11. Найдите значение выражения: а) $$9-3\frac{1}{2}\cdot(1\frac{3}{7}+2\frac{1}{2}):2\frac{1}{7}$$; б) $$3\frac{7}{19}\cdot(\frac{5}{12}+\frac{3}{8}):1\frac{1}{3}-1\frac{1}{8}:(1\frac{1}{5}-\frac{1}{4})$$; в) $$2:3\frac{1}{5}+(3\frac{1}{4}-\frac{2}{3}):\frac{2}{3}-(2\frac{5}{18}-\frac{17}{36})\cdot\frac{18}{65}$$; г) $$\frac{4}{75}:(\frac{4}{5}\cdot1\frac{1}{4}):(\frac{23}{25}-\frac{13}{15})\cdot\frac{1}{15}-\frac{1}{15}$$.

Решим данные примеры по действиям, соблюдая порядок выполнения операций.

а) $$9-3\frac{1}{2}\cdot(1\frac{3}{7}+2\frac{1}{2}):2\frac{1}{7}$$

1. $$1\frac{3}{7}+2\frac{1}{2}=\frac{10}{7}+\frac{5}{2}=\frac{10\cdot2+5\cdot7}{14}=\frac{20+35}{14}=\frac{55}{14}$$;
2. $$3\frac{1}{2}\cdot\frac{55}{14}=\frac{7}{2}\cdot\frac{55}{14}=\frac{1}{2}\cdot\frac{55}{2}=\frac{55}{4}$$;
3. $$\frac{55}{4}:2\frac{1}{7}=\frac{55}{4}:\frac{15}{7}=\frac{55}{4}\cdot\frac{7}{15}=\frac{11}{4}\cdot\frac{7}{3}=\frac{77}{12}$$;
4. $$9-\frac{77}{12}=\frac{9\cdot12-77}{12}=\frac{108-77}{12}=\frac{31}{12}=2\frac{7}{12}$$.

Ответ: $$2\frac{7}{12}$$

б) $$3\frac{7}{19}\cdot(\frac{5}{12}+\frac{3}{8}):1\frac{1}{3}-1\frac{1}{8}:(1\frac{1}{5}-\frac{1}{4})$$

1. $$\frac{5}{12}+\frac{3}{8}=\frac{5\cdot2+3\cdot3}{24}=\frac{10+9}{24}=\frac{19}{24}$$;
2. $$3\frac{7}{19}\cdot\frac{19}{24}=\frac{64}{19}\cdot\frac{19}{24}=\frac{64}{24}=\frac{8}{3}$$;
3. $$\frac{8}{3}:1\frac{1}{3}=\frac{8}{3}:\frac{4}{3}=\frac{8}{3}\cdot\frac{3}{4}=\frac{8}{4}=2$$;
4. $$1\frac{1}{5}-\frac{1}{4}=\frac{6}{5}-\frac{1}{4}=\frac{6\cdot4-1\cdot5}{20}=\frac{24-5}{20}=\frac{19}{20}$$;
5. $$1\frac{1}{8}:\frac{19}{20}=\frac{9}{8}:\frac{19}{20}=\frac{9}{8}\cdot\frac{20}{19}=\frac{9}{2}\cdot\frac{5}{19}=\frac{45}{38}$$;
6. $$2-\frac{45}{38}=\frac{2\cdot38-45}{38}=\frac{76-45}{38}=\frac{31}{38}$$.

Ответ: $$\frac{31}{38}$$

в) $$2:3\frac{1}{5}+(3\frac{1}{4}-\frac{2}{3}):\frac{2}{3}-(2\frac{5}{18}-\frac{17}{36})\cdot\frac{18}{65}$$

1. $$3\frac{1}{4}-\frac{2}{3}=\frac{13}{4}-\frac{2}{3}=\frac{13\cdot3-2\cdot4}{12}=\frac{39-8}{12}=\frac{31}{12}$$;
2. $$2:3\frac{1}{5}=2:\frac{16}{5}=2\cdot\frac{5}{16}=\frac{5}{8}$$;
3. $$\frac{31}{12}:\frac{2}{3}=\frac{31}{12}\cdot\frac{3}{2}=\frac{31}{4}\cdot\frac{1}{2}=\frac{31}{8}$$;
4. $$2\frac{5}{18}-\frac{17}{36}=\frac{41}{18}-\frac{17}{36}=\frac{41\cdot2-17}{36}=\frac{82-17}{36}=\frac{65}{36}$$;
5. $$\frac{65}{36}\cdot\frac{18}{65}=\frac{1}{2}$$;
6. $$\frac{5}{8}+\frac{31}{8}-\frac{1}{2}=\frac{5+31-4}{8}=\frac{32}{8}=4$$.

Ответ: 4

г) $$\frac{4}{75}:(\frac{4}{5}\cdot1\frac{1}{4}):(\frac{23}{25}-\frac{13}{15})\cdot\frac{1}{15}-\frac{1}{15}$$

1. $$\frac{4}{5}\cdot1\frac{1}{4}=\frac{4}{5}\cdot\frac{5}{4}=1$$;
2. $$\frac{4}{75}:1=\frac{4}{75}$$;
3. $$\frac{23}{25}-\frac{13}{15}=\frac{23\cdot3-13\cdot5}{75}=\frac{69-65}{75}=\frac{4}{75}$$;
4. $$\frac{4}{75}:\frac{4}{75}=1$$;
5. $$1\cdot\frac{1}{15}=\frac{1}{15}$$;
6. $$\frac{1}{15}-\frac{1}{15}=0$$.

Ответ: 0