8. Вычислите результат: a) \(\frac{3}{5}\) : \(\frac{15}{2}\) \(\cdot\) \(\frac{7}{8}\) \(\times\) \(\frac{5}{7}\) б) \(\frac{1}{6}\) + \(\frac{3}{4}\) : \(\frac{9}{2}\) \(\times\) \(\frac{1}{2}\) \(\times\) 12 в) \(\frac{7}{9}\) - \(\frac{1}{3}\) + \(\frac{1}{6}\) : \(\frac{5}{2}\) \(\times\) \(\frac{4}{1}\) \(\times\) \(\frac{1}{2}\) г) \(\frac{1}{5}\) + \(\frac{3}{3}\) \(\times\) \(\frac{10}{3}\) : \(\frac{2}{3}\) \(\times\) \(\frac{1}{10}\)

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Вопрос:

Ответ:

ФИО:Телефон:Емаил:Полное описание сути нарушения прав (почему распространение данной информации запрещено Правообладателем):

Accepted Answer

а) \( \frac{3}{5} : \frac{15}{2} \cdot \frac{7}{8} \times \frac{5}{7} = \frac{3}{5} \times \frac{2}{15} \times \frac{7}{8} \times \frac{5}{7} = \frac{3 \times 2 \times 7 \times 5}{5 \times 15 \times 8 \times 7} = \frac{3 \times 2}{15 \times 8} = \frac{6}{120} = \frac{1}{20} \)
б) \( \frac{1}{6} + \frac{3}{4} : \frac{9}{2} \times \frac{1}{2} \times 12 = \frac{1}{6} + \frac{3}{4} \times \frac{2}{9} \times \frac{1}{2} \times 12 = \frac{1}{6} + \frac{3 \times 2 \times 1 \times 12}{4 \times 9 \times 2} = \frac{1}{6} + \frac{72}{72} = \frac{1}{6} + 1 = 1\frac{1}{6} = \frac{7}{6} \)
в) \( \frac{7}{9} - \frac{1}{3} + \frac{1}{6} : \frac{5}{2} \times \frac{4}{1} \times \frac{1}{2} = \frac{7}{9} - \frac{3}{9} + \frac{1}{6} \times \frac{2}{5} \times 4 \times \frac{1}{2} = \frac{4}{9} + \frac{1 \times 2 \times 4 \times 1}{6 \times 5 \times 2} = \frac{4}{9} + \frac{8}{60} = \frac{4}{9} + \frac{2}{15} = \frac{20 + 6}{45} = \frac{26}{45} \)
г) \( \frac{1}{5} + \frac{3}{3} \times \frac{10}{3} : \frac{2}{3} \times \frac{1}{10} = \frac{1}{5} + 1 \times \frac{10}{3} \times \frac{3}{2} \times \frac{1}{10} = \frac{1}{5} + \frac{10 \times 3 \times 1}{3 \times 2 \times 10} = \frac{1}{5} + \frac{30}{60} = \frac{1}{5} + \frac{1}{2} = \frac{2+5}{10} = \frac{7}{10} \)

Ответ: а) \(\frac{1}{20}\); б) \(\frac{7}{6}\); в) \(\frac{26}{45}\); г) \(\frac{7}{10}\).