40. Сократите: 1) 9·16 / 8·27; 2) 25·12 / 8·28; 3) 2·3·5 / 4·9·25; 4) 7·13 - 7·2 / 35·9 + 35·2

Решение:

1. \( \frac{9 \cdot 16}{8 \cdot 27} = \frac{9}{27} \cdot \frac{16}{8} = \frac{1}{3} \cdot 2 = \frac{2}{3} \)
2. \( \frac{25 \cdot 12}{8 \cdot 28} = \frac{25}{28} \cdot \frac{12}{8} = \frac{25}{28} \cdot \frac{3}{2} = \frac{25 \cdot 3}{28 \cdot 2} = \frac{75}{56} \)
3. \( \frac{2 \cdot 3 \cdot 5}{4 \cdot 9 \cdot 25} = \frac{2}{4} \cdot \frac{3}{9} \cdot \frac{5}{25} = \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{5} = \frac{1}{30} \)
4. \( \frac{7 \cdot 13 - 7 \cdot 2}{35 \cdot 9 + 35 \cdot 2} = \frac{7(13-2)}{35(9+2)} = \frac{7 \cdot 11}{35 \cdot 11} = \frac{7}{35} = \frac{1}{5} \)

Ответ: 1) \(\frac{2}{3}\); 2) \(\frac{75}{56}\); 3) \(\frac{1}{30}\); 4) \(\frac{1}{5}\).