1104. Приведите подобные слагаемые: 1) -\(\frac{1}{6}\)x + \(\frac{1}{4}\)y + \(\frac{1}{9}\)x - \(\frac{1}{2}\)y; 3) -\(\frac{15}{16}\)m + \(\frac{7}{12}\)n + \(\frac{5}{12}\)m - \(\frac{3}{8}\)p - \(\frac{5}{8}\)n - \(\frac{1}{4}\)p. 2) \(\frac{3}{7}\)a - \(\frac{2}{15}\)b - \(\frac{5}{14}\)a + \(\frac{7}{30}\)b; 4) \(\frac{7}{18}\)b - \(\frac{13}{28}\)c - \(\frac{5}{14}\)c - \(\frac{23}{36}\)b + \(\frac{4}{7}\)c + \(\frac{4}{9}\)b.

Решение:

1. • \( (-\frac{1}{6} + \frac{1}{9})x + (\frac{1}{4} - \frac{1}{2})y = (-\frac{3}{18} + \frac{2}{18})x + (\frac{1}{4} - \frac{2}{4})y = -\frac{1}{18}x - \frac{1}{4}y \)
   • \( (\frac{3}{7} - \frac{5}{14})a + (-\frac{2}{15} + \frac{7}{30})b = (\frac{6}{14} - \frac{5}{14})a + (-\frac{4}{30} + \frac{7}{30})b = \frac{1}{14}a + \frac{3}{30}b = \frac{1}{14}a + \frac{1}{10}b \)
   • \( (-\frac{15}{16} + \frac{5}{12})m + (\frac{7}{12} - \frac{5}{8})n - (\frac{3}{8} + \frac{1}{4})p = (-\frac{45}{48} + \frac{20}{48})m + (\frac{14}{24} - \frac{15}{24})n - (\frac{3}{8} + \frac{2}{8})p = -\frac{25}{48}m - \frac{1}{24}n - \frac{5}{8}p \)
   • \( (\frac{7}{18} - \frac{23}{36})b + (-\frac{13}{28} - \frac{5}{14} + \frac{4}{7})c = (\frac{14}{36} - \frac{23}{36})b + (-\frac{13}{28} - \frac{10}{28} + \frac{16}{28})c = -\frac{9}{36}b + \frac{-13 - 10 + 16}{28}c = -\frac{1}{4}b - \frac{7}{28}c = -\frac{1}{4}b - \frac{1}{4}c \)

Ответ: 1) \(-\frac{1}{18}x - \frac{1}{4}y\); 2) \(\frac{1}{14}a + \frac{1}{10}b\); 3) \(-\frac{25}{48}m - \frac{1}{24}n - \frac{5}{8}p\); 4) \(-\frac{1}{4}b - \frac{1}{4}c\).