6. Вычислите: a) 6\( \frac{1}{3} \) - 8; б) \(-2\frac{2}{7} + 4\frac{3}{5}\); в) 5\( \frac{1}{3} \) \(\cdot\) 6\( \frac{1}{4} \); г) \(\frac{3}{8} : \left(-\frac{9}{16}\right)\); д) \(\frac{5}{12} \cdot (-6)\); e) \(-3\frac{2}{9} \cdot 3\); ж) \(\frac{4}{7} \cdot (-49)\); 3) \(-16 : \left(-\frac{4}{9}\right)\); и) \(-3\frac{1}{2} \cdot \left(-1\frac{3}{7}\right)\).

Решение:

1. \(6\frac{1}{3} - 8 = \frac{19}{3} - \frac{24}{3} = \frac{-5}{3} = -1\frac{2}{3}\)
2. \(-2\frac{2}{7} + 4\frac{3}{5} = -\frac{16}{7} + \frac{23}{5} = \frac{-16 \cdot 5 + 23 \cdot 7}{35} = \frac{-80 + 161}{35} = \frac{81}{35} = 2\frac{11}{35}\)
3. \(5\frac{1}{3} \cdot 6\frac{1}{4} = \frac{16}{3} \cdot \frac{25}{4} = \frac{16 \cdot 25}{3 \cdot 4} = \frac{4 \cdot 25}{3} = \frac{100}{3} = 33\frac{1}{3}\)
4. \(\frac{3}{8} : \left(-\frac{9}{16}\right) = \frac{3}{8} \cdot \left(-\frac{16}{9}\right) = -\frac{3 \cdot 16}{8 \cdot 9} = -\frac{1 \cdot 2}{1 \cdot 3} = -\frac{2}{3}\)
5. \(\frac{5}{12} \cdot (-6) = -\frac{5 \cdot 6}{12} = -\frac{5}{2} = -2\frac{1}{2}\)
6. \(-3\frac{2}{9} \cdot 3 = -\frac{29}{9} \cdot 3 = -\frac{29 \cdot 3}{9} = -\frac{29}{3} = -9\frac{2}{3}\)
7. \(\frac{4}{7} \cdot (-49) = -\frac{4 \cdot 49}{7} = -4 \cdot 7 = -28\)
8. \(-16 : \left(-\frac{4}{9}\right) = 16 \cdot \frac{9}{4} = \frac{16 \cdot 9}{4} = 4 \cdot 9 = 36\)
9. \(-3\frac{1}{2} \cdot \left(-1\frac{3}{7}\right) = \left(-\frac{7}{2}\right) \cdot \left(-\frac{10}{7}\right) = \frac{7 \cdot 10}{2 \cdot 7} = \frac{10}{2} = 5\)

Ответ: а) \(-1\frac{2}{3}\); б) \(2\frac{11}{35}\); в) \(33\frac{1}{3}\); г) \(-\frac{2}{3}\); д) \(-2\frac{1}{2}\); е) \(-9\frac{2}{3}\); ж) \(-28\); з) \(36\); и) \(5\).