5.470 Найдите значение выражения: a) \(\frac{6}{7} \cdot \frac{7}{12} : \frac{5}{3}\); б) \(\frac{3}{4} \cdot \frac{10}{13} : \frac{39}{40}\); в) \(11 \cdot \frac{5}{33} : \frac{3}{10}\); г) \(\frac{3}{4} : \frac{4}{5} \cdot \frac{5}{6} : 12\); д) \((\frac{2}{3})^{2} + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18}\); e) \((\frac{3}{7} - \frac{1}{7})^{2} + \frac{49}{16} : (1\frac{1}{2})^{2}\)

a)

\(\frac{6}{7} \cdot \frac{7}{12} : \frac{5}{3} = \frac{6 \cdot 7 \cdot 3}{7 \cdot 12 \cdot 5} = \frac{6 \cdot 3}{12 \cdot 5} = \frac{18}{60} = \frac{3}{10}\)

Ответ: \(\frac{3}{10}\)

б)

\(\frac{3}{4} \cdot \frac{10}{13} : \frac{39}{40} = \frac{3 \cdot 10 \cdot 40}{4 \cdot 13 \cdot 39} = \frac{3 \cdot 10 \cdot 10}{13 \cdot 39} = \frac{300}{507} = \frac{100}{169}\)

Ответ: \(\frac{100}{169}\)

в)

\(11 \cdot \frac{5}{33} : \frac{3}{10} = \frac{11 \cdot 5 \cdot 10}{33 \cdot 3} = \frac{5 \cdot 10}{3 \cdot 3} = \frac{50}{9} = 5\frac{5}{9}\)

Ответ: \(5\frac{5}{9}\)

г)

\(\frac{3}{4} : \frac{4}{5} \cdot \frac{5}{6} : 12 = \frac{3 \cdot 5 \cdot 5}{4 \cdot 4 \cdot 6 \cdot 12} = \frac{3 \cdot 25}{16 \cdot 6 \cdot 12} = \frac{75}{1152} = \frac{25}{384}\)

Ответ: \(\frac{25}{384}\)

д)

\((\frac{2}{3})^{2} + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1}{3 \cdot 2} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{8 + 3 - 5}{18} = \frac{6}{18} = \frac{1}{3}\)

Ответ: \(\frac{1}{3}\)

е)

\((\frac{3}{7} - \frac{1}{7})^{2} + \frac{49}{16} : (1\frac{1}{2})^{2} = (\frac{2}{7})^{2} + \frac{49}{16} : (\frac{3}{2})^{2} = \frac{4}{49} + \frac{49}{16} : \frac{9}{4} = \frac{4}{49} + \frac{49}{16} \cdot \frac{4}{9} = \frac{4}{49} + \frac{49}{4 \cdot 9} = \frac{4}{49} + \frac{49}{36} = \frac{4 \cdot 36 + 49 \cdot 49}{49 \cdot 36} = \frac{144 + 2401}{1764} = \frac{2545}{1764} = 1\frac{781}{1764}\)

Ответ: \(1\frac{781}{1764}\)