891. Сократите дробь: а) \(\frac{7\cdot8}{4\cdot15}\); б) \(\frac{6\cdot15}{30\cdot18}\); в) \(\frac{8\cdot9}{27\cdot6}\); г) \(\frac{35\cdot42}{30\cdot49}\); д) \(\frac{18\cdot45}{40\cdot27}\); е) \(\frac{63\cdot56}{49\cdot45}\); ж) \(\frac{12\cdot15\cdot26}{13\cdot120}\); з) \(\frac{48\cdot5\cdot12}{30\cdot16\cdot8}\)

Решение:

а) \(\frac{7\cdot8}{4\cdot15}=\frac{7\cdot2\cdot4}{4\cdot15}=\frac{7\cdot2}{15}=\frac{14}{15}\)

б) \(\frac{6\cdot15}{30\cdot18}=\frac{6\cdot15}{2\cdot15\cdot3\cdot6}=\frac{1}{2\cdot3}=\frac{1}{6}\)

в) \(\frac{8\cdot9}{27\cdot6}=\frac{8\cdot9}{3\cdot9\cdot6}=\frac{8}{3\cdot6}=\frac{2\cdot4}{3\cdot2\cdot3}=\frac{4}{9}\)

г) \(\frac{35\cdot42}{30\cdot49}=\frac{7\cdot5\cdot6\cdot7}{6\cdot5\cdot7\cdot7}=\frac{7\cdot5\cdot6\cdot7}{6\cdot5\cdot7\cdot7}=1\)

д) \(\frac{18\cdot45}{40\cdot27}=\frac{9\cdot2\cdot9\cdot5}{8\cdot5\cdot9\cdot3}=\frac{9\cdot2}{8\cdot3}=\frac{3\cdot3\cdot2}{2\cdot4\cdot3}=\frac{3}{4}\)

е) \(\frac{63\cdot56}{49\cdot45}=\frac{7\cdot9\cdot7\cdot8}{7\cdot7\cdot9\cdot5}=\frac{7\cdot9\cdot7\cdot8}{7\cdot7\cdot9\cdot5}=\frac{8}{5}\)

ж) \(\frac{12\cdot15\cdot26}{13\cdot120}=\frac{12\cdot15\cdot2\cdot13}{13\cdot10\cdot12}=\frac{15\cdot2}{10}=\frac{5\cdot3\cdot2}{5\cdot2}=3\)

з) \(\frac{48\cdot5\cdot12}{30\cdot16\cdot8}=\frac{6\cdot8\cdot5\cdot3\cdot4}{6\cdot5\cdot8\cdot2\cdot8}=\frac{3\cdot4}{2\cdot8}=\frac{3\cdot4}{2\cdot2\cdot4}=\frac{3}{4}\)

Ответ: a) \(\frac{14}{15}\); б) \(\frac{1}{6}\); в) \(\frac{4}{9}\); г) 1; д) \(\frac{3}{4}\); е) \(\frac{8}{5}\); ж) 3; з) \(\frac{3}{4}\)