4. Найдите значение выражения: 1) \(\left(-\frac{4}{15} + \frac{14}{25}\right) : \left(-\frac{11}{35}\right)\); 2) \(\left(\frac{3}{14} - \left(-\frac{17}{21}\right)\) : \(\left\)\(-7\frac{1}{6}\right\)\); 3) \(\left(\frac{7}{16} - \left(-\frac{5}{24}\right)\) : \(\left\)\(-1\frac{15}{16}\right\)\); 4) \(-4\frac{1}{7} + 2\frac{1}{4} \cdot \left(-11\frac{2}{9} - (-5,4)\right) : \frac{9}{35}\).

Решение:

1. \(\left(-\frac{4}{15} + \frac{14}{25}\right) : \left(-\frac{11}{35}\right)\)
   \(= \left(-\frac{20}{75} + \frac{42}{75}\right) : \left(-\frac{11}{35}\right)\)
   \(= \frac{22}{75} : \left(-\frac{11}{35}\right)\)
   \(= \frac{22}{75} \times \left(-\frac{35}{11}\right)\)
   \(= -\frac{22 \times 35}{75 \times 11}\)
   \(= -\frac{2 \times 11 \times 5 \times 7}{3 \times 25 \times 11}\)
   \(= -\frac{2 \times 5 \times 7}{3 \times 25}\)
   \(= -\frac{70}{75} = -\frac{14}{15}\)
2. \(\left(\frac{3}{14} - \left(-\frac{17}{21}\right)\) : \(\left\)\(-7\frac{1}{6}\right\)\)
   \(= \left(\frac{3}{14} + \frac{17}{21}\right) : \left(-\frac{43}{6}\right)\)
   \(= \left(\frac{9}{42} + \frac{34}{42}\right) : \left(-\frac{43}{6}\right)\)
   \(= \frac{43}{42} : \left(-\frac{43}{6}\right)\)
   \(= \frac{43}{42} \times \left(-\frac{6}{43}\right)\)
   \(= -\frac{43 \times 6}{42 \times 43}\)
   \(= -\frac{6}{42} = -\frac{1}{7}\)
3. \(\left(\frac{7}{16} - \left(-\frac{5}{24}\right)\) : \(\left\)\(-1\frac{15}{16}\right\)\)
   \(= \left(\frac{7}{16} + \frac{5}{24}\right) : \left(-\frac{31}{16}\right)\)
   \(= \left(\frac{21}{48} + \frac{10}{48}\right) : \left(-\frac{31}{16}\right)\)
   \(= \frac{31}{48} : \left(-\frac{31}{16}\right)\)
   \(= \frac{31}{48} \times \left(-\frac{16}{31}\right)\)
   \(= -\frac{31 \times 16}{48 \times 31}\)
   \(= -\frac{16}{48} = -\frac{1}{3}\)
4. \(-4\frac{1}{7} + 2\frac{1}{4} \cdot \left(-11\frac{2}{9} - (-5,4)\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} + 5,4\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} + \frac{54}{10}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} + \frac{27}{5}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{505}{45} + \frac{243}{45}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{262}{45}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \left(-\frac{9 \times 262}{4 \times 45}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \left(-\frac{262}{4 \times 5}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \left(-\frac{131}{10}\right) : \frac{9}{35}\)
   \(= -\frac{29}{7} + \left(-\frac{131}{10}\right) \times \frac{35}{9}\)
   \(= -\frac{29}{7} - \frac{131 \times 35}{10 \times 9}\)
   \(= -\frac{29}{7} - \frac{131 \times 7}{2 \times 9}\)
   \(= -\frac{29}{7} - \frac{917}{18}\)
   \(= -\frac{29 \times 18}{7 \times 18} - \frac{917 \times 7}{18 \times 7}\)
   \(= -\frac{522}{126} - \frac{6419}{126}\)
   \(= -\frac{6941}{126}\)

Ответ: 1) \(-\frac{14}{15}\); 2) \(-\frac{1}{7}\); 3) \(-\frac{1}{3}\); 4) \(-\frac{6941}{126}\).