6. Найдите сумму: 1) -6 + (-5); 2) -0,7 + (-2,8); 3) -0,82 + (-0,18); 4) -5/7 + (-9/14); 5) -1/4 + (-1/6); 6) -3/8 + 0. 7. Найдите сумму: 1) -9 + (-13); 2) -3,6 + (-1,5); 3) -5/16 + (-7/16); 4) -3/7 + (-4/9). 58. Вычислите значение выражения: 1) 2/15 + (-3/10); 2) -2/3 + 13/15; 3) 13/16 + (-9/32); 4) -4 5/9 + (-7 1/6); 5) -5 7/8 + (-6 3/10); 6) -5 13/18 + 12 11/12; 7) -13 + 7 3/16; 8) -2 3/8 + (-1 5/9); 9) -8 + 4 5/22; 10) -2 9/20 + 5 7/30; 11) -5 1/4 + 1 3/8; 12) 4 3/7 + (-8 9/14).

6. Найдите сумму:

Давай разберем по порядку каждый пример:

1) \[ -6 + (-5) = -6 - 5 = -11 \]

2) \[ -0.7 + (-2.8) = -0.7 - 2.8 = -3.5 \]

3) \[ -0.82 + (-0.18) = -0.82 - 0.18 = -1 \]

4) \[ -\frac{5}{7} + (-\frac{9}{14}) = -\frac{5}{7} - \frac{9}{14} = -\frac{5 \cdot 2}{7 \cdot 2} - \frac{9}{14} = -\frac{10}{14} - \frac{9}{14} = -\frac{19}{14} = -1\frac{5}{14} \]

5) \[ -\frac{1}{4} + (-\frac{1}{6}) = -\frac{1}{4} - \frac{1}{6} = -\frac{1 \cdot 3}{4 \cdot 3} - \frac{1 \cdot 2}{6 \cdot 2} = -\frac{3}{12} - \frac{2}{12} = -\frac{5}{12} \]

6) \[ -\frac{3}{8} + 0 = -\frac{3}{8} \]

7. Найдите сумму:

1) \[ -9 + (-13) = -9 - 13 = -22 \]

2) \[ -3.6 + (-1.5) = -3.6 - 1.5 = -5.1 \]

3) \[ -\frac{5}{16} + (-\frac{7}{16}) = -\frac{5}{16} - \frac{7}{16} = -\frac{12}{16} = -\frac{3}{4} \]

4) \[ -\frac{3}{7} + (-\frac{4}{9}) = -\frac{3}{7} - \frac{4}{9} = -\frac{3 \cdot 9}{7 \cdot 9} - \frac{4 \cdot 7}{9 \cdot 7} = -\frac{27}{63} - \frac{28}{63} = -\frac{55}{63} \]

58. Вычислите значение выражения:

1) \[ \frac{2}{15} + (-\frac{3}{10}) = \frac{2}{15} - \frac{3}{10} = \frac{2 \cdot 2}{15 \cdot 2} - \frac{3 \cdot 3}{10 \cdot 3} = \frac{4}{30} - \frac{9}{30} = -\frac{5}{30} = -\frac{1}{6} \]

2) \[ -\frac{2}{3} + \frac{13}{15} = -\frac{2 \cdot 5}{3 \cdot 5} + \frac{13}{15} = -\frac{10}{15} + \frac{13}{15} = \frac{3}{15} = \frac{1}{5} \]

3) \[ \frac{13}{16} + (-\frac{9}{32}) = \frac{13}{16} - \frac{9}{32} = \frac{13 \cdot 2}{16 \cdot 2} - \frac{9}{32} = \frac{26}{32} - \frac{9}{32} = \frac{17}{32} \]

4) \[ -4\frac{5}{9} + (-7\frac{1}{6}) = -4\frac{5}{9} - 7\frac{1}{6} = -4 - \frac{5}{9} - 7 - \frac{1}{6} = -11 - \frac{5}{9} - \frac{1}{6} = -11 - \frac{5 \cdot 2}{9 \cdot 2} - \frac{1 \cdot 3}{6 \cdot 3} = -11 - \frac{10}{18} - \frac{3}{18} = -11 - \frac{13}{18} = -11\frac{13}{18} \]

5) \[ -5\frac{7}{8} + (-6\frac{3}{10}) = -5\frac{7}{8} - 6\frac{3}{10} = -5 - \frac{7}{8} - 6 - \frac{3}{10} = -11 - \frac{7}{8} - \frac{3}{10} = -11 - \frac{7 \cdot 5}{8 \cdot 5} - \frac{3 \cdot 4}{10 \cdot 4} = -11 - \frac{35}{40} - \frac{12}{40} = -11 - \frac{47}{40} = -11 - 1\frac{7}{40} = -12\frac{7}{40} \]

6) \[ -5\frac{13}{18} + 12\frac{11}{12} = -5 - \frac{13}{18} + 12 + \frac{11}{12} = 7 + \frac{11}{12} - \frac{13}{18} = 7 + \frac{11 \cdot 3}{12 \cdot 3} - \frac{13 \cdot 2}{18 \cdot 2} = 7 + \frac{33}{36} - \frac{26}{36} = 7 + \frac{7}{36} = 7\frac{7}{36} \]

7) \[ -13 + 7\frac{3}{16} = -13 + 7 + \frac{3}{16} = -6 + \frac{3}{16} = -5 - 1 + \frac{3}{16} = -5 - \frac{16}{16} + \frac{3}{16} = -5 - \frac{13}{16} = -5\frac{13}{16} \]

8) \[ -2\frac{3}{8} + (-1\frac{5}{9}) = -2\frac{3}{8} - 1\frac{5}{9} = -2 - \frac{3}{8} - 1 - \frac{5}{9} = -3 - \frac{3}{8} - \frac{5}{9} = -3 - \frac{3 \cdot 9}{8 \cdot 9} - \frac{5 \cdot 8}{9 \cdot 8} = -3 - \frac{27}{72} - \frac{40}{72} = -3 - \frac{67}{72} = -3\frac{67}{72} \]

9) \[ -8 + 4\frac{5}{22} = -8 + 4 + \frac{5}{22} = -4 + \frac{5}{22} = -3 - 1 + \frac{5}{22} = -3 - \frac{22}{22} + \frac{5}{22} = -3 - \frac{17}{22} = -3\frac{17}{22} \]

10) \[ -2\frac{9}{20} + 5\frac{7}{30} = -2 - \frac{9}{20} + 5 + \frac{7}{30} = 3 + \frac{7}{30} - \frac{9}{20} = 3 + \frac{7 \cdot 2}{30 \cdot 2} - \frac{9 \cdot 3}{20 \cdot 3} = 3 + \frac{14}{60} - \frac{27}{60} = 3 - \frac{13}{60} = 2 + 1 - \frac{13}{60} = 2 + \frac{60}{60} - \frac{13}{60} = 2 + \frac{47}{60} = 2\frac{47}{60} \]

11) \[ -5\frac{1}{4} + 1\frac{3}{8} = -5 - \frac{1}{4} + 1 + \frac{3}{8} = -4 + \frac{3}{8} - \frac{1}{4} = -4 + \frac{3}{8} - \frac{1 \cdot 2}{4 \cdot 2} = -4 + \frac{3}{8} - \frac{2}{8} = -4 + \frac{1}{8} = -3 - 1 + \frac{1}{8} = -3 - \frac{8}{8} + \frac{1}{8} = -3 - \frac{7}{8} = -3\frac{7}{8} \]

12) \[ 4\frac{3}{7} + (-8\frac{9}{14}) = 4\frac{3}{7} - 8\frac{9}{14} = 4 + \frac{3}{7} - 8 - \frac{9}{14} = -4 + \frac{3}{7} - \frac{9}{14} = -4 + \frac{3 \cdot 2}{7 \cdot 2} - \frac{9}{14} = -4 + \frac{6}{14} - \frac{9}{14} = -4 - \frac{3}{14} = -4\frac{3}{14} \]

Ответ: результаты вычислений выше

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