1104. Приведите подобные слагаемые:

Решение:

1. \( \frac{1}{6}x + \frac{1}{9}y - \frac{1}{2}x - \frac{2}{9}y = \left(\frac{1}{6} - \frac{1}{2}\right)x + \left(\frac{1}{9} - \frac{2}{9}\right)y = \left(\frac{1-3}{6}\right)x + \left(-\frac{1}{9}\right)y = -\frac{2}{6}x - \frac{1}{9}y = -\frac{1}{3}x - \frac{1}{9}y \)
2. \( \frac{7}{15}m + \frac{7}{12}n + \frac{5}{12}m - \frac{3}{8}n - \frac{5}{8}p = \left(\frac{7}{15} + \frac{5}{12}\right)m + \left(\frac{7}{12} - \frac{3}{8}\right)n - \frac{5}{8}p = \left(\frac{28+25}{60}\right)m + \left(\frac{14-9}{24}\right)n - \frac{5}{8}p = \frac{53}{60}m + \frac{5}{24}n - \frac{5}{8}p \)
3. \( \frac{7}{13}b - \frac{13}{14}c - \frac{5}{14}c - \frac{23}{36}b + \frac{4}{7}b + \frac{4}{9}b = \left(\frac{7}{13} - \frac{23}{36} + \frac{4}{7} + \frac{4}{9}\right)b + \left(-\frac{13}{14} - \frac{5}{14}\right)c = \left(\frac{7}{13} - \frac{23}{36} + \frac{4}{7} + \frac{4}{9}\right)b - \frac{18}{14}c = \left(\frac{7}{13} - \frac{23}{36} + \frac{4}{7} + \frac{4}{9}\right)b - \frac{9}{7}c \)

Ответ: 1) -1/3x - 1/9y; 2) 53/60m + 5/24n - 5/8p; 3) (7/13 - 23/36 + 4/7 + 4/9)b - 9/7c.