5.86 Упростите выражение: a) 0,4n - 0,7m - 0,9n + 0,7m; б) 6c - 8c - 4c + 21 - 13; в) \( \frac{3}{4}a + \frac{5}{6}b - \frac{1}{8}a - \frac{1}{3}b \); г) \( \frac{7}{9}x - \frac{3}{4} - \frac{11}{18}x - \frac{1}{4} \); д) 0,3m - \(\frac{2}{7}\) - 3m + \(\frac{6}{7}\); e) \( \frac{1}{7}a + \frac{1}{4}c - \frac{1}{7}a + \frac{3}{4}c \).

Решение:

1. а) \( 0,4n - 0,7m - 0,9n + 0,7m = (0,4n - 0,9n) + (-0,7m + 0,7m) = -0,5n + 0 = -0,5n \)
2. б) \( 6c - 8c - 4c + 21 - 13 = (6c - 8c - 4c) + (21 - 13) = -6c + 8 \)
3. в) \( \frac{3}{4}a + \frac{5}{6}b - \frac{1}{8}a - \frac{1}{3}b = (\frac{3}{4}a - \frac{1}{8}a) + (\frac{5}{6}b - \frac{1}{3}b) = (\frac{6}{8}a - \frac{1}{8}a) + (\frac{5}{6}b - \frac{2}{6}b) = \frac{5}{8}a + \frac{3}{6}b = \frac{5}{8}a + \frac{1}{2}b \)
4. г) \( \frac{7}{9}x - \frac{3}{4} - \frac{11}{18}x - \frac{1}{4} = (\frac{7}{9}x - \frac{11}{18}x) + (-\frac{3}{4} - \frac{1}{4}) = (\frac{14}{18}x - \frac{11}{18}x) + (-1) = \frac{3}{18}x - 1 = \frac{1}{6}x - 1 \)
5. д) \( 0,3m - \frac{2}{7} - 3m + \frac{6}{7} = (0,3m - 3m) + (-\frac{2}{7} + \frac{6}{7}) = -2,7m + \frac{4}{7} \)
6. е) \( \frac{1}{7}a + \frac{1}{4}c - \frac{1}{7}a + \frac{3}{4}c = (\frac{1}{7}a - \frac{1}{7}a) + (\frac{1}{4}c + \frac{3}{4}c) = 0 + c = c \)