Ответ:

  1. \(2\frac14+3\frac23=\frac94+\frac{11}{3}=\frac{51}{12}=\frac{17}{4}\).
    \(8\frac12-1\frac25=\frac{17}{2}-\frac75=\frac{71}{10}\), а \(1,2=\frac65\).
    \(\frac{17}{4}:\frac{71}{10}\cdot\frac65=\frac{17}{4}\cdot\frac{10}{71}\cdot\frac65=\frac{51}{71}\).
  2. \(1\frac{9}{16}\cdot3\frac15=\frac{25}{16}\cdot\frac{16}{5}=5\).
    \(9:2\frac25=9:\frac{12}{5}=\frac{15}{4}\).
    Числитель: \(5+1\frac23-\frac{15}{4}=5+\frac53-\frac{15}{4}=\frac{17}{12}\).
    Знаменатель: \(17\frac{7}{12}-6\frac13=\frac{211}{12}-\frac{76}{12}=\frac{135}{12}=\frac{45}{4}\).
    \(\frac{17}{12}:\frac{45}{4}=\frac{17}{12}\cdot\frac4{45}=\frac{17}{135}\).

Ответ: 1) \(\frac{51}{71}\); 2) \(\frac{17}{135}\).