894. a) \(\frac{1}{2}\cdot\frac{2}{3}\); б) \(\frac{6}{7}\cdot\frac{5}{6}\); в) \(\frac{9}{10}\cdot\frac{10}{11}\); г) \(\frac{13}{15}\cdot\frac{15}{17}\); д) \(\frac{14}{15}\cdot\frac{5}{42}\); e) \(\frac{13}{15}\cdot\frac{45}{26}\); ж) \(\frac{15}{28}\cdot\frac{7}{30}\); з) \(\frac{35}{51}\cdot\frac{17}{15}\)

Решение:

а) \(\frac{1}{2}\cdot\frac{2}{3}=\frac{1\cdot2}{2\cdot3}=\frac{2}{6}=\frac{2}{2\cdot3}=\frac{1}{3}\)

б) \(\frac{6}{7}\cdot\frac{5}{6}=\frac{6\cdot5}{7\cdot6}=\frac{5}{7}\)

в) \(\frac{9}{10}\cdot\frac{10}{11}=\frac{9\cdot10}{10\cdot11}=\frac{9}{11}\)

г) \(\frac{13}{15}\cdot\frac{15}{17}=\frac{13\cdot15}{15\cdot17}=\frac{13}{17}\)

д) \(\frac{14}{15}\cdot\frac{5}{42}=\frac{14\cdot5}{15\cdot42}=\frac{2\cdot7\cdot5}{3\cdot5\cdot6\cdot7}=\frac{2}{3\cdot6}=\frac{2}{18}=\frac{2}{2\cdot9}=\frac{1}{9}\)

е) \(\frac{13}{15}\cdot\frac{45}{26}=\frac{13\cdot45}{15\cdot26}=\frac{13\cdot3\cdot15}{15\cdot13\cdot2}=\frac{3}{2}\)

ж) \(\frac{15}{28}\cdot\frac{7}{30}=\frac{15\cdot7}{28\cdot30}=\frac{3\cdot5\cdot7}{4\cdot7\cdot6\cdot5}=\frac{3}{4\cdot6}=\frac{3}{24}=\frac{3}{3\cdot8}=\frac{1}{8}\)

з) \(\frac{35}{51}\cdot\frac{17}{15}=\frac{35\cdot17}{51\cdot15}=\frac{7\cdot5\cdot17}{3\cdot17\cdot3\cdot5}=\frac{7}{3\cdot3}=\frac{7}{9}\)

Ответ: a) \(\frac{1}{3}\); б) \(\frac{5}{7}\); в) \(\frac{9}{11}\); г) \(\frac{13}{17}\); д) \(\frac{1}{9}\); e) \(\frac{3}{2}\); ж) \(\frac{1}{8}\); з) \(\frac{7}{9}\)