1.58. Вычислите:

Решение:

А) \( 10 \cdot \left( 3 - \frac{2}{15} \right) + 12 \cdot \left( 5 + \frac{5}{6} + \frac{3}{4} \right) = 10 \cdot \left( \frac{45-2}{15} \right) + 12 \cdot \left( \frac{60+50+45}{60} \right) = 10 \cdot \frac{43}{15} + 12 \cdot \frac{155}{60} = \frac{430}{15} + \frac{1860}{60} = \frac{430}{15} + \frac{155}{5} = \frac{430 + 3 \cdot 155}{15} = \frac{430 + 465}{15} = \frac{895}{15} = \frac{179}{3} \)

Б) \( \left( \frac{2}{3} + \frac{5}{8} + \frac{11}{12} \right) - 5 \frac{1}{3} = \left( \frac{16+45+44}{24} \right) - \frac{16}{3} = \frac{105}{24} - \frac{16}{3} = \frac{35}{8} - \frac{16}{3} = \frac{105 - 128}{24} = -\frac{23}{24} \)

В) \( \left( 2 \frac{1}{2} - 1 \frac{3}{8} \right) \cdot \frac{3}{5} - \left( 1 \frac{5}{6} - \frac{1}{3} \right) = \left( \frac{5}{2} - \frac{11}{8} \right) \cdot \frac{3}{5} - \left( \frac{5}{6} \right) = \left( \frac{20-11}{8} \right) \cdot \frac{3}{5} - \frac{5}{6} = \frac{9}{8} \cdot \frac{3}{5} - \frac{5}{6} = \frac{27}{40} - \frac{5}{6} = \frac{81 - 100}{120} = -\frac{19}{120} \)

Г) \( \left( 8 \frac{1}{2} - 7 \frac{3}{8} \right) \cdot \frac{5}{2} - 4 \cdot \left( 3 \frac{1}{3} - 2 \frac{7}{9} \right) = \left( \frac{17}{2} - \frac{59}{8} \right) \cdot \frac{5}{2} - 4 \cdot \left( \frac{10}{3} - \frac{25}{9} \right) = \left( \frac{68-59}{8} \right) \cdot \frac{5}{2} - 4 \cdot \left( \frac{30-25}{9} \right) = \frac{9}{8} \cdot \frac{5}{2} - 4 \cdot \frac{5}{9} = \frac{45}{16} - \frac{20}{9} = \frac{405 - 320}{144} = \frac{85}{144} \)

Д) \( \left( \frac{7}{12} - 3 \frac{17}{36} \right) : 2 + 4 \frac{1}{3} - \frac{3}{26} + \frac{1}{2} = \left( \frac{21-117}{36} \right) : 2 + \frac{13}{3} - \frac{3}{26} + \frac{1}{2} = \frac{-96}{36} : 2 + \frac{13}{3} - \frac{3}{26} + \frac{1}{2} = \frac{-8}{3} \cdot \frac{1}{2} + \frac{13}{3} - \frac{3}{26} + \frac{1}{2} = \frac{-4}{3} + \frac{13}{3} - \frac{3}{26} + \frac{1}{2} = \frac{9}{3} - \frac{3}{26} + \frac{1}{2} = 3 - \frac{3}{26} + \frac{1}{2} = \frac{78 - 3 + 13}{26} = \frac{88}{26} = \frac{44}{13} \)

Е) \( \left[ \frac{3}{5} + 2 \frac{1}{10} \right] : \frac{3}{17} - \left( 2 \frac{23}{45} - 1 \frac{69}{80} \right) : \frac{1}{3} = \left[ \frac{3}{5} + \frac{21}{10} \right] : \frac{3}{17} - \left( \frac{113}{45} - \frac{149}{80} \right) : \frac{1}{3} = \left[ \frac{6+21}{10} \right] : \frac{3}{17} - \left( \frac{113 \cdot 16 - 149 \cdot 9}{720} \right) : \frac{1}{3} = \frac{27}{10} : \frac{3}{17} - \left( \frac{1808 - 1341}{720} \right) : \frac{1}{3} = \frac{27}{10} \cdot \frac{17}{3} - \frac{467}{720} \cdot 3 = \frac{9 \cdot 17}{10} - \frac{467}{240} = \frac{153}{10} - \frac{467}{240} = \frac{3672 - 467}{240} = \frac{3205}{240} = \frac{641}{48} \)

Ё) \( 8 \frac{4}{11} \cdot \left( \frac{3}{4} + 7 \frac{2}{9} \right) + 15 \cdot \left( 5 \frac{7}{8} - 3 \frac{3}{47} \right) - 2 \frac{31}{3 \cdot 55} \) — неразборчивое условие

Ж) \( \frac{3}{8} + 5 \frac{1}{4} - 2 \frac{1}{6} - \frac{9}{10} \right) \cdot 6 = \left( \frac{3}{8} + \frac{21}{4} - \frac{13}{6} - \frac{9}{10} \right) \cdot 6 = \left( \frac{45 + 315 - 260 - 108}{120} \right) \cdot 6 = \frac{-8}{120} \cdot 6 = -\frac{1}{15} \cdot 6 = -\frac{6}{15} = -\frac{2}{5} \)

З) \( \left( \frac{7}{15} + \frac{7}{30} + 5 \right) : \left( 2 - \frac{1}{1} - \frac{1}{2} \right) = \left( \frac{14+7+150}{30} \right) : \left( 2-1-\frac{1}{2} \right) = \frac{171}{30} : \left( 1-\frac{1}{2} \right) = \frac{57}{10} : \frac{1}{2} = \frac{57}{10} \cdot 2 = \frac{57}{5} \)

И) \( \left( \frac{1}{6} + \frac{1}{10} + \frac{1}{15} \right) : \left( \frac{3}{5} - \frac{1}{3} - \frac{1}{4} \right) = \left( \frac{5+3+2}{30} \right) : \left( \frac{36-20-15}{60} \right) = \frac{10}{30} : \frac{-1}{60} = \frac{1}{3} : \frac{-1}{60} = \frac{1}{3} \cdot (-60) = -20 \)

Ответ: А) \(\frac{179}{3}\), Б) \(-\frac{23}{24}\), В) \(-\frac{19}{120}\), Г) \(\frac{85}{144}\), Д) \(\frac{44}{13}\), Е) \(\frac{641}{48}\), Ж) \(-\frac{2}{5}\), З) \(\frac{57}{5}\), И) -20. Ё) условие неразборчиво.