Контрольные задания > 959. Вычислите значение выражения: 1) -\frac{1}{4} + \frac{3}{5}; 2) 11 + (-\frac{2}{5}); 3) -\frac{20}{21} + \frac{3}{7}; 4) -8\frac{9}{14} + 3\frac{3}{7}; 5) 7\frac{5}{12} + (-\frac{3}{24}); 6) -6\frac{11}{12} + (-8\frac{5}{18}); 7) -5\frac{12}{35} + 10; 8) -2\frac{3}{8} + 1\frac{2}{9}; 9) -3\frac{1}{12} + 1\frac{1}{6}; 10) 3\frac{3}{7} + (-6\frac{4}{9}); 11) 9\frac{1}{6} + (-5\frac{3}{4}); 12) -3\frac{8}{9} + (-\frac{2}{12}).
Вопрос:

959. Вычислите значение выражения: 1) -\frac{1}{4} + \frac{3}{5}; 2) 11 + (-\frac{2}{5}); 3) -\frac{20}{21} + \frac{3}{7}; 4) -8\frac{9}{14} + 3\frac{3}{7}; 5) 7\frac{5}{12} + (-\frac{3}{24}); 6) -6\frac{11}{12} + (-8\frac{5}{18}); 7) -5\frac{12}{35} + 10; 8) -2\frac{3}{8} + 1\frac{2}{9}; 9) -3\frac{1}{12} + 1\frac{1}{6}; 10) 3\frac{3}{7} + (-6\frac{4}{9}); 11) 9\frac{1}{6} + (-5\frac{3}{4}); 12) -3\frac{8}{9} + (-\frac{2}{12}).

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Ответ:

Выполним вычисления:

  1. $$-\frac{1}{4} + \frac{3}{5} = -\frac{1*5}{4*5} + \frac{3*4}{5*4} = -\frac{5}{20} + \frac{12}{20} = \frac{12-5}{20} = \frac{7}{20}.$$
  2. $$11 + (-\frac{2}{5}) = 11 - \frac{2}{5} = \frac{11*5}{5} - \frac{2}{5} = \frac{55}{5} - \frac{2}{5} = \frac{55-2}{5} = \frac{53}{5} = 10\frac{3}{5}.$$
  3. $$-\frac{20}{21} + \frac{3}{7} = -\frac{20}{21} + \frac{3*3}{7*3} = -\frac{20}{21} + \frac{9}{21} = \frac{-20+9}{21} = -\frac{11}{21}.$$
  4. $$-8\frac{9}{14} + 3\frac{3}{7} = -8\frac{9}{14} + 3\frac{3*2}{7*2} = -8\frac{9}{14} + 3\frac{6}{14} = -(8\frac{9}{14} - 3\frac{6}{14}) = -(8-3 + \frac{9}{14} - \frac{6}{14}) = -(5 + \frac{3}{14}) = -5\frac{3}{14}.$$
  5. $$7\frac{5}{12} + (-\frac{3}{24}) = 7\frac{5}{12} - \frac{3}{24} = 7\frac{5*2}{12*2} - \frac{3}{24} = 7\frac{10}{24} - \frac{3}{24} = 7\frac{10-3}{24} = 7\frac{7}{24}.$$
  6. $$-6\frac{11}{12} + (-8\frac{5}{18}) = -6\frac{11}{12} - 8\frac{5}{18} = -(6\frac{11}{12} + 8\frac{5}{18}) = -(6\frac{11*3}{12*3} + 8\frac{5*2}{18*2}) = -(6\frac{33}{36} + 8\frac{10}{36}) = -(6+8 + \frac{33}{36} + \frac{10}{36}) = -(14 + \frac{43}{36}) = -(14 + \frac{36+7}{36}) = -(14 + 1\frac{7}{36}) = -15\frac{7}{36}.$$
  7. $$-5\frac{12}{35} + 10 = 10 - 5\frac{12}{35} = 9\frac{35}{35} - 5\frac{12}{35} = 9-5 + \frac{35}{35} - \frac{12}{35} = 4 + \frac{35-12}{35} = 4 + \frac{23}{35} = 4\frac{23}{35}.$$
  8. $$-2\frac{3}{8} + 1\frac{2}{9} = -2\frac{3}{8} + 1\frac{2}{9} = -(2\frac{3}{8} - 1\frac{2}{9}) = -(2\frac{3*9}{8*9} - 1\frac{2*8}{9*8}) = -(2\frac{27}{72} - 1\frac{16}{72}) = -(2-1 + \frac{27}{72} - \frac{16}{72}) = -(1 + \frac{11}{72}) = -1\frac{11}{72}.$$
  9. $$-3\frac{1}{12} + 1\frac{1}{6} = -3\frac{1}{12} + 1\frac{1*2}{6*2} = -3\frac{1}{12} + 1\frac{2}{12} = -(3\frac{1}{12} - 1\frac{2}{12}) = -(2\frac{13}{12} - 1\frac{2}{12}) = -(2-1 + \frac{13}{12} - \frac{2}{12}) = -(1 + \frac{11}{12}) = -1\frac{11}{12}.$$
  10. $$3\frac{3}{7} + (-6\frac{4}{9}) = 3\frac{3}{7} - 6\frac{4}{9} = -(6\frac{4}{9} - 3\frac{3}{7}) = -(6\frac{4*7}{9*7} - 3\frac{3*9}{7*9}) = -(6\frac{28}{63} - 3\frac{27}{63}) = -(6-3 + \frac{28}{63} - \frac{27}{63}) = -(3 + \frac{1}{63}) = -3\frac{1}{63}.$$
  11. $$9\frac{1}{6} + (-5\frac{3}{4}) = 9\frac{1}{6} - 5\frac{3}{4} = 9\frac{1*2}{6*2} - 5\frac{3}{4} = 9\frac{2}{12} - 5\frac{3*3}{4*3} = 9\frac{2}{12} - 5\frac{9}{12} = 8\frac{14}{12} - 5\frac{9}{12} = 8-5 + \frac{14}{12} - \frac{9}{12} = 3 + \frac{5}{12} = 3\frac{5}{12}.$$
  12. $$-3\frac{8}{9} + (-\frac{2}{12}) = -3\frac{8}{9} - \frac{2}{12} = -3\frac{8}{9} - \frac{1}{6} = -3\frac{8*2}{9*2} - \frac{1*3}{6*3} = -3\frac{16}{18} - \frac{3}{18} = -(3 + \frac{16}{18} + \frac{3}{18}) = -(3 + \frac{19}{18}) = -(3 + 1\frac{1}{18}) = -4\frac{1}{18}.$$

Ответ: 1) $$\frac{7}{20}$$; 2) $$10\frac{3}{5}$$; 3) $$-\frac{11}{21}$$; 4) $$-5\frac{3}{14}$$; 5) $$7\frac{7}{24}$$; 6) $$-15\frac{7}{36}$$; 7) $$4\frac{23}{35}$$; 8) $$-1\frac{11}{72}$$; 9) $$-1\frac{11}{12}$$; 10) $$-3\frac{1}{63}$$; 11) $$3\frac{5}{12}$$; 12) $$-4\frac{1}{18}$$.

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