Вопрос:

Вычисли: 1) \(\frac{8}{27}:\frac{4}{9}\); 2) \(\frac{36}{47}:18\); 3) \(42:\frac{6}{7}\); 4) \(3\frac{1}{9}:2\frac{11}{12}\); 5) \(\frac{8}{25}:3\frac{1}{5}:1\frac{1}{4}\); 6) \(2{,}04:\frac{3}{5}\).

Ответ:

  1. \[\frac{8}{27}:\frac{4}{9}=\frac{8}{27}\cdot\frac{9}{4}=\frac{2}{3}.\]
  2. \[\frac{36}{47}:18=\frac{36}{47}\cdot\frac{1}{18}=\frac{2}{47}.\]
  3. \[42:\frac{6}{7}=42\cdot\frac{7}{6}=49.\]
  4. \[3\frac{1}{9}:2\frac{11}{12}=\frac{28}{9}:\frac{35}{12}=\frac{28}{9}\cdot\frac{12}{35}=\frac{16}{15}=1\frac{1}{15}.\]
  5. \[\frac{8}{25}:3\frac{1}{5}:1\frac{1}{4}=\frac{8}{25}:\frac{16}{5}:\frac{5}{4}=\frac{8}{25}\cdot\frac{5}{16}\cdot\frac{4}{5}=\frac{2}{25}.\]
  6. \[2.04:\frac{3}{5}=\frac{204}{100}\cdot\frac{5}{3}=\frac{17}{5}\cdot\frac{5}{3}=\frac{17}{3}=5\frac{2}{3}.\]

Ответ: 1) \(\frac{2}{3}\); 2) \(\frac{2}{47}\); 3) \(49\); 4) \(1\frac{1}{15}\); 5) \(\frac{2}{25}\); 6) \(5\frac{2}{3}\).