211 Выполните сложение: a) -26 + (-17); б) -4,8 + (-5,7); в) -3\frac{4}{7} + (-4\frac{1}{7}); г) -\frac{5}{9} + (-\frac{1}{3}); д) -0,75 + (-\frac{1}{4}); е) -1 + (-\frac{1}{11}); ж) -0,4 + (-\frac{1}{30}); з) \frac{9}{13} + 2 + (-\frac{9}{13}); и) -26 + (-20\frac{17}{19}).

Выполним сложение рациональных чисел:

1. a) $$-26 + (-17) = -26 - 17 = -43$$
2. б) $$-4.8 + (-5.7) = -4.8 - 5.7 = -10.5$$
3. в) $$-3\frac{4}{7} + (-4\frac{1}{7}) = -3\frac{4}{7} - 4\frac{1}{7} = - (3\frac{4}{7} + 4\frac{1}{7}) = - (3+4 + \frac{4}{7} + \frac{1}{7}) = - (7 + \frac{5}{7}) = -7\frac{5}{7}$$
4. г) $$-\frac{5}{9} + (-\frac{1}{3}) = -\frac{5}{9} - \frac{1}{3} = -\frac{5}{9} - \frac{1\cdot 3}{3\cdot 3} = -\frac{5}{9} - \frac{3}{9} = -\frac{5+3}{9} = -\frac{8}{9}$$
5. д) $$-0.75 + (-\frac{1}{4}) = -0.75 - \frac{1}{4} = -0.75 - 0.25 = -1$$
6. е) $$-1 + (-\frac{1}{11}) = -1 - \frac{1}{11} = -1\frac{1}{11}$$
7. ж) $$-0.4 + (-\frac{1}{30}) = -0.4 - \frac{1}{30} = -\frac{4}{10} - \frac{1}{30} = -\frac{4 \cdot 3}{10 \cdot 3} - \frac{1}{30} = -\frac{12}{30} - \frac{1}{30} = -\frac{13}{30}$$
8. з) $$\frac{9}{13} + 2 + (-\frac{9}{13}) = \frac{9}{13} + 2 - \frac{9}{13} = \frac{9}{13} - \frac{9}{13} + 2 = 0 + 2 = 2$$
9. и) $$-26 + (-20\frac{17}{19}) = -26 - 20\frac{17}{19} = - (26 + 20\frac{17}{19}) = - (26 + 20 + \frac{17}{19}) = - (46 + \frac{17}{19}) = -46\frac{17}{19}$$

Ответ: a) -43; б) -10.5; в) -7\frac{5}{7}; г) -\frac{8}{9}; д) -1; е) -1\frac{1}{11}; ж) -\frac{13}{30}; з) 2; и) -46\frac{17}{19}.