4.209 Выполните сложение: a) \(4\frac{7}{13} + (-\frac{4}{13})\); v) \(-1 + \frac{3}{8}\); d) \(-1\frac{2}{5} + \frac{3}{4}\); ж) \(-2\frac{1}{3} + 3\frac{2}{5}\) б) \(2\frac{1}{4} + (-\frac{1}{6})\) г) \(-5\frac{5}{8} + 3\frac{1}{4}\) e) \(-\frac{4}{5} + 5\frac{4}{15}\)

**Решение:** a) \(4\frac{7}{13} + (-\frac{4}{13}) = 4\frac{7}{13} - \frac{4}{13} = 4 + \frac{7}{13} - \frac{4}{13} = 4 + \frac{7-4}{13} = 4 + \frac{3}{13} = 4\frac{3}{13}\) v) \(-1 + \frac{3}{8} = -\frac{8}{8} + \frac{3}{8} = \frac{-8+3}{8} = \frac{-5}{8} = -\frac{5}{8}\) d) \(-1\frac{2}{5} + \frac{3}{4} = -\frac{7}{5} + \frac{3}{4} = -\frac{7 \times 4}{5 \times 4} + \frac{3 \times 5}{4 \times 5} = -\frac{28}{20} + \frac{15}{20} = \frac{-28+15}{20} = \frac{-13}{20} = -\frac{13}{20}\) ж) \(-2\frac{1}{3} + 3\frac{2}{5} = -\frac{7}{3} + \frac{17}{5} = -\frac{7 \times 5}{3 \times 5} + \frac{17 \times 3}{5 \times 3} = -\frac{35}{15} + \frac{51}{15} = \frac{-35+51}{15} = \frac{16}{15} = 1\frac{1}{15}\) б) \(2\frac{1}{4} + (-\frac{1}{6}) = \frac{9}{4} - \frac{1}{6} = \frac{9 \times 3}{4 \times 3} - \frac{1 \times 2}{6 \times 2} = \frac{27}{12} - \frac{2}{12} = \frac{27-2}{12} = \frac{25}{12} = 2\frac{1}{12}\) г) \(-5\frac{5}{8} + 3\frac{1}{4} = -\frac{45}{8} + \frac{13}{4} = -\frac{45}{8} + \frac{13 \times 2}{4 \times 2} = -\frac{45}{8} + \frac{26}{8} = \frac{-45+26}{8} = \frac{-19}{8} = -2\frac{3}{8}\) e) \(-\frac{4}{5} + 5\frac{4}{15} = -\frac{4}{5} + \frac{79}{15} = -\frac{4 \times 3}{5 \times 3} + \frac{79}{15} = -\frac{12}{15} + \frac{79}{15} = \frac{-12+79}{15} = \frac{67}{15} = 4\frac{7}{15}\) **Ответы:** a) \(4\frac{3}{13}\) v) \(-\frac{5}{8}\) d) \(-\frac{13}{20}\) ж) \(1\frac{1}{15}\) б) \(2\frac{1}{12}\) г) \(-2\frac{3}{8}\) e) \(4\frac{7}{15}\)