Выполнить действия:

Решение:

1. \( \frac{5}{9} \cdot \frac{2}{7} = \frac{5 \cdot 2}{9 \cdot 7} = \frac{10}{63} \)
2. \( \frac{4}{27} \cdot \frac{9}{16} = \frac{4 \cdot 9}{27 \cdot 16} = \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12} \)
3. \( 5\frac{2}{5} \cdot 2\frac{2}{9} = \frac{27}{5} \cdot \frac{20}{9} = \frac{3}{1} \cdot \frac{4}{1} = 12 \)
4. \( 1\frac{5}{12} \cdot 24 = \frac{17}{12} \cdot 24 = 17 \cdot 2 = 34 \)
5. \( \frac{1}{10} : \frac{2}{5} = \frac{1}{10} \cdot \frac{5}{2} = \frac{1 \cdot 5}{10 \cdot 2} = \frac{5}{20} = \frac{1}{4} \)
6. \( \frac{4}{9} : \frac{16}{45} = \frac{4}{9} \cdot \frac{45}{16} = \frac{1}{1} \cdot \frac{5}{4} = \frac{5}{4} = 1\frac{1}{4} \)
7. \( 4\frac{1}{2} : 5\frac{1}{4} = \frac{9}{2} : \frac{21}{4} = \frac{9}{2} \cdot \frac{4}{21} = \frac{3}{1} \cdot \frac{2}{7} = \frac{6}{7} \)
8. \( \frac{35}{41} : 5 = \frac{35}{41} \cdot \frac{1}{5} = \frac{7}{41} \cdot \frac{1}{1} = \frac{7}{41} \)

Ответ: 1) \( \frac{10}{63} \); 2) \( \frac{1}{12} \); 3) 12; 4) 34; 5) \( \frac{1}{4} \); 6) \( 1\frac{1}{4} \); 7) \( \frac{6}{7} \); 8) \( \frac{7}{41} \).