5. Решите уравнение:
1) $$8\frac{5}{7}-x = 4\frac{9}{14}$$;
$$x = 8\frac{5}{7}-4\frac{9}{14}$$;
$$x = 8\frac{10}{14}-4\frac{9}{14}$$;
$$x = 4\frac{1}{14}$$.
Ответ: $$x = 4\frac{1}{14}$$.
2) $$(x+7\frac{5}{8})-4\frac{13}{24}=5\frac{1}{16}$$;
$$x+7\frac{5}{8} = 5\frac{1}{16}+4\frac{13}{24}$$;
$$x+7\frac{5}{8} = 5\frac{3}{48}+4\frac{26}{48}$$;
$$x+7\frac{5}{8} = 9\frac{29}{48}$$;
$$x = 9\frac{29}{48}-7\frac{5}{8}$$;
$$x = 9\frac{29}{48}-7\frac{30}{48}$$;
$$x = 8\frac{77}{48}-7\frac{30}{48}$$;
$$x = 1\frac{47}{48}$$.
Ответ: $$x = 1\frac{47}{48}$$.
6. Выполните действия:
1) $$6\frac{8}{9}-3\frac{1}{2}+3\frac{1}{12}$$;
$$6\frac{8}{9}-3\frac{1}{2}+3\frac{1}{12} = 6\frac{32}{36}-3\frac{18}{36}+3\frac{3}{36} = 3\frac{14}{36}+3\frac{3}{36} = 6\frac{17}{36}$$.
Ответ: $$6\frac{17}{36}$$.
2) $$8\frac{7}{9}+6\frac{2}{15}-4,3$$;
$$8\frac{7}{9}+6\frac{2}{15}-4,3 = 8\frac{35}{45}+6\frac{6}{45}-4,3 = 14\frac{41}{45}-4,3 = 14\frac{41}{45}-4\frac{3}{10} = 14\frac{82}{90}-4\frac{27}{90} = 10\frac{55}{90} = 10\frac{11}{18}$$.
Ответ: $$10\frac{11}{18}$$.
3) $$(19\frac{5}{21}-8\frac{3}{14})-6\frac{5}{7}$$;
$$(19\frac{5}{21}-8\frac{3}{14})-6\frac{5}{7} = (19\frac{10}{42}-8\frac{9}{42})-6\frac{5}{7} = 11\frac{1}{42}-6\frac{5}{7} = 11\frac{1}{42}-6\frac{30}{42} = 10\frac{43}{42}-6\frac{30}{42} = 4\frac{13}{42}$$.
Ответ: $$4\frac{13}{42}$$.
4) $$(19-8\frac{7}{8})-(4\frac{5}{6}-2\frac{8}{9})$$;
$$(19-8\frac{7}{8})-(4\frac{5}{6}-2\frac{8}{9}) = (18\frac{8}{8}-8\frac{7}{8})-(4\frac{15}{18}-2\frac{16}{18}) = 10\frac{1}{8}-(3\frac{33}{18}-2\frac{16}{18}) = 10\frac{1}{8}-1\frac{17}{18} = 10\frac{9}{72}-1\frac{68}{72} = 9\frac{81}{72}-1\frac{68}{72} = 8\frac{13}{72}$$.
Ответ: $$8\frac{13}{72}$$.