Найдите значение выражения: a) \( \frac{12}{17} : \left( -1 \frac{7}{17} \right) + 5,88 : (-14,7) – 0,1 \) б) \( \left( 8 - 5 \frac{3}{5} \right) \cdot 2 \frac{2}{3} + 8 - 6 \frac{1}{4} : 1 \frac{3}{4} \) г) \( 2 \frac{4}{5} : 1 \frac{2}{7} \cdot \frac{1}{5} - 4 \frac{7}{10} \) д) \( - \frac{5}{8} - \frac{4}{15} : \left( - \frac{33}{35} \right) \cdot \frac{14}{15} \)

Решение:

а) \( \frac{12}{17} : \left( -1 \frac{7}{17} \right) + 5,88 : (-14,7) – 0,1 \)

1. \( -1 \frac{7}{17} = - \frac{17 \cdot 1 + 7}{17} = - \frac{24}{17} \)
2. \( \frac{12}{17} : \left( - \frac{24}{17} \right) = \frac{12}{17} \cdot \left( - \frac{17}{24} \right) = - \frac{12}{24} = - \frac{1}{2} = -0,5 \)
3. \( 5,88 : (-14,7) = -0,4 \)
4. \( -0,5 + (-0,4) - 0,1 = -0,5 - 0,4 - 0,1 = -1 \)

б) \( \left( 8 - 5 \frac{3}{5} \right) \cdot 2 \frac{2}{3} + 8 - 6 \frac{1}{4} : 1 \frac{3}{4} \)

1. \( 5 \frac{3}{5} = \frac{5 \cdot 5 + 3}{5} = \frac{28}{5} \)
2. \( 8 - \frac{28}{5} = \frac{40}{5} - \frac{28}{5} = \frac{12}{5} \)
3. \( 2 \frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3} \)
4. \( \frac{12}{5} \cdot \frac{8}{3} = \frac{12 \cdot 8}{5 \cdot 3} = \frac{96}{15} = \frac{32}{5} = 6,4 \)
5. \( 6 \frac{1}{4} = \frac{6 \cdot 4 + 1}{4} = \frac{25}{4} \)
6. \( 1 \frac{3}{4} = \frac{1 \cdot 4 + 3}{4} = \frac{7}{4} \)
7. \( \frac{25}{4} : \frac{7}{4} = \frac{25}{4} \cdot \frac{4}{7} = \frac{25}{7} \)
8. \( 6,4 + 8 - \frac{25}{7} = 14,4 - \frac{25}{7} = \frac{144}{10} - \frac{25}{7} = \frac{72}{5} - \frac{25}{7} = \frac{72 \cdot 7 - 25 \cdot 5}{35} = \frac{504 - 125}{35} = \frac{379}{35} \)

г) \( 2 \frac{4}{5} : 1 \frac{2}{7} \cdot \frac{1}{5} - 4 \frac{7}{10} \)

1. \( 2 \frac{4}{5} = \frac{2 \cdot 5 + 4}{5} = \frac{14}{5} \)
2. \( 1 \frac{2}{7} = \frac{1 \cdot 7 + 2}{7} = \frac{9}{7} \)
3. \( \frac{14}{5} : \frac{9}{7} = \frac{14}{5} \cdot \frac{7}{9} = \frac{98}{45} \)
4. \( \frac{98}{45} \cdot \frac{1}{5} = \frac{98}{225} \)
5. \( 4 \frac{7}{10} = \frac{4 \cdot 10 + 7}{10} = \frac{47}{10} \)
6. \( \frac{98}{225} - \frac{47}{10} = \frac{98 \cdot 2 - 47 \cdot 45}{450} = \frac{196 - 2115}{450} = - \frac{1919}{450} \)

д) \( - \frac{5}{8} - \frac{4}{15} : \left( - \frac{33}{35} \right) \cdot \frac{14}{15} \)

1. \( \frac{4}{15} : \left( - \frac{33}{35} \right) = \frac{4}{15} \cdot \left( - \frac{35}{33} \right) = - \frac{4 \cdot 35}{15 \cdot 33} = - \frac{4 \cdot 7}{3 \cdot 33} = - \frac{28}{99} \)
2. \( - \frac{28}{99} \cdot \frac{14}{15} = - \frac{28 \cdot 14}{99 \cdot 15} = - \frac{392}{1485} \)
3. \( - \frac{5}{8} - \left( - \frac{392}{1485} \right) = - \frac{5}{8} + \frac{392}{1485} = \frac{-5 \cdot 1485 + 392 \cdot 8}{11880} = \frac{-7425 + 3136}{11880} = - \frac{4289}{11880} \)

Ответ: а) -1; б) \( \frac{379}{35} \); в) \( -\frac{1919}{450} \); г) \( -\frac{4289}{11880} \).