1. Вычислите: 1) \(\frac{4}{27} \cdot \frac{9}{16}\) 2) \(\frac{13}{16} \cdot 32\) 3) \(\frac{12}{35} : \frac{2}{5}\) 4) \(\frac{15}{17} : 5\) 5) \(4 : \frac{20}{21}\)

Решение:

1. \(\frac{4}{27} \cdot \frac{9}{16} = \frac{4 \cdot 9}{27 \cdot 16} = \frac{36}{432}\). Сокращаем: \(\frac{36}{432} = \frac{1}{12}\).
2. \(\frac{13}{16} \cdot 32 = \frac{13 \cdot 32}{16} = 13 \cdot 2 = 26\).
3. \(\frac{12}{35} : \frac{2}{5} = \frac{12}{35} \cdot \frac{5}{2} = \frac{12 \cdot 5}{35 \cdot 2} = \frac{60}{70}\). Сокращаем: \(\frac{60}{70} = \frac{6}{7}\).
4. \(\frac{15}{17} : 5 = \frac{15}{17 \cdot 5} = \frac{15}{85}\). Сокращаем: \(\frac{15}{85} = \frac{3}{17}\).
5. \(4 : \frac{20}{21} = 4 \cdot \frac{21}{20} = \frac{4 \cdot 21}{20} = \frac{84}{20}\). Сокращаем: \(\frac{84}{20} = \frac{21}{5} = 4\frac{1}{5}\).

Ответ: 1) \(\frac{1}{12}\); 2) \(26\); 3) \(\frac{6}{7}\); 4) \(\frac{3}{17}\); 5) \(4\frac{1}{5}\).