5.282. Вычислите значение выражения: a) 14 9/13 - 1 5/13 + 12 11/13; б) 7 24/25 - 3 12/25 - 1 7/25; в) 17 7/40 + 3 9/40 - 17/40; г) 23 15/49 - 13 19/49 - 1 30/49.

a) $$14\frac{9}{13} - 1\frac{5}{13} + 12\frac{11}{13} = (14 - 1 + 12) + (\frac{9}{13} - \frac{5}{13} + \frac{11}{13}) = 25 + \frac{9-5+11}{13} = 25 + \frac{15}{13} = 25 + 1\frac{2}{13} = 26\frac{2}{13}$$ б) $$7\frac{24}{25} - 3\frac{12}{25} - 1\frac{7}{25} = (7 - 3 - 1) + (\frac{24}{25} - \frac{12}{25} - \frac{7}{25}) = 3 + \frac{24-12-7}{25} = 3 + \frac{5}{25} = 3\frac{5}{25}$$. Можно сократить: $$3\frac{5}{25} = 3\frac{1}{5}$$ в) $$17\frac{7}{40} + 3\frac{9}{40} - \frac{17}{40} = (17+3) + (\frac{7}{40} + \frac{9}{40} - \frac{17}{40}) = 20 + \frac{7+9-17}{40} = 20 + \frac{-1}{40} = 20 - \frac{1}{40} = 19 + 1 - \frac{1}{40} = 19 + \frac{40}{40} - \frac{1}{40} = 19 + \frac{39}{40} = 19\frac{39}{40}$$ г) $$23\frac{15}{49} - 13\frac{19}{49} - 1\frac{30}{49} = (23 - 13 - 1) + (\frac{15}{49} - \frac{19}{49} - \frac{30}{49}) = 9 + \frac{15-19-30}{49} = 9 + \frac{-34}{49} = 9 - \frac{34}{49} = 8 + 1 - \frac{34}{49} = 8 + \frac{49}{49} - \frac{34}{49} = 8 + \frac{15}{49} = 8\frac{15}{49}$$ **Ответ:** a) $$26\frac{2}{13}$$, б) $$3\frac{1}{5}$$, в) $$19\frac{39}{40}$$, г) $$8\frac{15}{49}$$