Ответ:

  1. \(2\frac12\left(\frac2{15}-3\frac56\right)+\frac14=\frac52\left(\frac2{15}-\frac{23}6\right)+\frac14=\frac52\cdot\left(-\frac{109}{30}\right)+\frac14=-\frac{217}{24}\).
  2. \(-1\frac17\left(\frac45+\frac{19}{20}\right)\left(6\frac56+4\frac23\right)=-\frac87\cdot\frac74\cdot\frac{69}{6}=-23\).
  3. \(\left(6\frac38-2\frac34\right)(-4)+\frac7{18}\cdot9=\frac{29}{8}(-4)+\frac72=-\frac{51}{8}\).
  4. \(9\frac16:(4\frac13-8)+24\cdot\frac38=\frac{55}{6}:\left(-\frac{11}{3}\right)+9=-\frac52+9=\frac{13}{2}\).

Жауабы: 1) \(-\frac{217}{24}\); 2) −23; 3) \(-\frac{51}{8}\); 4) \(\frac{13}{2}\).