Вопрос:

3. Выполните действие: а) 9/4 + 6/5; б) -1 7/8 * 1 1/3; в) 1 2/3 : (-3 1/3); г) -9 3/4 - 2 1/12

Ответ:

a) \(\frac{9}{4} + \frac{6}{5} = \frac{9 \cdot 5 + 6 \cdot 4}{20} = \frac{45 + 24}{20} = \frac{69}{20} = 3\frac{9}{20}\) б) \(-1\frac{7}{8}\) * \(1\frac{1}{3}\) = \(-\frac{15}{8}\) * \(\frac{4}{3}\) = \(-\frac{15 \cdot 4}{8 \cdot 3}\) = \(-\frac{60}{24}\) = \(-\frac{5}{2}\) = \(-2\frac{1}{2}\) в) \(1\frac{2}{3}\) : \((-3\frac{1}{3})\) = \(\frac{5}{3}\) : \((-\frac{10}{3})\) = \(\frac{5}{3} \cdot (-\frac{3}{10})\) = \(-\frac{5 \cdot 3}{3 \cdot 10}\) = \(-\frac{15}{30}\) = \(-\frac{1}{2}\) г) \(-1\frac{3}{4}\) - \(2\frac{1}{12}\) = \(-\frac{7}{4}\) - \(\frac{25}{12}\) = \(-\frac{7 \cdot 3}{12}\) - \(\frac{25}{12}\) = \(-\frac{21}{12}\) - \(\frac{25}{12}\) = \(-\frac{21+25}{12}\) = \(-\frac{46}{12}\) = \(-\frac{23}{6}\) = \(-3\frac{5}{6}\)
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