Ответ:

  1. \(15\frac49-4\frac49\cdot3\frac38=\frac{139}{9}-\frac{40}{9}\cdot\frac{27}{8}=\frac{139}{9}-15=\frac49\).
  2. \(\frac{81}{88}\left(6-1\frac{13}{15}\cdot1\frac{19}{21}\right)=\frac{81}{88}\left(6-\frac{28}{15}\cdot\frac{40}{21}\right)=\frac{81}{88}(6-\frac{16}{9})=\frac{81}{88}\cdot\frac{38}{9}=\frac{171}{44}\).
  3. \(\left(5\frac1{16}-1\frac18\right)\left(\frac56+\frac3{14}\right)=\left(\frac{81}{16}-\frac98\right)\left(\frac56+\frac3{14}\right)=\frac{63}{16}\cdot\frac{22}{21}=\frac{33}{8}=4\frac18\).
  4. \(5\frac1{16}-1\frac18\left(\frac56+\frac3{14}\right)=\frac{81}{16}-\frac98\cdot\frac{22}{21}=\frac{81}{16}-\frac{33}{28}=\frac{501}{112}=4\frac{53}{112}\).

Ответ: 1) \(\frac49\); 2) \(\frac{171}{44}\); 3) 4\(\frac18\); 4) 4\(\frac{53}{112}\).