893. a) \(\frac{1}{2}\cdot\frac{4}{5}\cdot\frac{5}{6}\); б) \(\frac{7}{8}\cdot\frac{4}{35}\cdot\frac{10}{9}\); в) \(\frac{13}{12}\cdot\frac{24}{65}\cdot\frac{15}{32}\); г) \(\frac{5}{16}\cdot\frac{8}{15}\cdot\frac{4}{3}\); д) \(\frac{42}{56}\cdot\frac{16}{5}\cdot\frac{15}{36}\); e) \(\frac{5}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)

Решение:

a) \(\frac{1}{2}\cdot\frac{4}{5}\cdot\frac{5}{6}=\frac{1\cdot4\cdot5}{2\cdot5\cdot6}=\frac{4}{2\cdot6}=\frac{4}{12}=\frac{4}{4\cdot3}=\frac{1}{3}\)

б) \(\frac{7}{8}\cdot\frac{4}{35}\cdot\frac{10}{9}=\frac{7\cdot4\cdot10}{8\cdot35\cdot9}=\frac{7\cdot4\cdot2\cdot5}{8\cdot5\cdot7\cdot9}=\frac{4\cdot2}{8\cdot9}=\frac{8}{8\cdot9}=\frac{1}{9}\)

в) \(\frac{13}{12}\cdot\frac{24}{65}\cdot\frac{15}{32}=\frac{13\cdot24\cdot15}{12\cdot65\cdot32}=\frac{13\cdot12\cdot2\cdot3\cdot5}{12\cdot13\cdot5\cdot32}=\frac{2\cdot3}{32}=\frac{2\cdot3}{2\cdot16}=\frac{3}{16}\)

г) \(\frac{5}{16}\cdot\frac{8}{15}\cdot\frac{4}{3}=\frac{5\cdot8\cdot4}{16\cdot15\cdot3}=\frac{5\cdot8\cdot4}{8\cdot2\cdot5\cdot3\cdot3}=\frac{4}{2\cdot3\cdot3}=\frac{2\cdot2}{2\cdot3\cdot3}=\frac{2}{9}\)

д) \(\frac{42}{56}\cdot\frac{16}{5}\cdot\frac{15}{36}=\frac{42\cdot16\cdot15}{56\cdot5\cdot36}=\frac{7\cdot6\cdot4\cdot4\cdot3\cdot5}{7\cdot8\cdot5\cdot4\cdot9}=\frac{6\cdot4\cdot3}{8\cdot9}=\frac{3\cdot2\cdot4\cdot3}{4\cdot2\cdot3\cdot3}=\frac{3\cdot4\cdot3}{4\cdot2\cdot3\cdot3}=1\)

e) \(\frac{5}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}=\frac{5\cdot8\cdot9}{8\cdot9\cdot10}=\frac{5\cdot8\cdot9}{8\cdot9\cdot5\cdot2}=\frac{1}{2}\)

Ответ: a) \(\frac{1}{3}\); б) \(\frac{1}{9}\); в) \(\frac{3}{16}\); г) \(\frac{2}{9}\); д) 1; e) \(\frac{1}{2}\)