1. Найдите значение выражения: a) $$(2 \frac{3}{4}+\frac{3}{2}) \cdot 42$$; б) $$(2 \frac{1}{2} - 1 \frac{4}{11}) \cdot 8$$. 2. Вычислите: $$4 \frac{1}{6} \cdot 3 \frac{2}{7} + 2 \frac{5}{7} \cdot 4 \frac{6}{11}$$. 3. Упростите выражение $$2 \frac{3}{11}x - 1 \frac{2}{11}x + \frac{9}{11}x$$.

1. Найдите значение выражения: а) $$(2 \frac{3}{4}+\frac{3}{2}) \cdot 42$$; $$2 \frac{3}{4} = \frac{2 \cdot 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$$. $$\frac{3}{2} = \frac{3 \cdot 2}{2 \cdot 2} = \frac{6}{4}$$. $$\frac{11}{4} + \frac{6}{4} = \frac{11+6}{4} = \frac{17}{4}$$. $$\frac{17}{4} \cdot 42 = \frac{17 \cdot 42}{4} = \frac{17 \cdot 21}{2} = \frac{357}{2} = 178 \frac{1}{2}$$. б) $$(2 \frac{1}{2} - 1 \frac{4}{11}) \cdot 8$$. $$2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2} = \frac{5}{2}$$. $$1 \frac{4}{11} = \frac{1 \cdot 11 + 4}{11} = \frac{15}{11}$$. $$\frac{5}{2} - \frac{15}{11} = \frac{5 \cdot 11}{2 \cdot 11} - \frac{15 \cdot 2}{11 \cdot 2} = \frac{55}{22} - \frac{30}{22} = \frac{25}{22}$$. $$\frac{25}{22} \cdot 8 = \frac{25 \cdot 8}{22} = \frac{25 \cdot 4}{11} = \frac{100}{11} = 9 \frac{1}{11}$$. 2. Вычислите: $$4 \frac{1}{6} \cdot 3 \frac{2}{7} + 2 \frac{5}{7} \cdot 4 \frac{6}{11}$$. $$4 \frac{1}{6} = \frac{4 \cdot 6 + 1}{6} = \frac{25}{6}$$. $$3 \frac{2}{7} = \frac{3 \cdot 7 + 2}{7} = \frac{23}{7}$$. $$2 \frac{5}{7} = \frac{2 \cdot 7 + 5}{7} = \frac{19}{7}$$. $$4 \frac{6}{11} = \frac{4 \cdot 11 + 6}{11} = \frac{50}{11}$$. $$\frac{25}{6} \cdot \frac{23}{7} = \frac{25 \cdot 23}{6 \cdot 7} = \frac{575}{42}$$. $$\frac{19}{7} \cdot \frac{50}{11} = \frac{19 \cdot 50}{7 \cdot 11} = \frac{950}{77}$$. $$\frac{575}{42} + \frac{950}{77} = \frac{575 \cdot 11}{42 \cdot 11} + \frac{950 \cdot 6}{77 \cdot 6} = \frac{6325}{462} + \frac{5700}{462} = \frac{12025}{462} = 25 \frac{475}{462} = 25 + \frac{462 + 13}{462} = 26 \frac{13}{462}$$. 3. Упростите выражение $$2 \frac{3}{11}x - 1 \frac{2}{11}x + \frac{9}{11}x$$. $$2 \frac{3}{11} = \frac{2 \cdot 11 + 3}{11} = \frac{25}{11}$$. $$1 \frac{2}{11} = \frac{1 \cdot 11 + 2}{11} = \frac{13}{11}$$. $$\frac{25}{11}x - \frac{13}{11}x + \frac{9}{11}x = (\frac{25}{11} - \frac{13}{11} + \frac{9}{11})x = (\frac{25-13+9}{11})x = \frac{21}{11}x = 1 \frac{10}{11}x$$. Ответ: 1. а) $$178 \frac{1}{2}$$, б) $$9 \frac{1}{11}$$. 2. $$26 \frac{13}{462}$$. 3. $$1 \frac{10}{11}x$$.