Ответ:

  1. \(\frac{5}{16}\cdot\frac{8}{15}=\frac{1}{6}\).
  2. \(-\frac{7}{11}\cdot\frac{55}{84}=-\frac{5}{12}\).
  3. \(\frac{17}{23}\cdot\left(-\frac{69}{34}\right)=-\frac{3}{2}\).
  4. \(2\frac{1}{3}\cdot1\frac{13}{35}=\frac{7}{3}\cdot\frac{48}{35}=\frac{16}{5}=3\frac{1}{5}\).
  5. \(-4\frac{1}{2}\cdot1\frac{1}{3}=-\frac{9}{2}\cdot\frac{4}{3}=-6\).
  6. \(-3\frac{1}{8}\cdot1\frac{3}{5}=-\frac{25}{8}\cdot\frac{8}{5}=-5\).
  7. \(\frac{5}{9}\div\left(-\frac{10}{27}\right)=\frac{5}{9}\cdot\left(-\frac{27}{10}\right)=-\frac{3}{2}\).
  8. \(-\frac{3}{5}\div\left(-2\frac{1}{10}\right)=-\frac{3}{5}\div\left(-\frac{21}{10}\right)=\frac{2}{7}\).
  9. \(41\frac{1}{3}\div3\frac{1}{41}=\frac{124}{3}\div\frac{124}{41}=\frac{41}{3}=13\frac{2}{3}\).
  10. \(\frac{7}{9}\cdot(-9)=-7\).
  11. \(-\frac{3}{5}\div7=-\frac{3}{35}\).
  12. \(-10\div\left(-1\frac{3}{7}\right)=-10\div\left(-\frac{10}{7}\right)=7\).

Ответ: 1) \(\frac{1}{6}\); 2) \(-\frac{5}{12}\); 3) \(-1\frac{1}{2}\); 4) \(3\frac{1}{5}\); 5) \(-6\); 6) \(-5\); 7) \(-1\frac{1}{2}\); 8) \(\frac{2}{7}\); 9) \(13\frac{2}{3}\); 10) \(-7\); 11) \(-\frac{3}{35}\); 12) \(7\).