289 Найди значение выражения:

Решение:

а) \(\frac{3}{11} \cdot \frac{22}{15} = \frac{3 \cdot 22}{11 \cdot 15} = \frac{3 \cdot 2 \cdot 11}{11 \cdot 3 \cdot 5} = \frac{2}{5}\)

б) \(\frac{12}{7} \cdot \frac{14}{27} = \frac{12 \cdot 14}{7 \cdot 27} = \frac{4 \cdot 3 \cdot 2 \cdot 7}{7 \cdot 9 \cdot 3} = \frac{8}{9}\)

в) \(\frac{18}{39} \cdot \frac{13}{36} = \frac{18 \cdot 13}{39 \cdot 36} = \frac{18 \cdot 13}{3 \cdot 13 \cdot 2 \cdot 18} = \frac{1}{6}\)

г) \(\frac{16}{81} \cdot \frac{45}{57} = \frac{16 \cdot 45}{81 \cdot 57} = \frac{16 \cdot 5 \cdot 9}{9 \cdot 9 \cdot 3 \cdot 19} = \frac{80}{171}\)

д) \(\frac{72}{49} \cdot \frac{5}{88} = \frac{72 \cdot 5}{49 \cdot 88} = \frac{8 \cdot 9 \cdot 5}{49 \cdot 8 \cdot 11} = \frac{45}{539}\)

е) \(\frac{18}{95} \cdot \frac{35}{42} = \frac{18 \cdot 35}{95 \cdot 42} = \frac{3 \cdot 6 \cdot 5 \cdot 7}{19 \cdot 5 \cdot 6 \cdot 7} = \frac{3}{19}\)

ж) \(\frac{24}{17} \cdot \frac{51}{40} = \frac{24 \cdot 51}{17 \cdot 40} = \frac{3 \cdot 8 \cdot 3 \cdot 17}{17 \cdot 5 \cdot 8} = \frac{9}{5}\)

з) \(\frac{20}{23} \cdot \frac{73}{48} = \frac{20 \cdot 73}{23 \cdot 48} = \frac{5 \cdot 4 \cdot 73}{23 \cdot 12 \cdot 4} = \frac{365}{276}\)

и) \(\left(\frac{1}{6}\right)^2 = \frac{1^2}{6^2} = \frac{1}{36}\)

к) \(\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}\)

л) \(\left(\frac{7}{8}\right)^2 = \frac{7^2}{8^2} = \frac{49}{64}\)

м) \(\left(\frac{5}{4}\right)^2 = \frac{5^2}{4^2} = \frac{25}{16}\)

Ответ: а) \(\frac{2}{5}\); б) \(\frac{8}{9}\); в) \(\frac{1}{6}\); г) \(\frac{80}{171}\); д) \(\frac{45}{539}\); е) \(\frac{3}{19}\); ж) \(\frac{9}{5}\); з) \(\frac{365}{276}\); и) \(\frac{1}{36}\); к) \(\frac{4}{9}\); л) \(\frac{49}{64}\); м) \(\frac{25}{16}\).