Ответ:

  1. \(4\div\frac{20}{23}+2\frac{4}{15}\cdot\left(\frac{2}{7}-4\frac{11}{14}\right)=4\cdot\frac{23}{20}+\frac{34}{15}\cdot\left(\frac{2}{7}-\frac{67}{14}\right)\).
    \(=\frac{23}{5}+\frac{34}{15}\cdot\left(-\frac{63}{14}\right)=\frac{23}{5}-\frac{51}{5}=-\frac{28}{5}=-5\frac{3}{5}\).
  2. \(3\frac{9}{10}-\left(2-1\frac{11}{35}\right)\div\frac{9}{49}+\frac{1}{2}\).
    \(2-1\frac{11}{35}=2-\frac{46}{35}=\frac{24}{35}\).
    \(\frac{24}{35}\div\frac{9}{49}=\frac{24}{35}\cdot\frac{49}{9}=\frac{56}{15}\).
    \(\frac{39}{10}-\frac{56}{15}+\frac{1}{2}=\frac{117-112+15}{30}=\frac{20}{30}=\frac{2}{3}\).

Ответ: 1) \(-5\frac{3}{5}\); 2) \(\frac{2}{3}\).