7. Амалдарды орындаңдар. 1) \(2\frac{1}{2}\cdot\left(\frac{2}{15}-3\frac{5}{6}\right)+\frac14\); 2) \(-1\frac17\cdot\left(\frac45+\frac{19}{20}\right)\cdot\left(6\frac56+4\frac23\right)\); 3) \(\left(6\frac38-2\frac34\right)\cdot(-4)+\frac7{18}\cdot9\); 4) \(9\frac16:\left(4\frac13-8\right)+24\cdot\frac38\).

1. \(2\frac12=\frac52\), \(3\frac56=\frac{23}{6}\).
   \(\frac{2}{15}-\frac{23}{6}=\frac{4-115}{30}=-\frac{111}{30}=-\frac{37}{10}\).
   \(\frac52\cdot\left(-\frac{37}{10}\right)+\frac14=-\frac{37}{4}+\frac14=-\frac{36}{4}=-9\).
2. \(-1\frac17=-\frac87\), \(\frac45+\frac{19}{20}=\frac{16}{20}+\frac{19}{20}=\frac74\).
   \(6\frac56=\frac{41}{6}\), \(4\frac23=\frac{14}{3}=\frac{28}{6}\), поэтому \(6\frac56+4\frac23=\frac{69}{6}=\frac{23}{2}\).
   \(-\frac87\cdot\frac74\cdot\frac{23}{2}=-2\cdot\frac{23}{2}=-23\).
3. \(6\frac38-2\frac34=\frac{51}{8}-\frac{22}{8}=\frac{29}{8}\).
   \(\frac{29}{8}\cdot(-4)+\frac7{18}\cdot9=-\frac{29}{2}+\frac72=-\frac{22}{2}=-11\).
4. \(9\frac16=\frac{55}{6}\), \(4\frac13-8=\frac{13}{3}-\frac{24}{3}=-\frac{11}{3}\).
   \(\frac{55}{6}:\left(-\frac{11}{3}\right)=-\frac52\), а \(24\cdot\frac38=9\).
   \(-\frac52+9=\frac{13}{2}\).

Ответ: 1) \(-9\); 2) \(-23\); 3) \(-11\); 4) \(\frac{13}{2}\).