61. Выполните сложение: a) \(\frac{3}{4} + \frac{2}{4}\); 6) \(\frac{3}{10} + \frac{2}{15}\); B) \(\frac{4}{9} + \frac{1}{6}\); 62. Выполните вычитание: a) \(\frac{6}{7} - \frac{2}{3}\); 6) \(\frac{11}{12} - \frac{5}{6}\); B) \(\frac{7}{12} - \frac{3}{8}\); 68. Выполните действие: a) \(\frac{3}{8} + \frac{1}{6}\); 6) \(\frac{4}{5} - \frac{3}{10}\); B) \(\frac{1}{12} + \frac{1}{10}\); 83. Выполните действие: a) \(7\frac{5}{12} + 4\frac{3}{8}\); 6) \(3\frac{11}{20} + 2\frac{19}{30}\); 84. Решите уравнение: a) \(8 - x = 3\frac{7}{9}\); 6) \(6\frac{1}{12} - k = 2\frac{5}{12}\).

61. Выполните сложение:

a) \(\frac{3}{4} + \frac{2}{4} = \frac{3+2}{4} = \frac{5}{4} = 1\frac{1}{4}\)

б) \(\frac{3}{10} + \frac{2}{15} = \frac{3 \cdot 3}{10 \cdot 3} + \frac{2 \cdot 2}{15 \cdot 2} = \frac{9}{30} + \frac{4}{30} = \frac{9+4}{30} = \frac{13}{30}\)

в) \(\frac{4}{9} + \frac{1}{6} = \frac{4 \cdot 2}{9 \cdot 2} + \frac{1 \cdot 3}{6 \cdot 3} = \frac{8}{18} + \frac{3}{18} = \frac{8+3}{18} = \frac{11}{18}\)

62. Выполните вычитание:

a) \(\frac{6}{7} - \frac{2}{3} = \frac{6 \cdot 3}{7 \cdot 3} - \frac{2 \cdot 7}{3 \cdot 7} = \frac{18}{21} - \frac{14}{21} = \frac{18-14}{21} = \frac{4}{21}\)

б) \(\frac{11}{12} - \frac{5}{6} = \frac{11}{12} - \frac{5 \cdot 2}{6 \cdot 2} = \frac{11}{12} - \frac{10}{12} = \frac{11-10}{12} = \frac{1}{12}\)

в) \(\frac{7}{12} - \frac{3}{8} = \frac{7 \cdot 2}{12 \cdot 2} - \frac{3 \cdot 3}{8 \cdot 3} = \frac{14}{24} - \frac{9}{24} = \frac{14-9}{24} = \frac{5}{24}\)

68. Выполните действие:

a) \(\frac{3}{8} + \frac{1}{6} = \frac{3 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4} = \frac{9}{24} + \frac{4}{24} = \frac{9+4}{24} = \frac{13}{24}\)

б) \(\frac{4}{5} - \frac{3}{10} = \frac{4 \cdot 2}{5 \cdot 2} - \frac{3}{10} = \frac{8}{10} - \frac{3}{10} = \frac{8-3}{10} = \frac{5}{10} = \frac{1}{2}\)

в) \(\frac{1}{12} + \frac{1}{10} = \frac{1 \cdot 5}{12 \cdot 5} + \frac{1 \cdot 6}{10 \cdot 6} = \frac{5}{60} + \frac{6}{60} = \frac{5+6}{60} = \frac{11}{60}\)

83. Выполните действие:

a) \(7\frac{5}{12} + 4\frac{3}{8} = 7 + \frac{5}{12} + 4 + \frac{3}{8} = (7+4) + (\frac{5}{12} + \frac{3}{8}) = 11 + (\frac{5 \cdot 2}{12 \cdot 2} + \frac{3 \cdot 3}{8 \cdot 3}) = 11 + (\frac{10}{24} + \frac{9}{24}) = 11 + \frac{19}{24} = 11\frac{19}{24}\)

б) \(3\frac{11}{20} + 2\frac{19}{30} = 3 + \frac{11}{20} + 2 + \frac{19}{30} = (3+2) + (\frac{11}{20} + \frac{19}{30}) = 5 + (\frac{11 \cdot 3}{20 \cdot 3} + \frac{19 \cdot 2}{30 \cdot 2}) = 5 + (\frac{33}{60} + \frac{38}{60}) = 5 + \frac{71}{60} = 5 + 1\frac{11}{60} = 6\frac{11}{60}\)

84. Решите уравнение:

a) \(8 - x = 3\frac{7}{9}\) \(x = 8 - 3\frac{7}{9}\) \(x = 7\frac{9}{9} - 3\frac{7}{9}\) \(x = (7-3) + (\frac{9}{9} - \frac{7}{9})\) \(x = 4 + \frac{2}{9}\) \(x = 4\frac{2}{9}\)

б) \(6\frac{1}{12} - k = 2\frac{5}{12}\) \(k = 6\frac{1}{12} - 2\frac{5}{12}\) \(k = 5\frac{13}{12} - 2\frac{5}{12}\) \(k = (5-2) + (\frac{13}{12} - \frac{5}{12})\) \(k = 3 + \frac{8}{12}\) \(k = 3\frac{2}{3}\)

Ответ: a) \(1\frac{1}{4}\), б) \(\frac{13}{30}\), в) \(\frac{11}{18}\); a) \(\frac{4}{21}\), б) \(\frac{1}{12}\), в) \(\frac{5}{24}\); a) \(\frac{13}{24}\), б) \(\frac{1}{2}\), в) \(\frac{11}{60}\); a) \(11\frac{19}{24}\), б) \(6\frac{11}{60}\); a) \(4\frac{2}{9}\), б) \(3\frac{2}{3}\)

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