Вычислите произведение (892-899). 892. a) \(\frac{5}{12}\cdot\frac{7}{8}\); б) \(\frac{6}{7}\cdot\frac{8}{9}\); в) \(\frac{12}{13}\cdot\frac{2}{3}\); г) \(\frac{4}{9}\cdot\frac{27}{16}\); д) \(\frac{14}{25}\cdot\frac{10}{49}\); e) \(\frac{13}{10}\cdot\frac{100}{39}\); ж) \(\frac{15}{14}\cdot\frac{7}{12}\); з) \(\frac{45}{34}\cdot\frac{17}{15}\)

Решение:

a) \(\frac{5}{12}\cdot\frac{7}{8}=\frac{5\cdot7}{12\cdot8}=\frac{35}{96}\)

б) \(\frac{6}{7}\cdot\frac{8}{9}=\frac{6\cdot8}{7\cdot9}=\frac{3\cdot2\cdot8}{7\cdot3\cdot3}=\frac{16}{21}\)

в) \(\frac{12}{13}\cdot\frac{2}{3}=\frac{12\cdot2}{13\cdot3}=\frac{3\cdot4\cdot2}{13\cdot3}=\frac{8}{13}\)

г) \(\frac{4}{9}\cdot\frac{27}{16}=\frac{4\cdot27}{9\cdot16}=\frac{4\cdot9\cdot3}{9\cdot4\cdot4}=\frac{3}{4}\)

д) \(\frac{14}{25}\cdot\frac{10}{49}=\frac{14\cdot10}{25\cdot49}=\frac{2\cdot7\cdot2\cdot5}{5\cdot5\cdot7\cdot7}=\frac{4}{35}\)

e) \(\frac{13}{10}\cdot\frac{100}{39}=\frac{13\cdot100}{10\cdot39}=\frac{13\cdot10\cdot10}{10\cdot13\cdot3}=\frac{10}{3}\)

ж) \(\frac{15}{14}\cdot\frac{7}{12}=\frac{15\cdot7}{14\cdot12}=\frac{15\cdot7}{2\cdot7\cdot12}=\frac{15}{2\cdot12}=\frac{3\cdot5}{2\cdot3\cdot4}=\frac{5}{8}\)

з) \(\frac{45}{34}\cdot\frac{17}{15}=\frac{45\cdot17}{34\cdot15}=\frac{15\cdot3\cdot17}{17\cdot2\cdot15}=\frac{3}{2}\)

Ответ: a) \(\frac{35}{96}\); б) \(\frac{16}{21}\); в) \(\frac{8}{13}\); г) \(\frac{3}{4}\); д) \(\frac{4}{35}\); e) \(\frac{10}{3}\); ж) \(\frac{5}{8}\); з) \(\frac{3}{2}\)