4.221 Выполните сложение: 3 6 a)-+; 7 7 5 3 б)-+; 11 11' 3 (-1 в) + (-); 4 6 г) -1 + 4; 7 д) -4 + 2 7; 8 е) 10 + (-8 5); 13 ж) 8 2 + (-7 5); 7 14 1 3) -9 + 8,5.

Давай выполним сложение чисел.

a) \[\frac{3}{7} + \frac{6}{7} = \frac{3+6}{7} = \frac{9}{7} = 1\frac{2}{7}\]

б) \[-\frac{5}{11} + \frac{3}{11} = \frac{-5+3}{11} = -\frac{2}{11}\]

в) \(\frac{3}{4} + (-\frac{1}{6}) = \frac{3}{4} - \frac{1}{6} = \frac{3 \cdot 3}{4 \cdot 3} - \frac{1 \cdot 2}{6 \cdot 2} = \frac{9}{12} - \frac{2}{12} = \frac{7}{12}\)

г) \[-1 + \frac{4}{7} = -\frac{7}{7} + \frac{4}{7} = \frac{-7+4}{7} = -\frac{3}{7}\]

д) \[-4 + 2\frac{7}{8} = -4 + \frac{2 \cdot 8 + 7}{8} = -4 + \frac{16+7}{8} = -4 + \frac{23}{8} = -\frac{4 \cdot 8}{8} + \frac{23}{8} = \frac{-32+23}{8} = -\frac{9}{8} = -1\frac{1}{8}\]

е) \(\10 + (-8\frac{5}{13}) = 10 - 8\frac{5}{13} = 10 - \frac{8 \cdot 13 + 5}{13} = 10 - \frac{104+5}{13} = 10 - \frac{109}{13} = \frac{10 \cdot 13}{13} - \frac{109}{13} = \frac{130-109}{13} = \frac{21}{13} = 1\frac{8}{13}\)

ж) \[8\frac{2}{7} + (-7\frac{5}{14}) = 8\frac{2}{7} - 7\frac{5}{14} = \frac{8 \cdot 7 + 2}{7} - \frac{7 \cdot 14 + 5}{14} = \frac{56+2}{7} - \frac{98+5}{14} = \frac{58}{7} - \frac{103}{14} = \frac{58 \cdot 2}{7 \cdot 2} - \frac{103}{14} = \frac{116}{14} - \frac{103}{14} = \frac{116-103}{14} = \frac{13}{14}\]

з) \[-9\frac{1}{7} + 8,5 = -9\frac{1}{7} + 8\frac{1}{2} = -\frac{9 \cdot 7 + 1}{7} + \frac{8 \cdot 2 + 1}{2} = -\frac{63+1}{7} + \frac{16+1}{2} = -\frac{64}{7} + \frac{17}{2} = -\frac{64 \cdot 2}{7 \cdot 2} + \frac{17 \cdot 7}{2 \cdot 7} = -\frac{128}{14} + \frac{119}{14} = \frac{-128+119}{14} = -\frac{9}{14}\]

Ответ: a) 1 2/7; б) -2/11; в) 7/12; г) -3/7; д) -1 1/8; е) 1 8/13; ж) 13/14; з) -9/14

Ты молодец! У тебя всё получится!