Вопрос:

1. Выполните действие: 4-+2; +2-; 2-+3 ; 3-+-; 8-+6-; 1- -; 5-3; 9-8-;6-2-; 4--; 8-6-. 2. Выполните действия: ( 3. Решите уравнение:

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Ответ:

Краткое пояснение: Необходимо выполнить сложение и вычитание смешанных чисел, приводя дроби к общему знаменателю, где это требуется. Разберем решение по частям.

1. Выполните действие:

  • 4\(\frac{2}{5}\) + 2\(\frac{1}{5}\) = (4 + 2) + \(\frac{2}{5}\) + \(\frac{1}{5}\) = 6 + \(\frac{3}{5}\) = 6\(\frac{3}{5}\)

  • \(\frac{3}{5}\) + 2\(\frac{4}{5}\) = (\(\frac{3}{5}\) + \(\frac{4}{5}\)) + 2 = \(\frac{7}{5}\) + 2 = 1\(\frac{2}{5}\) + 2 = 3\(\frac{2}{5}\)

  • 2\(\frac{5}{13}\) + 3\(\frac{7}{13}\) = (2 + 3) + \(\frac{5}{13}\) + \(\frac{7}{13}\) = 5 + \(\frac{12}{13}\) = 5\(\frac{12}{13}\)

  • 3\(\frac{2}{7}\) + \(\frac{4}{7}\) = 3 + \(\frac{2}{7}\) + \(\frac{4}{7}\) = 3 + \(\frac{6}{7}\) = 3\(\frac{6}{7}\)

  • 8\(\frac{8}{13}\) + 6\(\frac{5}{13}\) = (8 + 6) + \(\frac{8}{13}\) + \(\frac{5}{13}\) = 14 + \(\frac{13}{13}\) = 14 + 1 = 15

  • 1\(\frac{6}{11}\) - \(\frac{7}{11}\) = 1 + \(\frac{6}{11}\) - \(\frac{7}{11}\) = \(\frac{17}{11}\) - \(\frac{7}{11}\) = \(\frac{10}{11}\)

  • 5\(\frac{3}{8}\) - 3 = 5 - 3 + \(\frac{3}{8}\) = 2 + \(\frac{3}{8}\) = 2\(\frac{3}{8}\)

  • 9\(\frac{3}{13}\) - 8\(\frac{9}{13}\) = 9 - 8 + \(\frac{3}{13}\) - \(\frac{9}{13}\) = 1 + \(\frac{3}{13}\) - \(\frac{9}{13}\) = \(\frac{16}{13}\) - \(\frac{9}{13}\) = \(\frac{7}{13}\)

  • 6 - 2\(\frac{1}{3}\) = 6 - \(\frac{7}{3}\) = \(\frac{18}{3}\) - \(\frac{7}{3}\) = \(\frac{11}{3}\) = 3\(\frac{2}{3}\)

  • 4 - \(\frac{1}{6}\) = \(\frac{24}{6}\) - \(\frac{1}{6}\) = \(\frac{23}{6}\) = 3\(\frac{5}{6}\)

  • 8 - 6\(\frac{5}{7}\) = 8 - \(\frac{47}{7}\) = \(\frac{56}{7}\) - \(\frac{47}{7}\) = \(\frac{9}{7}\) = 1\(\frac{2}{7}\)

2. Выполните действия:

  • \(\(3\frac{5}{12} + 4\frac{7}{12}\) - 5\frac{2}{9}\) = \((3 + 4) + \frac{5}{12} + \frac{7}{12}\) - 5\frac{2}{9} = \(7 + \frac{12}{12}\) - 5\frac{2}{9} = 8 - 5\frac{2}{9} = 7\frac{9}{9} - 5\frac{2}{9} = 2\frac{7}{9}\)

  • 12\(\frac{2}{15}\) - \(\(7\frac{11}{15} + 2\frac{8}{15}\)\) = 12\(\frac{2}{15}\) - \((7 + 2) + \frac{11}{15} + \frac{8}{15}\) = 12\(\frac{2}{15}\) - \(9 + \frac{19}{15}\) = 12\(\frac{2}{15}\) - 10\(\frac{4}{15}\) = (12 - 10) + \(\frac{2}{15}\) - \(\frac{4}{15}\) = 2 - \(\frac{2}{15}\) = 1\(\frac{15}{15}\) - \(\frac{2}{15}\) = 1\(\frac{13}{15}\)

Ответ: Решения выше

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