Решение:
а) $18\frac{5}{9} + (-22\frac{2}{9}) = (18 - 22) + (\frac{5}{9} - \frac{2}{9}) = -4 + \frac{3}{9} = -4 + \frac{1}{3} = -3 + (-\frac{3}{3} + \frac{1}{3}) = -3 - \frac{2}{3} = -3\frac{2}{3}$;
б) $25\frac{3}{4} + (-51\frac{1}{4}) = (25 - 51) + (\frac{3}{4} - \frac{1}{4}) = -26 + \frac{2}{4} = -26 + \frac{1}{2} = -25 + (-\frac{2}{2} + \frac{1}{2}) = -25 -\frac{1}{2} = -25\frac{1}{2}$;
в) $-6\frac{2}{9} + (1\frac{2}{3}) = (-6 + 1) + (-\frac{2}{9} + \frac{2}{3}) = -5 + (-\frac{2}{9} + \frac{6}{9}) = -5 + \frac{4}{9} = -4 + (-\frac{9}{9} + \frac{4}{9}) = -5 - \frac{5}{9} = -4\frac{5}{9}$;
г) $7\frac{1}{12} + (-8\frac{3}{4}) = (7 - 8) + (\frac{1}{12} - \frac{3}{4}) = -1 + (\frac{1}{12} - \frac{9}{12}) = -1 - \frac{8}{12} = -1 - \frac{8}{12} = -1\frac{2}{3}$;
д) $18\frac{5}{6} + (-7\frac{1}{2}) = (18 - 7) + (\frac{5}{6} - \frac{1}{2}) = 11 + (\frac{5}{6} - \frac{3}{6}) = 11 + \frac{2}{6} = 11 + \frac{1}{3} = 11\frac{1}{3}$;
е) $2\frac{1}{5} + (-\frac{4}{15}) = 2 + (\frac{1}{5} - \frac{4}{15}) = 2 + (\frac{3}{15} - \frac{4}{15}) = 2 + (-\frac{1}{15}) = 1 + (\frac{15}{15} - \frac{1}{15}) = 1 + \frac{14}{15} = 1\frac{14}{15}$.
Ответ:
а) $-3\frac{2}{3}$;
б) $-25\frac{1}{2}$;
в) $-4\frac{5}{9}$;
г) $-1\frac{2}{3}$;
д) $11\frac{1}{3}$;
е) $1\frac{14}{15}$.