Вопрос:

2. Выполнить деление: 1) \(\frac{5}{9}:\frac{10}{27}\); 2) \(\frac{4}{21}:\frac{12}{35}\); 3) \(\frac{35}{36}:\frac{5}{12}\); 4) \(\frac{16}{49}:\frac{32}{63}\); 5) \(25:\frac{5}{6}\); 6) \(\frac{9}{10}:36\); 7) \(12\frac{1}{2}:3\frac{3}{4}\); 8) \(3\frac{4}{7}:1\frac{1}{14}\).

Ответ:

  1. \(\frac{5}{9}:\frac{10}{27}=\frac{5}{9}\cdot\frac{27}{10}=\frac{3}{2}\).
  2. \(\frac{4}{21}:\frac{12}{35}=\frac{4}{21}\cdot\frac{35}{12}=\frac{5}{9}\).
  3. \(\frac{35}{36}:\frac{5}{12}=\frac{35}{36}\cdot\frac{12}{5}=\frac{7}{3}=2\frac{1}{3}\).
  4. \(\frac{16}{49}:\frac{32}{63}=\frac{16}{49}\cdot\frac{63}{32}=\frac{9}{14}\).
  5. \(25:\frac{5}{6}=25\cdot\frac{6}{5}=30\).
  6. \(\frac{9}{10}:36=\frac{9}{10}\cdot\frac{1}{36}=\frac{1}{40}\).
  7. \(12\frac{1}{2}:3\frac{3}{4}=\frac{25}{2}:\frac{15}{4}=\frac{25}{2}\cdot\frac{4}{15}=\frac{10}{3}=3\frac{1}{3}\).
  8. \(3\frac{4}{7}:1\frac{1}{14}=\frac{25}{7}:\frac{15}{14}=\frac{25}{7}\cdot\frac{14}{15}=\frac{10}{3}=3\frac{1}{3}\).

Ответ: 1) \(\frac{3}{2}\); 2) \(\frac{5}{9}\); 3) \(2\frac{1}{3}\); 4) \(\frac{9}{14}\); 5) \(30\); 6) \(\frac{1}{40}\); 7) \(3\frac{1}{3}\); 8) \(3\frac{1}{3}\).