Вычислите: a) 2 1/7:(3 6/7); 6) (1 2/9+1 5/9)⋅4 4/5; B) (7 1/3-5 1/6):3 1/3; г) (2 2/15-1 2/5)⋅6 1/4; д) (4 2/3+1 5/6):4 1/2; е) (8 1/8-7 1/8):4 1/5

Решение:

1. а) 2\(\frac{1}{7}\) : (3\(\frac{6}{7}\)) = \(\frac{15}{7}\) : \(\frac{27}{7}\) = \(\frac{15}{7}\) × \(\frac{7}{27}\) = \(\frac{15}{27}\) = \(\frac{5}{9}\)

2. б) (1\(\frac{2}{9}\) + 1\(\frac{5}{9}\)) ⋅ 4\(\frac{4}{5}\) = (\(\frac{11}{9}\) + \(\frac{14}{9}\)) ⋅ \(\frac{24}{5}\) = \(\frac{25}{9}\) ⋅ \(\frac{24}{5}\) = \(\frac{5}{3}\) ⋅ \(\frac{8}{1}\) = \(\frac{40}{3}\) = 13\(\frac{1}{3}\)

3. в) (7\(\frac{1}{3}\) - 5\(\frac{1}{6}\)) : 3\(\frac{1}{3}\) = (\(\frac{22}{3}\) - \(\frac{31}{6}\)) : \(\frac{10}{3}\) = (\(\frac{44}{6}\) - \(\frac{31}{6}\)) : \(\frac{10}{3}\) = \(\frac{13}{6}\) : \(\frac{10}{3}\) = \(\frac{13}{6}\) ⋅ \(\frac{3}{10}\) = \(\frac{13}{2}\) ⋅ \(\frac{1}{10}\) = \(\frac{13}{20}\)

4. г) (2\(\frac{2}{15}\) - 1\(\frac{2}{5}\)) ⋅ 6\(\frac{1}{4}\) = (\(\frac{32}{15}\) - \(\frac{7}{5}\)) ⋅ \(\frac{25}{4}\) = (\(\frac{32}{15}\) - \(\frac{21}{15}\)) ⋅ \(\frac{25}{4}\) = \(\frac{11}{15}\) ⋅ \(\frac{25}{4}\) = \(\frac{11}{3}\) ⋅ \(\frac{5}{4}\) = \(\frac{55}{12}\) = 4\(\frac{7}{12}\)

5. д) (4\(\frac{2}{3}\) + 1\(\frac{5}{6}\)) : 4\(\frac{1}{2}\) = (\(\frac{14}{3}\) + \(\frac{11}{6}\)) : \(\frac{9}{2}\) = (\(\frac{28}{6}\) + \(\frac{11}{6}\)) : \(\frac{9}{2}\) = \(\frac{39}{6}\) : \(\frac{9}{2}\) = \(\frac{13}{2}\) : \(\frac{9}{2}\) = \(\frac{13}{2}\) ⋅ \(\frac{2}{9}\) = \(\frac{13}{9}\) = 1\(\frac{4}{9}\)

6. е) (8\(\frac{1}{8}\) - 7\(\frac{1}{8}\)) : 4\(\frac{1}{5}\) = \(\frac{8\frac{1}{8} - 7\frac{1}{8}}{4\frac{1}{5}}\) = \(\frac{1}{4\frac{1}{5}}\) = \(\frac{1}{\frac{21}{5}}\) = 1 × \(\frac{5}{21}\) = \(\frac{5}{21}\)