1. Выполните действие: а) \(\frac{11}{40} \cdot \frac{15}{22}\); б) \(1\frac{4}{35} \cdot 1\frac{2}{13}\); в) \(2\frac{5}{11} \cdot 3\frac{1}{18}\); г) \(2\frac{5}{24} \cdot 8\).

Решение:

1. \(\frac{11}{40} \cdot \frac{15}{22} = \frac{11 \cdot 15}{40 \cdot 22} = \frac{1 \cdot 3}{8 \cdot 2} = \frac{3}{16}\)
2. \(1\frac{4}{35} \cdot 1\frac{2}{13} = \frac{39}{35} \cdot \frac{15}{13} = \frac{39 \cdot 15}{35 \cdot 13} = \frac{3 \cdot 3}{7 \cdot 1} = \frac{9}{7} = 1\frac{2}{7}\)
3. \(2\frac{5}{11} \cdot 3\frac{1}{18} = \frac{27}{11} \cdot \frac{55}{18} = \frac{27 \cdot 55}{11 \cdot 18} = \frac{3 \cdot 5}{1 \cdot 2} = \frac{15}{2} = 7\frac{1}{2}\)
4. \(2\frac{5}{24} \cdot 8 = \frac{53}{24} \cdot 8 = \frac{53 \cdot 8}{24} = \frac{53 \cdot 1}{3} = \frac{53}{3} = 17\frac{2}{3}\)

Ответ: а) \(\frac{3}{16}\); б) \(1\frac{2}{7}\); в) \(7\frac{1}{2}\); г) \(17\frac{2}{3}\)