Выполните умножение: 1) \(\frac{4}{9} \cdot \frac{3}{32}\) 2) \(\frac{5}{9} \cdot \frac{7}{8}\) 3) \(\frac{27}{56} \cdot \frac{56}{45}\) 4) \(\frac{45}{64} \cdot \frac{40}{63}\)

Решение:

1. \(\frac{4}{9} \cdot \frac{3}{32} = \frac{4 \cdot 3}{9 \cdot 32} = \frac{12}{288} = \frac{1}{24}\)
2. \(\frac{5}{9} \cdot \frac{7}{8} = \frac{5 \cdot 7}{9 \cdot 8} = \frac{35}{72}\)
3. \(\frac{27}{56} \cdot \frac{56}{45} = \frac{27 \cdot 56}{56 \cdot 45} = \frac{27}{45} = \frac{3}{5}\)
4. \(\frac{45}{64} \cdot \frac{40}{63} = \frac{45 \cdot 40}{64 \cdot 63} = \frac{(5 \cdot 9) \cdot (5 \cdot 8)}{(8 \cdot 8) \cdot (7 \cdot 9)} = \frac{5 \cdot 5}{8 \cdot 7} = \frac{25}{56}\)

Ответ: 1) \(\frac{1}{24}\), 2) \(\frac{35}{72}\), 3) \(\frac{3}{5}\), 4) \(\frac{25}{56}\).