1. Найдите произведение a) \(\frac{5}{7}\) : \(\frac{6}{9}\) б) \(\frac{6}{25}\) : \(\frac{8}{18}\) в) \(1\frac{8}{25} \cdot \frac{4}{11}\) г) \(3\frac{5}{7} \cdot \frac{1}{14}\) д) \(2\frac{2}{3} \cdot 6\)

Решение:

1. \(\frac{5}{7} : \frac{6}{9} = \frac{5}{7} \cdot \frac{9}{6} = \frac{5 \cdot 3}{7 \cdot 2} = \frac{15}{14}\)
2. \(\frac{6}{25} : \frac{8}{18} = \frac{6}{25} \cdot \frac{18}{8} = \frac{3 \cdot 9}{25 \cdot 4} = \frac{27}{100}\)
3. \(1\frac{8}{25} \cdot \frac{4}{11} = \frac{33}{25} \cdot \frac{4}{11} = \frac{3 \cdot 4}{25} = \frac{12}{25}\)
4. \(3\frac{5}{7} \cdot \frac{1}{14} = \frac{26}{7} \cdot \frac{1}{14} = \frac{13}{7 \cdot 7} = \frac{13}{49}\)
5. \(2\frac{2}{3} \cdot 6 = \frac{8}{3} \cdot 6 = 8 \cdot 2 = 16\)

Ответ: а) \(\frac{15}{14}\), б) \(\frac{27}{100}\), в) \(\frac{12}{25}\), г) \(\frac{13}{49}\), д) 16.