4.76 Вычислите. a) \(\frac{2}{7}\) + \(\frac{4}{7}\) - \(\frac{1}{4}\) + \(\frac{2}{5}\) : \(\frac{5}{8}\) - \(\frac{3}{2}\) + \(\frac{2}{3}\) = ? б) 14 : \(\frac{6}{11}\) - \(\frac{2}{11}\) + \(\frac{1}{3}\) : 5 + 2 : 3 = ? г) 6 : 12 · 1,6 - 0,35 + 0,15 : 4 = ?

Ответ:

а) \(\frac{2}{7}\) + \(\frac{4}{7}\) - \(\frac{1}{4}\) + \(\frac{2}{5}\) : \(\frac{5}{8}\) - \(\frac{3}{2}\) + \(\frac{2}{3}\) =

= \(\frac{6}{7}\) - \(\frac{1}{4}\) + \(\frac{2}{5}\) * \(\frac{8}{5}\) - \(\frac{3}{2}\) + \(\frac{2}{3}\) =

= \(\frac{6}{7}\) - \(\frac{1}{4}\) + \(\frac{16}{25}\) - \(\frac{3}{2}\) + \(\frac{2}{3}\) =

= \(\frac{900 - 105 + 672 - 1575 + 700}{1050}\) = \(\frac{592}{1050}\) = \(\frac{296}{525}\)

б) 14 : \(\frac{6}{11}\) - \(\frac{2}{11}\) + \(\frac{1}{3}\) : 5 + \(\frac{2}{3}\) =

= 14 * \(\frac{11}{6}\) - \(\frac{2}{11}\) + \(\frac{1}{3}\) * \(\frac{1}{5}\) + \(\frac{2}{3}\) =

= \(\frac{77}{3}\) - \(\frac{2}{11}\) + \(\frac{1}{15}\) + \(\frac{2}{3}\) =

= \(\frac{8470 - 30 + 11 + 110}{165}\) = \(\frac{8561}{165}\)

г) 6 : 12 * 1,6 - 0,35 + 0,15 : 4 =

= \(\frac{1}{2}\) * 1,6 - 0,35 + 0,15 : 4 =

= 0,8 - 0,35 + 0,0375 = 0,45 + 0,0375 = 0,4875

Ответ: а) \(\frac{296}{525}\); б) \(\frac{8561}{165}\); г) 0,4875.