4. Найдите значение выражения: 1) (-4/15 + 14/25) : (-11/35); 2) (3/14 - (-17/21)) : (-7 1/6); 3) (7/16 - (-5/24)) : (-1 15/16); 4) -4 1/7 + 2 1/4 · (-11 2/9 - (-5,4) : 9/35).

Решение:

1. • \[ \left(-\frac{4}{15} + \frac{14}{25}\right) : \left(-\frac{11}{35}\right) \]
   • \[ \left(-\frac{20}{75} + \frac{42}{75}\right) : \left(-\frac{11}{35}\right) \]
   • \[ \frac{22}{75} : \left(-\frac{11}{35}\right) \]
   • \[ \frac{22}{75} \cdot \left(-\frac{35}{11}\right) = -\frac{22 \cdot 35}{75 \cdot 11} = -\frac{(2 \cdot 11) \cdot (5 \cdot 7)}{(3 \cdot 25) \cdot 11} = -\frac{2 \cdot 5 \cdot 7}{3 \cdot 25} = -\frac{2 \cdot 7}{3 \cdot 5} = -\frac{14}{15} \]
2. • \[ \left(\frac{3}{14} - \left(-\frac{17}{21}\right)\right) : \left(-7 \frac{1}{6}\right) \]
   • \[ \left(\frac{3}{14} + \frac{17}{21}\right) : \left(-\frac{43}{6}\right) \]
   • \[ \left(\frac{9}{42} + \frac{34}{42}\right) : \left(-\frac{43}{6}\right) \]
   • \[ \frac{43}{42} : \left(-\frac{43}{6}\right) = \frac{43}{42} \cdot \left(-\frac{6}{43}\right) = -\frac{6}{42} = -\frac{1}{7} \]
3. • \[ \left(\frac{7}{16} - \left(-\frac{5}{24}\right)\right) : \left(-1 \frac{15}{16}\right) \]
   • \[ \left(\frac{7}{16} + \frac{5}{24}\right) : \left(-\frac{31}{16}\right) \]
   • \[ \left(\frac{21}{48} + \frac{10}{48}\right) : \left(-\frac{31}{16}\right) \]
   • \[ \frac{31}{48} : \left(-\frac{31}{16}\right) = \frac{31}{48} \cdot \left(-\frac{16}{31}\right) = -\frac{16}{48} = -\frac{1}{3} \]
4. • \[ -4 \frac{1}{7} + 2 \frac{1}{4} \cdot \left(-11 \frac{2}{9} - (-5,4) : \frac{9}{35}\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} - \left(-\frac{54}{10}\right) : \frac{9}{35}\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} - \left(-\frac{27}{5}\right) \cdot \frac{35}{9}\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} - \left(-\frac{27 \cdot 35}{5 \cdot 9}\right)\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} - \left(-\frac{3 \cdot 35}{5}\right)\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} - (-21)\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} + 21\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \left(-\frac{101}{9} + \frac{189}{9}\right) \]
   • \[ -\frac{29}{7} + \frac{9}{4} \cdot \frac{88}{9} \]
   • \[ -\frac{29}{7} + \frac{88}{4} \]
   • \[ -\frac{29}{7} + 22 = -\frac{29}{7} + \frac{154}{7} = \frac{125}{7} = 17 \frac{6}{7} \]

Ответ:

1. \[ -\frac{14}{15} \]
2. \[ -\frac{1}{7} \]
3. \[ -\frac{1}{3} \]
4. \[ 17 \frac{6}{7} \]