289 Найди значение выражения: a) \(\frac{3}{11} \cdot \frac{22}{45}\) б) \(\frac{12}{7} : \frac{14}{27}\) в) \(\frac{18}{39} : \frac{13}{36}\) г) \(\frac{24}{17} : \frac{51}{40}\) д) \(\left(\frac{1}{6}\right)^2\) е) \(\left(\frac{2}{3}\right)^2\) ж) \(\left(\frac{7}{8}\right)^2\)

Решение:

1. \(\frac{3}{11} \cdot \frac{22}{45} = \frac{3 \cdot 22}{11 \cdot 45} = \frac{3 \cdot 2 \cdot 11}{11 \cdot 3 \cdot 15} = \frac{2}{15}\)
2. \(\frac{12}{7} : \frac{14}{27} = \frac{12}{7} \cdot \frac{27}{14} = \frac{12 \cdot 27}{7 \cdot 14} = \frac{6 \cdot 2 \cdot 27}{7 \cdot 7 \cdot 2} = \frac{162}{49}\)
3. \(\frac{18}{39} : \frac{13}{36} = \frac{18}{39} \cdot \frac{36}{13} = \frac{18 \cdot 36}{39 \cdot 13} = \frac{18 \cdot 36}{3 \cdot 13 \cdot 13} = \frac{6 \cdot 36}{13 \cdot 13} = \frac{216}{169}\)
4. \(\frac{24}{17} : \frac{51}{40} = \frac{24}{17} \cdot \frac{40}{51} = \frac{24 \cdot 40}{17 \cdot 51} = \frac{3 \cdot 8 \cdot 40}{17 \cdot 3 \cdot 17} = \frac{320}{289}\)
5. \(\left(\frac{1}{6}\right)^2 = \frac{1^2}{6^2} = \frac{1}{36}\)
6. \(\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9}\)
7. \(\left(\frac{7}{8}\right)^2 = \frac{7^2}{8^2} = \frac{49}{64}\)