1. **Problem:** Calculate $\frac{3}{6} \times \frac{1}{4}$. Formula: Multiply numerators and denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. Calculation: $\frac{3}{6} \times \frac{1}{4} = \frac{3 \times 1}{6 \times 4} = \frac{3}{24} = \frac{\cancel{3}^1}{\cancel{24}^8} = \frac{1}{8}$. 2. **Problem:** Find $?$ such that $5 \times ? = 1$. Formula: $? = \frac{1}{5}$. 3. **Problem:** Find $?$ such that $-\frac{2}{5} \times ? = 1$. Formula: $? = \frac{1}{-\frac{2}{5}} = -\frac{5}{2}$. 4. **Problem:** Calculate $\frac{2}{3} \times 3$. Calculation: $\frac{2}{3} \times 3 = \frac{2 \times 3}{3} = \frac{\cancel{6}^2}{\cancel{3}^1} = 2$. 5. **Problem:** Calculate $5 \times \frac{1}{4} \times 2$. Calculation: $5 \times \frac{1}{4} \times 2 = 5 \times \frac{2}{4} = 5 \times \frac{1}{2} = \frac{5}{2}$. 6. **Problem:** Find $?$ such that $? \times \frac{2}{7} = 1$. Formula: $? = \frac{1}{\frac{2}{7}} = \frac{7}{2}$. 7. **Problem:** Calculate $-4 \times \frac{2}{3}$. Calculation: $-4 \times \frac{2}{3} = \frac{-8}{3}$. 8. **Problem:** Calculate $-\frac{1}{8} \times -2$. Calculation: $-\frac{1}{8} \times -2 = \frac{2}{8} = \frac{1}{4}$. 9. **Problem:** Find the reciprocal of $\frac{1}{5}$. Answer: $5$. 10. **Problem:** Find $?$ such that $\frac{1}{5} \times ? = \frac{3}{5}$. Calculation: $? = \frac{\frac{3}{5}}{\frac{1}{5}} = \frac{3}{5} \times \frac{5}{1} = 3$. 11. **Problem:** Calculate $-\left(\frac{2}{3}\right)^2$. Calculation: $-\left(\frac{2}{3}\right)^2 = -\frac{4}{9}$. 12. **Problem:** Find $?$ such that $\frac{3}{5} \times ? = 1$. Formula: $? = \frac{1}{\frac{3}{5}} = \frac{5}{3}$. 13. **Problem:** Find $?$ such that $\frac{3}{8} \times ? = \frac{12}{32}$. Simplify $\frac{12}{32} = \frac{3}{8}$. Calculation: $? = \frac{\frac{3}{8}}{\frac{3}{8}} = 1$. 14. **Problem:** Calculate $1 \frac{1}{2} \times \frac{1}{2}$. Convert mixed number: $1 \frac{1}{2} = \frac{3}{2}$. Calculation: $\frac{3}{2} \times \frac{1}{2} = \frac{3}{4}$. 15. **Problem:** Calculate $\frac{1}{3}$ of $18$. Calculation: $\frac{1}{3} \times 18 = 6$. 16. **Problem:** Find $?$ such that $12 \times ? = \frac{12}{5}$. Formula: $? = \frac{\frac{12}{5}}{12} = \frac{12}{5} \times \frac{1}{12} = \frac{1}{5}$. 17. **Problem:** Calculate $\left(\frac{4}{3}\right)^2$. Calculation: $\frac{16}{9}$. 18. **Problem:** Calculate $4 \times \frac{1}{4}$. Calculation: $1$. 19. **Problem:** Calculate $\left(-\frac{1}{5}\right)^2$. Calculation: $\frac{1}{25}$. 20. **Problem:** Find $?$ such that $-\frac{3}{8} \times ? = \frac{6}{8}$. Formula: $? = \frac{\frac{6}{8}}{-\frac{3}{8}} = \frac{6}{8} \times \frac{8}{-3} = -2$. 21. **Problem:** Calculate $2 \frac{1}{3} \times \frac{1}{5}$. Convert mixed number: $2 \frac{1}{3} = \frac{7}{3}$. Calculation: $\frac{7}{3} \times \frac{1}{5} = \frac{7}{15}$. 22. **Problem:** Calculate $-\frac{2}{3} \times -\frac{1}{6} \times \frac{3}{4}$. Calculation: $\frac{2}{3} \times \frac{1}{6} \times \frac{3}{4} = \frac{2 \times 1 \times 3}{3 \times 6 \times 4} = \frac{6}{72} = \frac{1}{12}$. 23. **Problem:** Calculate $-\frac{1}{4} \times -\frac{2}{3}$. Calculation: $\frac{2}{12} = \frac{1}{6}$. 24. **Problem:** Calculate $\frac{2}{3}$ of $\frac{1}{4}$. Calculation: $\frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$. 25. **Problem:** Calculate $\frac{2}{5}$ of $25$. Calculation: $\frac{2}{5} \times 25 = 10$. 26. **Problem:** Find the reciprocal of $3$. Answer: $\frac{1}{3}$. 27. **Problem:** Calculate $6 \times 1 \frac{1}{5}$. Convert mixed number: $1 \frac{1}{5} = \frac{6}{5}$. Calculation: $6 \times \frac{6}{5} = \frac{36}{5}$. 28. **Problem:** Find the reciprocal of $\frac{2}{4}$. Simplify $\frac{2}{4} = \frac{1}{2}$. Answer: $2$. **Final answers:** 1) $\frac{1}{8}$ 2) $\frac{1}{5}$ 3) $-\frac{5}{2}$ 4) $2$ 5) $\frac{5}{2}$ 6) $\frac{7}{2}$ 7) $-\frac{8}{3}$ 8) $\frac{1}{4}$ 9) $5$ 10) $3$ 11) $-\frac{4}{9}$ 12) $\frac{5}{3}$ 13) $1$ 14) $\frac{3}{4}$ 15) $6$ 16) $\frac{1}{5}$ 17) $\frac{16}{9}$ 18) $1$ 19) $\frac{1}{25}$ 20) $-2$ 21) $\frac{7}{15}$ 22) $\frac{1}{12}$ 23) $\frac{1}{6}$ 24) $\frac{1}{6}$ 25) $10$ 26) $\frac{1}{3}$ 27) $\frac{36}{5}$ 28) $2$