3}{6} - \frac{7}{6} = -\frac{4}{6} = -\frac{2}{3}$. --- 9. **Calculate** $\left(-\frac{9}{10}\right) \times (-15) \times \left(-\frac{2}{3}\right) \times (-1)$. 10. Multiply stepwise: $\left(-\frac{9}{10}\right) \times (-15) = \frac{135}{10} = 13.5$. $13.5 \times \left(-\frac{2}{3}\right) = -9$. $-9 \times (-1) = 9$. --- 11. **Calculate** $0.5 \div \left(-\frac{3}{4}\right) \times 12 \div \left(-\frac{5}{7}\right)$. 12. Convert $0.5$ to fraction: $\frac{1}{2}$. 13. Division by a fraction is multiplication by its reciprocal: $\frac{1}{2} \times \left(-\frac{4}{3}\right) \times 12 \times \left(-\frac{7}{5}\right)$. 14. Multiply stepwise: $\frac{1}{2} \times \left(-\frac{4}{3}\right) = -\frac{2}{3}$. $-\frac{2}{3} \times 12 = -8$. $-8 \times \left(-\frac{7}{5}\right) = \frac{56}{5} = 11.2$. --- **Final answers:** - Ordered numbers: $3$, $2$, $1$, $-2$, $-5$. - Problem 10: $-\frac{2}{3}$. - Problem 11: $9$. - Problem 12: $\frac{56}{5}$ or $11.2$.