П.20 Выполните действие: a) \(\frac{16}{27} \cdot \frac{9}{4}\) б) \(\frac{42}{5} \cdot \frac{55}{7}\) в) \(\frac{7}{12} : \frac{3}{12}\) г) \(\frac{14}{55} : \frac{7}{22}\)

Решение:

1. \(\text{а)} \quad \frac{16}{27} \cdot \frac{9}{4} = \frac{16 \cdot 9}{27 \cdot 4} = \frac{(4 \cdot 4) \cdot 9}{(3 \cdot 9) \cdot 4} = \frac{4}{3}\)
2. \(\text{б)} \quad \frac{42}{5} \cdot \frac{55}{7} = \frac{42 \cdot 55}{5 \cdot 7} = \frac{(6 \cdot 7) \cdot (5 \cdot 11)}{5 \cdot 7} = 6 \cdot 11 = 66\)
3. \(\text{в)} \quad \frac{7}{12} : \frac{3}{12} = \frac{7}{12} \cdot \frac{12}{3} = \frac{7 \cdot 12}{12 \cdot 3} = \frac{7}{3}\)
4. \(\text{г)} \quad \frac{14}{55} : \frac{7}{22} = \frac{14}{55} \cdot \frac{22}{7} = \frac{14 \cdot 22}{55 \cdot 7} = \frac{(2 \cdot 7) \cdot (2 \cdot 11)}{(5 \cdot 11) \cdot 7} = \frac{2 \cdot 2}{5} = \frac{4}{5}\)

Ответ: а) \(\frac{4}{3}\); б) 66; в) \(\frac{7}{3}\); г) \(\frac{4}{5}\).