Выполните действия: 1) 8 + 15/22; 2) 11/35 + 2...

Привет! Давай разберём эти примеры с дробями по порядку. ### 1. Выполните действия: 1) $8 + \frac{15}{22} = 8\frac{15}{22}$ 2) $\frac{11}{35} + 2 = 2\frac{11}{35}$ 3) $5\frac{7}{24} + 7\frac{5}{24} = (5 + 7) + (\frac{7}{24} + \frac{5}{24}) = 12 + \frac{12}{24} = 12 + \frac{1}{2} = 12\frac{1}{2}$ (или $12\frac{12}{24}$) 4) $12\frac{6}{7} - 5\frac{3}{7} = (12 - 5) + (\frac{6}{7} - \frac{3}{7}) = 7\frac{3}{7}$ 5) $10\frac{16}{27} - 6\frac{10}{27} + 4\frac{5}{27} = (10 - 6 + 4) + (\frac{16 - 10 + 5}{27}) = 8\frac{11}{27}$ 6) $15\frac{8}{10} - 9\frac{7}{10} + 8\frac{2}{10} = (15 - 9 + 8) + (\frac{8 - 7 + 2}{10}) = 14\frac{3}{10}$ ### 2. Вычислите: 1) $8\frac{4}{15} + 2\frac{11}{15} = 10\frac{15}{15} = 10 + 1 = 11$ 2) $4\frac{5}{9} + 3\frac{7}{9} = 7\frac{12}{9} = 7 + 1\frac{3}{9} = 8\frac{3}{9} = 8\frac{1}{3}$ 3) $1 - \frac{14}{23} = \frac{23}{23} - \frac{14}{23} = \frac{9}{23}$ 4) $6 - 3\frac{4}{9} = 5\frac{9}{9} - 3\frac{4}{9} = 2\frac{5}{9}$ 5) $9\frac{5}{12} - 4\frac{7}{12} = 8\frac{17}{12} - 4\frac{7}{12} = 4\frac{10}{12} = 4\frac{5}{6}$ 6) $24\frac{11}{36} - 5\frac{25}{36} = 23\frac{47}{36} - 5\frac{25}{36} = 18\frac{22}{36} = 18\frac{11}{18}$ ### 3. Решите уравнение: 1) $4\frac{5}{23} + x = 10\frac{2}{23}$ $x = 10\frac{2}{23} - 4\frac{5}{23}$ $x = 9\frac{25}{23} - 4\frac{5}{23}$ $x = 5\frac{20}{23}$ **Ответ:** $5\frac{20}{23}$ 2) $7\frac{9}{16} - (x - 2\frac{3}{16}) = 4\frac{11}{16}$ $x - 2\frac{3}{16} = 7\frac{9}{16} - 4\frac{11}{16}$ $x - 2\frac{3}{16} = 6\frac{25}{16} - 4\frac{11}{16}$ $x - 2\frac{3}{16} = 2\frac{14}{16}$ $x = 2\frac{14}{16} + 2\frac{3}{16}$ $x = 4\frac{17}{16} = 5\frac{1}{16}$ **Ответ:** $5\frac{1}{16}$