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

Решение:

1. а) \( 6 \frac{1}{3} - 8 = \frac{19}{3} - \frac{24}{3} = \frac{19 - 24}{3} = \frac{-5}{3} = -1 \frac{2}{3} \)
2. б) \( -2 \frac{2}{7} + 4 \frac{3}{5} = -\frac{16}{7} + \frac{23}{5} = \frac{-16 \cdot 5 + 23 \cdot 7}{35} = \frac{-80 + 161}{35} = \frac{81}{35} = 2 \frac{11}{35} \)
3. в) \( 5 \frac{1}{3} - 6 \frac{2}{9} = \frac{16}{3} - \frac{56}{9} = \frac{16 \cdot 3 - 56}{9} = \frac{48 - 56}{9} = \frac{-8}{9} \)
4. г) \( \frac{3}{8} : \frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{48}{72} = \frac{2}{3} \)
5. д) \( \frac{5}{12} \cdot (-6) = \frac{5 \cdot (-6)}{12} = \frac{-30}{12} = -\frac{5}{2} = -2,5 \)
6. е) \( -3 \frac{1}{2} \cdot \frac{3}{9} = -\frac{7}{2} \cdot \frac{1}{3} = \frac{-7 \cdot 1}{2 \cdot 3} = \frac{-7}{6} = -1 \frac{1}{6} \)

Ответ: а) \( -1 \frac{2}{3} \); б) \( 2 \frac{11}{35} \); в) \( -\frac{8}{9} \); г) \( \frac{2}{3} \); д) -2,5; е) \( -1 \frac{1}{6} \).