Вопрос:

Вычислить: 1) \(\frac{7}{48}:6\frac{6}{7}\); 2) \(6\frac{7}{35}:\frac{4}{39}\); 3) \(10\frac{3}{5}:1\frac{23}{30}\); 4) \(1\frac{7}{25}:2\frac{6}{25}\); 5) \(3\frac{5}{9}:1\); 6) \(15:6\frac{1}{4}\); 7) \(4\frac{1}{5}:7\); 8) \(1\frac{7}{9}:3\frac{3}{7}\); 9) \(43\frac{10}{29}:5\); 10) \(34\frac{17}{42}:14\).

Ответ:

  1. \(\frac{7}{48}:6\frac{6}{7}=\frac{7}{48}:\frac{48}{7}=\frac{7}{48}\cdot\frac{7}{48}=\frac{49}{2304}\).
  2. \(6\frac{7}{35}:\frac{4}{39}=\frac{31}{5}\cdot\frac{39}{4}=\frac{1209}{20}=60\frac{9}{20}\).
  3. \(10\frac{3}{5}:1\frac{23}{30}=\frac{53}{5}:\frac{53}{30}=\frac{53}{5}\cdot\frac{30}{53}=6\).
  4. \(1\frac{7}{25}:2\frac{6}{25}=\frac{32}{25}:\frac{56}{25}=\frac{32}{25}\cdot\frac{25}{56}=\frac{4}{7}\).
  5. \(3\frac{5}{9}:1=3\frac{5}{9}\).
  6. \(15:6\frac{1}{4}=15:\frac{25}{4}=15\cdot\frac{4}{25}=\frac{12}{5}=2\frac{2}{5}\).
  7. \(4\frac{1}{5}:7=\frac{21}{5}:7=\frac{21}{5}\cdot\frac{1}{7}=\frac{3}{5}\).
  8. \(1\frac{7}{9}:3\frac{3}{7}=\frac{16}{9}:\frac{24}{7}=\frac{16}{9}\cdot\frac{7}{24}=\frac{14}{27}\).
  9. \(43\frac{10}{29}:5=\frac{1257}{29}:5=\frac{1257}{145}=8\frac{97}{145}\).
  10. \(34\frac{17}{42}:14=\frac{1445}{42}:14=\frac{1445}{588}=2\frac{269}{588}\).

Ответ: 1) \(\frac{49}{2304}\); 2) \(60\frac{9}{20}\); 3) \(6\); 4) \(\frac{4}{7}\); 5) \(3\frac{5}{9}\); 6) \(2\frac{2}{5}\); 7) \(\frac{3}{5}\); 8) \(\frac{14}{27}\); 9) \(8\frac{97}{145}\); 10) \(2\frac{269}{588}\).