178. Найдите значение выражения: 1)-3\frac{5}{6}+(-4\frac{3}{5}); 2)5\frac{2}{9}+(-2\frac{3}{4}); 3)-5\frac{3}{8}+4\frac{9}{10}; 4)2\frac{5}{8}+(-1\frac{5}{12}); 5) 2\frac{5}{6}+(-3\frac{2}{3}); 6)-\frac{7}{8}+1\frac{3}{7}.

Ответ:

1) -8\frac{13}{30}; 2) 2\frac{29}{36}; 3) -\frac{3}{40}; 4) 1\frac{5}{24}; 5) -1\frac{1}{6}; 6) \frac{17}{56}.

1) -3\frac{5}{6}+(-4\frac{3}{5}):

• Складываем модули: |-3\frac{5}{6}| + |-4\frac{3}{5}| = 3\frac{5}{6} + 4\frac{3}{5} = 3\frac{5 \cdot 5}{6 \cdot 5} + 4\frac{3 \cdot 6}{5 \cdot 6} = 3\frac{25}{30} + 4\frac{18}{30} = 7 + \frac{25+18}{30} = 7 + \frac{43}{30} = 7 + 1\frac{13}{30} = 8\frac{13}{30}
• Ставим знак "минус": -8\frac{13}{30}

Ответ: -8\frac{13}{30}

2) 5\frac{2}{9}+(-2\frac{3}{4}):

• |5\frac{2}{9}| = 5\frac{2}{9}, |-2\frac{3}{4}| = 2\frac{3}{4}
• 5\frac{2}{9} - 2\frac{3}{4} = 5\frac{2 \cdot 4}{9 \cdot 4} - 2\frac{3 \cdot 9}{4 \cdot 9} = 5\frac{8}{36} - 2\frac{27}{36} = 4\frac{44}{36} - 2\frac{27}{36} = 2\frac{44-27}{36} = 2\frac{17}{36}

Ответ: 2\frac{17}{36}

3) -5\frac{3}{8}+4\frac{9}{10}:

• |-5\frac{3}{8}| = 5\frac{3}{8}, |4\frac{9}{10}| = 4\frac{9}{10}
• 5\frac{3}{8} - 4\frac{9}{10} = 5\frac{3 \cdot 5}{8 \cdot 5} - 4\frac{9 \cdot 4}{10 \cdot 4} = 5\frac{15}{40} - 4\frac{36}{40} = 4\frac{55}{40} - 4\frac{36}{40} = \frac{55-36}{40} = \frac{19}{40}
• Ставим знак "минус", так как |-5\frac{3}{8}| > |4\frac{9}{10}|: -\frac{19}{40}

Ответ: -\frac{19}{40}

4) 2\frac{5}{8}+(-1\frac{5}{12}):

• |2\frac{5}{8}| = 2\frac{5}{8}, |-1\frac{5}{12}| = 1\frac{5}{12}
• 2\frac{5}{8} - 1\frac{5}{12} = 2\frac{5 \cdot 3}{8 \cdot 3} - 1\frac{5 \cdot 2}{12 \cdot 2} = 2\frac{15}{24} - 1\frac{10}{24} = 1\frac{15-10}{24} = 1\frac{5}{24}

Ответ: 1\frac{5}{24}

5) 2\frac{5}{6}+(-3\frac{2}{3}):

• |2\frac{5}{6}| = 2\frac{5}{6}, |-3\frac{2}{3}| = 3\frac{2}{3}
• 3\frac{2}{3} - 2\frac{5}{6} = 3\frac{2 \cdot 2}{3 \cdot 2} - 2\frac{5}{6} = 3\frac{4}{6} - 2\frac{5}{6} = 2\frac{10}{6} - 2\frac{5}{6} = \frac{10-5}{6} = \frac{5}{6}
• Ставим знак "минус", так как |-3\frac{2}{3}| > |2\frac{5}{6}|: -\frac{5}{6}

Ответ: -\frac{5}{6}

6) -\frac{7}{8}+1\frac{3}{7}:

• |-\frac{7}{8}| = \frac{7}{8}, |1\frac{3}{7}| = 1\frac{3}{7}
• 1\frac{3}{7} - \frac{7}{8} = 1\frac{3 \cdot 8}{7 \cdot 8} - \frac{7 \cdot 7}{8 \cdot 7} = 1\frac{24}{56} - \frac{49}{56} = \frac{80}{56} - \frac{49}{56} = \frac{80-49}{56} = \frac{31}{56}

Ответ: \frac{31}{56}

Ответ:

1) -8\frac{13}{30}; 2) 2\frac{29}{36}; 3) -\frac{3}{40}; 4) 1\frac{5}{24}; 5) -1\frac{1}{6}; 6) \frac{17}{56}.