$-\frac{1}{6}x + \frac{1}{4}y + \frac{1}{9}x - \frac{1}{2}y = (-\frac{1}{6}x + \frac{1}{9}x) + (\frac{1}{4}y - \frac{1}{2}y) = (-\frac{3}{18}x + \frac{2}{18}x) + (\frac{1}{4}y - \frac{2}{4}y) = -\frac{1}{18}x - \frac{1}{4}y$

$\frac{3}{7}a - \frac{2}{15}b - \frac{5}{14}a + \frac{7}{30}b = (\frac{3}{7}a - \frac{5}{14}a) + (-\frac{2}{15}b + \frac{7}{30}b) = (\frac{6}{14}a - \frac{5}{14}a) + (-\frac{4}{30}b + \frac{7}{30}b) = \frac{1}{14}a + \frac{3}{30}b = \frac{1}{14}a + \frac{1}{10}b$

$-\frac{15}{16}m + \frac{7}{12}n + \frac{5}{12}m - \frac{3}{8}p - \frac{5}{8}n - \frac{1}{4}p = (-\frac{15}{16}m + \frac{5}{12}m) + (\frac{7}{12}n - \frac{5}{8}n) + (-\frac{3}{8}p - \frac{1}{4}p) = (-\frac{45}{48}m + \frac{20}{48}m) + (\frac{14}{24}n - \frac{15}{24}n) + (-\frac{3}{8}p - \frac{2}{8}p) = -\frac{25}{48}m - \frac{1}{24}n - \frac{5}{8}p$

$\frac{7}{18}b - \frac{13}{28}c - \frac{5}{14}c - \frac{23}{36}b + \frac{4}{7}c + \frac{4}{9}b = (\frac{7}{18}b - \frac{23}{36}b + \frac{4}{9}b) + (-\frac{13}{28}c - \frac{5}{14}c + \frac{4}{7}c) = (\frac{14}{36}b - \frac{23}{36}b + \frac{16}{36}b) + (-\frac{13}{28}c - \frac{10}{28}c + \frac{16}{28}c) = \frac{7}{36}b - \frac{7}{28}c = \frac{7}{36}b - \frac{1}{4}c$