2.303 Выполните умножение: a) \(3\frac{3}{7} \cdot 1\frac{3}{5}\); б) \(1\frac{7}{23} \cdot 3\frac{5}{6}\); в) \(\frac{15}{29} \cdot 1\frac{9}{20}\); г) \(8\frac{23}{34} \cdot \frac{17}{59}\); д) \(2\frac{1}{2} \cdot 1\frac{5}{14} \cdot 1\frac{4}{7}\); е) \(1\frac{4}{9} \cdot 3\frac{6}{7} \cdot \frac{3}{13}\).

a) \(3\frac{3}{7} \cdot 1\frac{3}{5} = \frac{24}{7} \cdot \frac{8}{5} = \frac{24 \cdot 8}{7 \cdot 5} = \frac{192}{35} = 5\frac{17}{35}\) б) \(1\frac{7}{23} \cdot 3\frac{5}{6} = \frac{30}{23} \cdot \frac{23}{6} = \frac{30 \cdot 23}{23 \cdot 6} = \frac{5 \cdot 1}{1 \cdot 1} = 5\) в) \(\frac{15}{29} \cdot 1\frac{9}{20} = \frac{15}{29} \cdot \frac{29}{20} = \frac{15 \cdot 29}{29 \cdot 20} = \frac{3 \cdot 1}{1 \cdot 4} = \frac{3}{4}\) г) \(8\frac{23}{34} \cdot \frac{17}{59} = \frac{34 \cdot 8 + 23}{34} \cdot \frac{17}{59} = \frac{295}{34} \cdot \frac{17}{59} = \frac{5 \cdot 59}{2 \cdot 17} \cdot \frac{17}{59} = \frac{5 \cdot 1}{2 \cdot 1} \cdot \frac{1}{1} = \frac{5}{2} = 2\frac{1}{2}\) д) \(2\frac{1}{2} \cdot 1\frac{5}{14} \cdot 1\frac{4}{7} = \frac{5}{2} \cdot \frac{19}{14} \cdot \frac{11}{7} = \frac{5 \cdot 19 \cdot 11}{2 \cdot 14 \cdot 7} = \frac{1045}{196} = 5\frac{65}{196}\) е) \(1\frac{4}{9} \cdot 3\frac{6}{7} \cdot \frac{3}{13} = \frac{13}{9} \cdot \frac{27}{7} \cdot \frac{3}{13} = \frac{13 \cdot 27 \cdot 3}{9 \cdot 7 \cdot 13} = \frac{1 \cdot 3 \cdot 3}{1 \cdot 7 \cdot 1} = \frac{9}{7} = 1\frac{2}{7}\) Ответ: a) \(5\frac{17}{35}\); б) 5; в) \(\frac{3}{4}\); г) \(2\frac{1}{2}\); д) \(5\frac{65}{196}\); е) \(1\frac{2}{7}\)