1. Выполни действия:

Решение:

1. \( \frac{5}{7} \cdot \frac{3}{8} = \frac{5 \cdot 3}{7 \cdot 8} = \frac{15}{56} \)
2. \( \frac{5}{9} : \frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{5 \cdot 3 \cdot 9}{9 \cdot 2 \cdot 5} = \frac{3}{2} = 1\frac{1}{2} \)
3. \( 4\frac{4}{9} : 2\frac{2}{3} = \frac{40}{9} : \frac{8}{3} = \frac{40}{9} \cdot \frac{3}{8} = \frac{40 \cdot 3}{9 \cdot 8} = \frac{5 \cdot 8 \cdot 3}{3 \cdot 3 \cdot 8} = \frac{5}{3} = 1\frac{2}{3} \)
4. \( 32 : \frac{8}{9} = 32 \cdot \frac{9}{8} = \frac{32 \cdot 9}{8} = 4 \cdot 9 = 36 \)
5. \( \frac{12}{13} : 6 = \frac{12}{13} \cdot \frac{1}{6} = \frac{12}{13 \cdot 6} = \frac{2 \cdot 6}{13 \cdot 6} = \frac{2}{13} \)

Ответ: а) \(\frac{15}{56}\); б) \(1\frac{1}{2}\); в) \(1\frac{2}{3}\); г) 36; д) \(\frac{2}{13}\).