3. Найдите произведение или частное: 1) a) \(\frac{9}{13} \cdot \frac{26}{27}\) 2) a) \(1\frac{2}{3} \cdot 1\frac{1}{5}\) 3) a) \(\frac{1}{2} : \left(-\frac{1}{32}\right)\) б) \(-\frac{5}{14} \cdot \frac{42}{75}\) б) \(-3\frac{1}{5} \cdot 1\frac{1}{4}\) б) \(-\frac{5}{7} : \left(-1\frac{4}{21}\right)\) в) \(\frac{17}{24} \cdot \left(-\frac{48}{51}\right)\) в) \(-4\frac{1}{6} \cdot \left(-2\frac{2}{5}\right)\) в) \(5\frac{1}{3} : 2\frac{2}{9}\)

Решение:

1. a) \(\frac{9}{13} \cdot \frac{26}{27} = \frac{9 \cdot 26}{13 \cdot 27} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}\)
2. a) \(1\frac{2}{3} \cdot 1\frac{1}{5} = \frac{5}{3} \cdot \frac{6}{5} = \frac{5 \cdot 6}{3 \cdot 5} = \frac{1 \cdot 2}{1 \cdot 1} = 2\)
3. a) \(\frac{1}{2} : \left(-\frac{1}{32}\right) = \frac{1}{2} \cdot \left(-\frac{32}{1}\right) = -\frac{32}{2} = -16\)
4. б) \(-\frac{5}{14} \cdot \frac{42}{75} = -\frac{5 \cdot 42}{14 \cdot 75} = -\frac{1 \cdot 3}{1 \cdot 15} = -\frac{3}{15} = -\frac{1}{5}\)
5. б) \(-3\frac{1}{5} \cdot 1\frac{1}{4} = -\frac{16}{5} \cdot \frac{5}{4} = -\frac{16 \cdot 5}{5 \cdot 4} = -\frac{4}{1} = -4\)
6. б) \(-\frac{5}{7} : \left(-1\frac{4}{21}\right) = \frac{5}{7} : \frac{25}{21} = \frac{5}{7} \cdot \frac{21}{25} = \frac{5 \cdot 21}{7 \cdot 25} = \frac{1 \cdot 3}{1 \cdot 5} = \frac{3}{5}\)
7. в) \(\frac{17}{24} \cdot \left(-\frac{48}{51}\right) = -\frac{17 \cdot 48}{24 \cdot 51} = -\frac{17 \cdot 2}{1 \cdot 51} = -\frac{1 \cdot 2}{1 \cdot 3} = -\frac{2}{3}\)
8. в) \(-4\frac{1}{6} \cdot \left(-2\frac{2}{5}\right) = \frac{25}{6} \cdot \frac{12}{5} = \frac{25 \cdot 12}{6 \cdot 5} = \frac{5 \cdot 2}{1 \cdot 1} = 10\)
9. в) \(5\frac{1}{3} : 2\frac{2}{9} = \frac{16}{3} : \frac{20}{9} = \frac{16}{3} \cdot \frac{9}{20} = \frac{16 \cdot 9}{3 \cdot 20} = \frac{4 \cdot 3}{1 \cdot 5} = \frac{12}{5} = 2\frac{2}{5}\)

Ответ: 1) a) \(\frac{2}{3}\); 2) a) 2; 3) a) -16; б) \(-\frac{1}{5}\); б) -4; б) \(\frac{3}{5}\); в) \(-\frac{2}{3}\); в) 10; в) \(2\frac{2}{5}\).