4. Выполните действия с дробями 12-\frac{4}{11} 5-\frac{6}{13}-2\frac{2}{13}+\frac{10}{13} 4\frac{7}{5}+\frac{15}{2} 6\frac{2}{3}+2\frac{1}{2}

Решение примеров:

1. \[12 - \frac{4}{11} = \frac{12 \cdot 11}{11} - \frac{4}{11} = \frac{132}{11} - \frac{4}{11} = \frac{132 - 4}{11} = \frac{128}{11} = 11\frac{7}{11}\]
2. \[5\frac{6}{13} - 2\frac{2}{13} + \frac{10}{13} = (5 - 2) + (\frac{6}{13} - \frac{2}{13} + \frac{10}{13}) = 3 + \frac{6 - 2 + 10}{13} = 3 + \frac{14}{13} = 3 + 1\frac{1}{13} = 4\frac{1}{13}\]
3. \[4\frac{7}{5} + \frac{15}{2} = \frac{4 \cdot 5 + 7}{5} + \frac{15}{2} = \frac{27}{5} + \frac{15}{2} = \frac{27 \cdot 2}{5 \cdot 2} + \frac{15 \cdot 5}{2 \cdot 5} = \frac{54}{10} + \frac{75}{10} = \frac{54 + 75}{10} = \frac{129}{10} = 12\frac{9}{10}\]
4. \[6\frac{2}{3} + 2\frac{1}{2} = \frac{6 \cdot 3 + 2}{3} + \frac{2 \cdot 2 + 1}{2} = \frac{20}{3} + \frac{5}{2} = \frac{20 \cdot 2}{3 \cdot 2} + \frac{5 \cdot 3}{2 \cdot 3} = \frac{40}{6} + \frac{15}{6} = \frac{40 + 15}{6} = \frac{55}{6} = 9\frac{1}{6}\]

Ответы:

• \[12 - \frac{4}{11} = 11\frac{7}{11}\]
• \[5\frac{6}{13} - 2\frac{2}{13} + \frac{10}{13} = 4\frac{1}{13}\]
• \[4\frac{7}{5} + \frac{15}{2} = 12\frac{9}{10}\]
• \[6\frac{2}{3} + 2\frac{1}{2} = 9\frac{1}{6}\]