1. Multiply $\frac{1}{2} \times 1 \frac{1}{10}$. Convert mixed number to improper fraction: $1 \frac{1}{10} = \frac{11}{10}$. Multiply fractions: $\frac{1}{2} \times \frac{11}{10} = \frac{1 \times 11}{2 \times 10} = \frac{11}{20}$. 2. Multiply $4 \frac{1}{3} \times \frac{7}{9}$. Convert mixed number: $4 \frac{1}{3} = \frac{13}{3}$. Multiply: $\frac{13}{3} \times \frac{7}{9} = \frac{13 \times 7}{3 \times 9} = \frac{91}{27} = 3 \frac{10}{27}$. 3. Multiply $\frac{7}{8} \times \frac{6}{4}$. Simplify $\frac{6}{4} = \frac{3}{2}$. Multiply: $\frac{7}{8} \times \frac{3}{2} = \frac{21}{16} = 1 \frac{5}{16}$. 4. Multiply $3 \frac{1}{2} \times 1 \frac{1}{8}$. Convert: $3 \frac{1}{2} = \frac{7}{2}$, $1 \frac{1}{8} = \frac{9}{8}$. Multiply: $\frac{7}{2} \times \frac{9}{8} = \frac{63}{16} = 3 \frac{15}{16}$. 5. Multiply $6 \frac{1}{4} \times 2 \frac{2}{3}$. Convert: $6 \frac{1}{4} = \frac{25}{4}$, $2 \frac{2}{3} = \frac{8}{3}$. Multiply: $\frac{25}{4} \times \frac{8}{3} = \frac{200}{12} = \frac{50}{3} = 16 \frac{2}{3}$. 6. Multiply $9 \frac{1}{3} \times 2 \frac{1}{4}$. Convert: $9 \frac{1}{3} = \frac{28}{3}$, $2 \frac{1}{4} = \frac{9}{4}$. Multiply: $\frac{28}{3} \times \frac{9}{4} = \frac{252}{12} = 21$. 7. Multiply $7 \frac{1}{2} \times 2 \frac{5}{6}$. Convert: $7 \frac{1}{2} = \frac{15}{2}$, $2 \frac{5}{6} = \frac{17}{6}$. Multiply: $\frac{15}{2} \times \frac{17}{6} = \frac{255}{12} = 21 \frac{1}{4}$. 8. Multiply $3 \frac{1}{8} \times 1 \frac{3}{10}$. Convert: $3 \frac{1}{8} = \frac{25}{8}$, $1 \frac{3}{10} = \frac{13}{10}$. Multiply: $\frac{25}{8} \times \frac{13}{10} = \frac{325}{80} = 4 \frac{5}{16}$. 9. Multiply $3 \frac{7}{10} \times 4 \frac{1}{6}$. Convert: $3 \frac{7}{10} = \frac{37}{10}$, $4 \frac{1}{6} = \frac{25}{6}$. Multiply: $\frac{37}{10} \times \frac{25}{6} = \frac{925}{60} = 15 \frac{25}{60} = 15 \frac{5}{12}$. 10. Multiply $6 \frac{1}{6} \times 4 \frac{1}{3}$. Convert: $6 \frac{1}{6} = \frac{37}{6}$, $4 \frac{1}{3} = \frac{13}{3}$. Multiply: $\frac{37}{6} \times \frac{13}{3} = \frac{481}{18} = 26 \frac{13}{18}$. 11. Multiply $15 \frac{3}{4} \times 2 \frac{4}{9}$. Convert: $15 \frac{3}{4} = \frac{63}{4}$, $2 \frac{4}{9} = \frac{22}{9}$. Multiply: $\frac{63}{4} \times \frac{22}{9} = \frac{1386}{36} = 38 \frac{18}{36} = 38 \frac{1}{2}$. 12. Multiply $2 \frac{7}{9} \times 2 \frac{7}{10}$. Convert: $2 \frac{7}{9} = \frac{25}{9}$, $2 \frac{7}{10} = \frac{27}{10}$. Multiply: $\frac{25}{9} \times \frac{27}{10} = \frac{675}{90} = 7 \frac{1}{2}$. 13. Multiply $9 \frac{1}{8} \times 5 \frac{1}{8}$. Convert: $9 \frac{1}{8} = \frac{73}{8}$, $5 \frac{1}{8} = \frac{41}{8}$. Multiply: $\frac{73}{8} \times \frac{41}{8} = \frac{2993}{64} = 46 \frac{49}{64}$. 14. Multiply $6 \frac{3}{10} \times 2 \frac{1}{5}$. Convert: $6 \frac{3}{10} = \frac{63}{10}$, $2 \frac{1}{5} = \frac{11}{5}$. Multiply: $\frac{63}{10} \times \frac{11}{5} = \frac{693}{50} = 13 \frac{43}{50}$. 15. Multiply $3 \frac{2}{3} \times \frac{3}{22}$. Convert: $3 \frac{2}{3} = \frac{11}{3}$. Multiply: $\frac{11}{3} \times \frac{3}{22} = \frac{33}{66} = \frac{1}{2}$. Final answers for first problem: $\frac{11}{20}, 3 \frac{10}{27}, 1 \frac{5}{16}, 3 \frac{15}{16}, 16 \frac{2}{3}, 21, 21 \frac{1}{4}, 4 \frac{5}{16}, 15 \frac{5}{12}, 26 \frac{13}{18}, 38 \frac{1}{2}, 7 \frac{1}{2}, 46 \frac{49}{64}, 13 \frac{43}{50}, \frac{1}{2}$.