Вычислите: 1) 4/27 * 9/16; 2) 13/16 * 32; 3) 12/35 : 2/5; 4) 15/17 : 5; 5) 4 : 20/21.

Решение:

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

Ответ: 1) 1/12; 2) 26; 3) 6/7; 4) 3/17; 5) 21/5 или 4 1/5.