Вопрос:

1. Вычислите: а) \(\frac{2}{3}\cdot\frac{4}{5}\); б) \(\frac{3}{7}\cdot\frac{7}{8}\); в) \(\frac{11}{12}\cdot\frac{8}{9}\); г) \(\left(\frac{2}{3}\right)^3\); д) \(\frac{2}{3}:\frac{5}{7}\); е) \(\frac{9}{16}:\frac{3}{2}\); ж) \(\frac{3}{4}:4\); з) \(3:\frac{9}{8}\).

Ответ:

  1. а) \(\frac{2}{3}\cdot\frac{4}{5}=\frac{8}{15}\).
  2. б) \(\frac{3}{7}\cdot\frac{7}{8}=\frac{3}{8}\).
  3. в) \(\frac{11}{12}\cdot\frac{8}{9}=\frac{22}{27}\).
  4. г) \(\left(\frac{2}{3}\right)^3=\frac{2^3}{3^3}=\frac{8}{27}\).
  5. д) \(\frac{2}{3}:\frac{5}{7}=\frac{2}{3}\cdot\frac{7}{5}=\frac{14}{15}\).
  6. е) \(\frac{9}{16}:\frac{3}{2}=\frac{9}{16}\cdot\frac{2}{3}=\frac{3}{8}\).
  7. ж) \(\frac{3}{4}:4=\frac{3}{4}\cdot\frac{1}{4}=\frac{3}{16}\).
  8. з) \(3:\frac{9}{8}=3\cdot\frac{8}{9}=\frac{8}{3}\).

Ответ: а) \(\frac{8}{15}\); б) \(\frac{3}{8}\); в) \(\frac{22}{27}\); г) \(\frac{8}{27}\); д) \(\frac{14}{15}\); е) \(\frac{3}{8}\); ж) \(\frac{3}{16}\); з) \(\frac{8}{3}\).