1. Выполните действие:

Решение:

1. \( \frac{2}{3} \cdot \frac{8}{13} = \frac{2 \cdot 8}{3 \cdot 13} = \frac{16}{39} \)
2. \( 2 \frac{5}{11} \cdot 2 \frac{4}{9} = \frac{27}{11} \cdot \frac{22}{9} = \frac{27 \cdot 22}{11 \cdot 9} = \frac{3 \cdot 9 \cdot 2 \cdot 11}{11 \cdot 9} = 3 \cdot 2 = 6 \)
3. \( \frac{6}{7} : \frac{12}{35} = \frac{6}{7} \cdot \frac{35}{12} = \frac{6 \cdot 35}{7 \cdot 12} = \frac{6 \cdot 5 \cdot 7}{7 \cdot 2 \cdot 6} = \frac{5}{2} = 2 \frac{1}{2} \)
4. \( \frac{12}{49} \cdot \frac{7}{24} = \frac{12 \cdot 7}{49 \cdot 24} = \frac{12 \cdot 7}{7 \cdot 7 \cdot 2 \cdot 12} = \frac{1}{14} \)
5. \( 2 \frac{4}{5} \cdot 10 = \frac{14}{5} \cdot 10 = \frac{14 \cdot 10}{5} = 14 \cdot 2 = 28 \)
6. \( \frac{14}{15} : 7 = \frac{14}{15} \cdot \frac{1}{7} = \frac{14}{15 \cdot 7} = \frac{2 \cdot 7}{15 \cdot 7} = \frac{2}{15} \)

Ответ: а) $$\frac{16}{39}$$; б) $$6$$; в) $$2\frac{1}{2}$$; г) $$\frac{1}{14}$$; д) $$28$$; е) $$\frac{2}{15}$$.