Вопрос:

1. Найти сумму или разность: 1) a) 1/4 + 7/8; 2) a) 3/7 - 1/9; 3) a) 9/58 - 85/87; б) 5/7 - 1/21; б) 11/13 + 1/3; б) 3 7/20 - 4 11/80; в) 5 8/9 + 7 13/36; в) 5 13/22 - 3 1/11; в) 9 1/5 - 13 2/15.

Ответ:

1. Нахождение суммы или разности:

  1. а) \( \frac{1}{4} + \frac{7}{8} = \frac{2}{8} + \frac{7}{8} = \frac{9}{8} = 1\frac{1}{8} \)
  2. а) \( \frac{3}{7} - \frac{1}{9} = \frac{27}{63} - \frac{7}{63} = \frac{20}{63} \)
  3. а) \( \frac{9}{58} - \frac{85}{87} = \frac{9 \cdot 3}{174} - \frac{85 \cdot 2}{174} = \frac{27 - 170}{174} = -\frac{143}{174} \)
  4. б) \( \frac{5}{7} - \frac{1}{21} = \frac{15}{21} - \frac{1}{21} = \frac{14}{21} = \frac{2}{3} \)
  5. б) \( \frac{11}{13} + \frac{1}{3} = \frac{33}{39} + \frac{13}{39} = \frac{46}{39} = 1\frac{7}{39} \)
  6. б) \( 3\frac{7}{20} - 4\frac{11}{80} = \frac{67}{20} - \frac{331}{80} = \frac{67 \cdot 4}{80} - \frac{331}{80} = \frac{268 - 331}{80} = -\frac{63}{80} \)
  7. в) \( 5\frac{8}{9} + 7\frac{13}{36} = \frac{53}{9} + \frac{265}{36} = \frac{53 \cdot 4}{36} + \frac{265}{36} = \frac{212 + 265}{36} = \frac{477}{36} = 13\frac{9}{36} = 13\frac{1}{4} \)
  8. в) \( 5\frac{13}{22} - 3\frac{1}{11} = \frac{123}{22} - \frac{34}{11} = \frac{123}{22} - \frac{34 \cdot 2}{22} = \frac{123 - 68}{22} = \frac{55}{22} = 2\frac{11}{22} = 2\frac{1}{2} \)
  9. в) \( 9\frac{1}{5} - 13\frac{2}{15} = \frac{46}{5} - \frac{197}{15} = \frac{46 \cdot 3}{15} - \frac{197}{15} = \frac{138 - 197}{15} = -\frac{59}{15} = -3\frac{14}{15} \)
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