1. Вычислите: a) 1$$\frac{2}{5}$$+3$$\frac{7}{15}$$; б) 4$$\frac{3}{14}$$-1$$\frac{2}{21}$$; в) 3$$\frac{5}{6}$$+2$$\frac{7}{15}$$-1$$\frac{29}{30}$$. 2. Вычислите: a) 4$$\frac{1}{6}$$·3$$\frac{3}{5}$$; б) 1$$\frac{2}{13}$$:1$$\frac{4}{11}$$; в) 2$$\frac{2}{3}$$·1$$\frac{1}{8}$$:6$$\frac{2}{3}$$. 3. Вычислите: 2:2$$\frac{2}{3}$$+1$$\frac{4}{5}$$·3$$\frac{1}{3}$$-2$$\frac{5}{6}$$.

Решение:

1. Вычислите:
   • a) $$1\frac{2}{5}+3\frac{7}{15}$$ = $$1\frac{6}{15}+3\frac{7}{15}$$ = $$4\frac{13}{15}$$

   Ответ: $$4\frac{13}{15}$$

   • б) $$4\frac{3}{14}-1\frac{2}{21}$$ = $$4\frac{9}{42}-1\frac{4}{42}$$=$$3\frac{5}{42}$$

   Ответ: $$3\frac{5}{42}$$

   • в) $$3\frac{5}{6}+2\frac{7}{15}-1\frac{29}{30}$$ = $$3\frac{25}{30}+2\frac{14}{30}-1\frac{29}{30}$$=$$4\frac{10}{30}$$=$$4\frac{1}{3}$$

   Ответ: $$4\frac{1}{3}$$

2. Вычислите:
   • a) $$4\frac{1}{6}\cdot3\frac{3}{5}$$ = $$\frac{25}{6}\cdot\frac{18}{5}$$ = $$\frac{5}{1}\cdot\frac{3}{1}$$=15

   Ответ: 15

   • б) $$1\frac{2}{13}:1\frac{4}{11}$$ = $$\frac{15}{13}:\frac{15}{11}$$ = $$\frac{15}{13}\cdot\frac{11}{15}$$ = $$\frac{1}{13}\cdot\frac{11}{1}$$ = $$\frac{11}{13}$$

   Ответ: $$\frac{11}{13}$$

   • в) $$2\frac{2}{3}\cdot1\frac{1}{8}:6\frac{2}{3}$$ = $$\frac{8}{3}\cdot\frac{9}{8}:\frac{20}{3}$$ = $$\frac{1}{1}\cdot\frac{3}{1}:\frac{20}{3}$$ = $$\frac{3}{1}:\frac{20}{3}$$ = $$\frac{3}{1}\cdot\frac{3}{20}$$ = $$\frac{9}{20}$$

   Ответ: $$\frac{9}{20}$$

3. Вычислите: $$2:2\frac{2}{3}+1\frac{4}{5}\cdot3\frac{1}{3}-2\frac{5}{6}$$ = $$2:\frac{8}{3}+\frac{9}{5}\cdot\frac{10}{3}-\frac{17}{6}$$ = $$2\cdot\frac{3}{8}+\frac{3}{1}\cdot\frac{2}{1}-\frac{17}{6}$$ = $$\frac{3}{4}+6-\frac{17}{6}$$ = $$\frac{9}{12}+\frac{72}{12}-\frac{34}{12}$$ = $$\frac{47}{12}$$ = $$3\frac{11}{12}$$

Ответ: $$3\frac{11}{12}$$