2. Найдите частное: 1) 12 1/2 : 3 3/4; 2) 1 3/5 : 5 1/3; 3) 2 5/8 : 7/32.

Решение:

1. \(12\frac{1}{2} : 3\frac{3}{4}\) = \(\frac{25}{2} : \frac{15}{4}\) = \(\frac{25}{2} \cdot \frac{4}{15}\) = \(\frac{25 \cdot 4}{2 \cdot 15}\) = \(\frac{5 \cdot 2}{1 \cdot 3}\) = \(\frac{10}{3}\) = \(3\frac{1}{3}\)
2. \(1\frac{3}{5} : 5\frac{1}{3}\) = \(\frac{8}{5} : \frac{16}{3}\) = \(\frac{8}{5} \cdot \frac{3}{16}\) = \(\frac{8 \cdot 3}{5 \cdot 16}\) = \(\frac{1 \cdot 3}{5 \cdot 2}\) = \(\frac{3}{10}\)
3. \(2\frac{5}{8} : \frac{7}{32}\) = \(\frac{21}{8} : \frac{7}{32}\) = \(\frac{21}{8} \cdot \frac{32}{7}\) = \(\frac{21 \cdot 32}{8 \cdot 7}\) = \(\frac{3 \cdot 4}{1 \cdot 1}\) = 12

Ответ: 1) \(3\frac{1}{3}\); 2) \(\frac{3}{10}\); 3) 12.