1.17 Найдите значение выражения:

Решение:

1. a) \( \frac{12}{17} : \left( -1 \right) + 5,88 : \left( -14,7 \right) - 0,1 \)
   \( \frac{12}{17} : \left( -1 \right) + 5,88 : \left( -14,7 \right) - 0,1 = - \frac{12}{17} - 0,4 - 0,1 = - \frac{12}{17} - 0,5 \)
   \( = - \frac{12}{17} - \frac{1}{2} = \frac{-24 - 17}{34} = - \frac{41}{34} \)
2. б) \( \left( 8 - 5 \frac{3}{4} \right) \cdot 2 \frac{2}{5} + \left( 8 - 6 \frac{1}{4} \right) : 1 \frac{3}{5} \)
   \( \left( 8 - 5 \frac{3}{4} \right) \cdot 2 \frac{2}{5} + \left( 8 - 6 \frac{1}{4} \right) : 1 \frac{3}{5} = \left( 8 - \frac{23}{4} \right) \cdot \frac{12}{5} + \left( 8 - \frac{25}{4} \right) : \frac{8}{5} \)
   \( = \left( \frac{32 - 23}{4} \right) \cdot \frac{12}{5} + \left( \frac{32 - 25}{4} \right) : \frac{8}{5} = \frac{9}{4} \cdot \frac{12}{5} + \frac{7}{4} : \frac{8}{5} \)
   \( = \frac{9 \cdot 3}{5} + \frac{7}{4} \cdot \frac{5}{8} = \frac{27}{5} + \frac{35}{32} = \frac{27 \cdot 32 + 35 \cdot 5}{160} = \frac{864 + 175}{160} = \frac{1039}{160} \)
3. в) \( 5 \frac{1}{2} - 3 \frac{3}{4} \cdot \left( 1 \frac{1}{3} + 1 \frac{1}{5} \right) \)
   \( 5 \frac{1}{2} - 3 \frac{3}{4} \cdot \left( 1 \frac{1}{3} + 1 \frac{1}{5} \right) = \frac{11}{2} - \frac{15}{4} \cdot \left( \frac{4}{3} + \frac{6}{5} \right) = \frac{11}{2} - \frac{15}{4} \cdot \left( \frac{20 + 18}{15} \right) = \frac{11}{2} - \frac{15}{4} \cdot \frac{38}{15} \)
   \( = \frac{11}{2} - \frac{38}{4} = \frac{11}{2} - \frac{19}{2} = \frac{11 - 19}{2} = \frac{-8}{2} = -4 \)
4. г) \( 2 \frac{1}{5} : 1 \frac{1}{7} - 4 \frac{2}{7} \cdot \left( 1 \frac{1}{2} \right)^3 \)
   \( 2 \frac{1}{5} : 1 \frac{1}{7} - 4 \frac{2}{7} \cdot \left( 1 \frac{1}{2} \right)^3 = \frac{11}{5} : \frac{8}{7} - \frac{30}{7} \cdot \left( \frac{3}{2} \right)^3 = \frac{11}{5} \cdot \frac{7}{8} - \frac{30}{7} \cdot \frac{27}{8} \)
   \( = \frac{77}{40} - \frac{30 \cdot 27}{7 \cdot 8} = \frac{77}{40} - \frac{810}{56} = \frac{77}{40} - \frac{405}{28} = \frac{77 \cdot 7 - 405 \cdot 10}{280} = \frac{539 - 4050}{280} = \frac{-3511}{280} \)
5. д) \( \frac{2}{7} \cdot \left( 3 \frac{1}{2} \right)^2 - \frac{13}{10} : 1 \frac{9}{3} \)
   \( \frac{2}{7} \cdot \left( 3 \frac{1}{2} \right)^2 - \frac{13}{10} : 1 \frac{9}{3} = \frac{2}{7} \cdot \left( \frac{7}{2} \right)^2 - \frac{13}{10} : \frac{12}{3} = \frac{2}{7} \cdot \frac{49}{4} - \frac{13}{10} : 4 \)
   \( = \frac{2 \cdot 7}{4} - \frac{13}{10 \cdot 4} = \frac{14}{4} - \frac{13}{40} = \frac{7}{2} - \frac{13}{40} = \frac{7 \cdot 20 - 13}{40} = \frac{140 - 13}{40} = \frac{127}{40} \)
6. е) \( \frac{5}{8} \cdot \frac{14}{15} : \left( - \frac{7}{11} + 1 \right) \)
   \( \frac{5}{8} \cdot \frac{14}{15} : \left( - \frac{7}{11} + 1 \right) = \frac{5 \cdot 14}{8 \cdot 15} : \left( \frac{-7 + 11}{11} \right) = \frac{70}{120} : \frac{4}{11} = \frac{7}{12} : \frac{4}{11} \)
   \( = \frac{7}{12} \cdot \frac{11}{4} = \frac{77}{48} \)

Ответ: а) \( -\frac{41}{34} \); б) \( \frac{1039}{160} \); в) -4; г) \( -\frac{3511}{280} \); д) \( \frac{127}{40} \); е) \( \frac{77}{48} \).