Ответ:

Используем правило: \(a\frac{b}{c}=\frac{ac+b}{c}\).

  1. \(10\frac{2}{9}=\frac{10\cdot9+2}{9}=\frac{92}{9}\).
  2. \(12\frac{1}{6}=\frac{12\cdot6+1}{6}=\frac{73}{6}\).
  3. \(31\frac{2}{3}=\frac{31\cdot3+2}{3}=\frac{95}{3}\).
  4. \(35\frac{4}{9}=\frac{35\cdot9+4}{9}=\frac{319}{9}\).
  5. \(14\frac{2}{7}=\frac{14\cdot7+2}{7}=\frac{100}{7}\).
  6. \(60\frac{5}{8}=\frac{60\cdot8+5}{8}=\frac{485}{8}\).
  7. \(5\frac{6}{9}=\frac{5\cdot9+6}{9}=\frac{51}{9}\).
  8. \(22\frac{2}{4}=\frac{22\cdot4+2}{4}=\frac{90}{4}\).
  9. \(40\frac{7}{9}=\frac{40\cdot9+7}{9}=\frac{367}{9}\).

Ответ: а) \(\frac{92}{9}\); б) \(\frac{73}{6}\); в) \(\frac{95}{3}\); г) \(\frac{319}{9}\); д) \(\frac{100}{7}\); е) \(\frac{485}{8}\); ж) \(\frac{51}{9}\); з) \(\frac{90}{4}\); и) \(\frac{367}{9}\).