2.368 Упростите выражение: a) $$\frac{8}{7} a + \frac{2}{7} a$$; б) $$\frac{9}{14} b - \frac{3}{14} b$$; в) $$\frac{7}{9} c - \frac{11}{18} c$$; г) $$\frac{4}{13} p + \frac{9}{13} p$$; д) $$\frac{7}{8} x - \frac{5}{6} x$$; е) $$\frac{4}{11} a + a$$; ж) $$z - \frac{1}{9} z$$; з) $$1\frac{3}{4} t - \frac{7}{8} t$$.

Упростим выражение:

1. a) $$\frac{8}{7} a + \frac{2}{7} a = (\frac{8}{7} + \frac{2}{7}) a = \frac{8+2}{7} a = \frac{10}{7} a = 1\frac{3}{7} a$$
2. б) $$\frac{9}{14} b - \frac{3}{14} b = (\frac{9}{14} - \frac{3}{14}) b = \frac{9-3}{14} b = \frac{6}{14} b = \frac{3}{7} b$$
3. в) $$\frac{7}{9} c - \frac{11}{18} c = (\frac{7}{9} - \frac{11}{18}) c = (\frac{7 \cdot 2}{9 \cdot 2} - \frac{11}{18}) c = (\frac{14}{18} - \frac{11}{18}) c = \frac{14-11}{18} c = \frac{3}{18} c = \frac{1}{6} c$$
4. г) $$\frac{4}{13} p + \frac{9}{13} p = (\frac{4}{13} + \frac{9}{13}) p = \frac{4+9}{13} p = \frac{13}{13} p = 1 p = p$$
5. д) $$\frac{7}{8} x - \frac{5}{6} x = (\frac{7}{8} - \frac{5}{6}) x = (\frac{7 \cdot 3}{8 \cdot 3} - \frac{5 \cdot 4}{6 \cdot 4}) x = (\frac{21}{24} - \frac{20}{24}) x = \frac{21-20}{24} x = \frac{1}{24} x$$
6. е) $$\frac{4}{11} a + a = \frac{4}{11} a + 1a = (\frac{4}{11} + 1) a = (\frac{4}{11} + \frac{11}{11}) a = \frac{4+11}{11} a = \frac{15}{11} a = 1\frac{4}{11} a$$
7. ж) $$z - \frac{1}{9} z = 1z - \frac{1}{9} z = (1 - \frac{1}{9}) z = (\frac{9}{9} - \frac{1}{9}) z = \frac{9-1}{9} z = \frac{8}{9} z$$
8. з) $$1\frac{3}{4} t - \frac{7}{8} t = \frac{1 \cdot 4 + 3}{4} t - \frac{7}{8} t = \frac{7}{4} t - \frac{7}{8} t = (\frac{7}{4} - \frac{7}{8}) t = (\frac{7 \cdot 2}{4 \cdot 2} - \frac{7}{8}) t = (\frac{14}{8} - \frac{7}{8}) t = \frac{14-7}{8} t = \frac{7}{8} t$$

Ответ: a) $$1\frac{3}{7} a$$; б) $$\frac{3}{7} b$$; в) $$\frac{1}{6} c$$; г) $$p$$; д) $$\frac{1}{24} x$$; е) $$1\frac{4}{11} a$$; ж) $$\frac{8}{9} z$$; з) $$\frac{7}{8} t$$