4.283 Выполните действия: a) (\(\frac{3}{16}\) – 5) \(\cdot\) (6\(\frac{26}{29}\) – 9); б) 11\(\frac{1}{5}\) \(\cdot\) \(\frac{7}{8}\) – 2\(\frac{5}{14}\) \(\cdot\) \(\frac{7}{9}\); в) 17,5 – 27 \(\cdot\) (\(\frac{5}{12}\) – \(\frac{3}{4}\)); г) (\(-\frac{1}{3}\) – \(\frac{4}{7}\) – \(\frac{20}{21}\)) \(\cdot\) \(\frac{7}{13}\) + \(\frac{11}{25}\); д) (6\(\frac{1}{3}\) – 4,2) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23; e) (\(-\frac{1}{4}\) – 0,75 – \(\frac{1}{5}\)) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2.

Решение:

Давай выполним действия по порядку. Начнем с примера а):

а) (\(\frac{3}{16}\) – 5) \(\cdot\) (6\(\frac{26}{29}\) – 9) = (\(\frac{3}{16}\) – \(\frac{80}{16}\)) \(\cdot\) (\(\frac{6\cdot29 + 26}{29}\) – 9) = (\(-\frac{77}{16}\)) \(\cdot\) (\(\frac{174 + 26}{29}\) – 9) = (\(-\frac{77}{16}\)) \(\cdot\) (\(\frac{200}{29}\) – \(\frac{9\cdot29}{29}\)) = (\(-\frac{77}{16}\)) \(\cdot\) (\(\frac{200}{29}\) – \(\frac{261}{29}\)) = (\(-\frac{77}{16}\)) \(\cdot\) (\(-\frac{61}{29}\)) = \(\frac{77 \cdot 61}{16 \cdot 29}\) = \(\frac{4697}{464}\) = 10\(\frac{57}{464}\)

Теперь пример б):

б) 11\(\frac{1}{5}\) \(\cdot\) \(\frac{7}{8}\) – 2\(\frac{5}{14}\) \(\cdot\) \(\frac{7}{9}\) = \(\frac{56}{5}\) \(\cdot\) \(\frac{7}{8}\) – \(\frac{33}{14}\) \(\cdot\) \(\frac{7}{9}\) = \(\frac{7\cdot7}{5}\) - \(\frac{11}{2\cdot9}\) = \(\frac{49}{5}\) - \(\frac{11}{18}\) = \(\frac{49\cdot18 - 11\cdot5}{5\cdot18}\) = \(\frac{882 - 55}{90}\) = \(\frac{827}{90}\) = 9\(\frac{17}{90}\)

Далее пример в):

в) 17,5 – 27 \(\cdot\) (\(\frac{5}{12}\) – \(\frac{3}{4}\)) = 17,5 – 27 \(\cdot\) (\(\frac{5}{12}\) – \(\frac{9}{12}\)) = 17,5 – 27 \(\cdot\) (\(-\frac{4}{12}\)) = 17,5 – 27 \(\cdot\) (\(-\frac{1}{3}\)) = 17,5 + 9 = 26,5

Пример г):

г) (\(-\frac{1}{3}\) – \(\frac{4}{7}\) – \(\frac{20}{21}\)) \(\cdot\) \(\frac{7}{13}\) + \(\frac{11}{25}\) = (\(-\frac{7}{21}\) – \(\frac{12}{21}\) – \(\frac{20}{21}\)) \(\cdot\) \(\frac{7}{13}\) + \(\frac{11}{25}\) = (\(-\frac{39}{21}\)) \(\cdot\) \(\frac{7}{13}\) + \(\frac{11}{25}\) = (\(-\frac{3}{21}\)\(\cdot\)7) + \(\frac{11}{25}\) = -1 + \(\frac{11}{25}\) = \(-\frac{25}{25}\) + \(\frac{11}{25}\) = -\(\frac{14}{25}\)

Пример д):

д) (6\(\frac{1}{3}\) – 4,2) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = (\(\frac{19}{3}\) – 4,2) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = (\(\frac{19}{3}\) – \(\frac{42}{10}\)) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = (\(\frac{190}{30}\) – \(\frac{126}{30}\)) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = \(\frac{64}{30}\) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = \(\frac{32}{15}\) \(\cdot\) (\(-\frac{9}{16}\)) – 4,23 = \(-\frac{2\cdot3}{5}\) – 4,23 = -\(\frac{6}{5}\) – 4,23 = -1,2 – 4,23 = -5,43

И последний пример e):

e) (\(-\frac{1}{4}\) – 0,75 – \(\frac{1}{5}\)) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2 = (\(-\frac{1}{4}\) – \(\frac{3}{4}\) – \(\frac{1}{5}\)) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2 = (-1 – \(\frac{1}{5}\)) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2 = (\(-\frac{5}{5}\) – \(\frac{1}{5}\)) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2 = \(-\frac{6}{5}\) \(\cdot\) (\(-\frac{2}{3}\)) + 4,2 = \(\frac{2\cdot2}{5}\) + 4,2 = \(\frac{4}{5}\) + 4,2 = 0,8 + 4,2 = 5

Ответ: а) 10\(\frac{57}{464}\); б) 9\(\frac{17}{90}\); в) 26,5; г) -\(\frac{14}{25}\); д) -5,43; е) 5

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