Ответ:

1) $$7 \frac{8}{9} - 2 \frac{2}{3} = 7 + \frac{8}{9} - 2 - \frac{2}{3} = (7 - 2) + (\frac{8}{9} - \frac{2}{3}) = 5 + (\frac{8}{9} - \frac{2 \cdot 3}{3 \cdot 3}) = 5 + (\frac{8}{9} - \frac{6}{9}) = 5 + \frac{2}{9} = 5 \frac{2}{9}$$

2) $$4 \frac{17}{18} - 2 \frac{7}{12} = 4 + \frac{17}{18} - 2 - \frac{7}{12} = (4 - 2) + (\frac{17}{18} - \frac{7}{12}) = 2 + (\frac{17 \cdot 2}{18 \cdot 2} - \frac{7 \cdot 3}{12 \cdot 3}) = 2 + (\frac{34}{36} - \frac{21}{36}) = 2 + \frac{13}{36} = 2 \frac{13}{36}$$

3) $$15 \frac{8}{21} - 6 \frac{5}{14} = 15 + \frac{8}{21} - 6 - \frac{5}{14} = (15 - 6) + (\frac{8}{21} - \frac{5}{14}) = 9 + (\frac{8 \cdot 2}{21 \cdot 2} - \frac{5 \cdot 3}{14 \cdot 3}) = 9 + (\frac{16}{42} - \frac{15}{42}) = 9 + \frac{1}{42} = 9 \frac{1}{42}$$

4) $$6 \frac{19}{48} - 5 \frac{11}{32} = 6 + \frac{19}{48} - 5 - \frac{11}{32} = (6 - 5) + (\frac{19}{48} - \frac{11}{32}) = 1 + (\frac{19 \cdot 2}{48 \cdot 2} - \frac{11 \cdot 3}{32 \cdot 3}) = 1 + (\frac{38}{96} - \frac{33}{96}) = 1 + \frac{5}{96} = 1 \frac{5}{96}$$

Ответ: 1) 5 2/9; 2) 2 13/36; 3) 9 1/42; 4) 1 5/96