4 Найдите значение выражения: а) \(\frac{3,1}{1,7} + \frac{6,7}{5,1};\) б) \(\frac{2,5}{4,4} + \frac{4,6}{13,2};\) в) \(\frac{6,8}{7,2} - \frac{2,7}{3,6};\)

Решение:

а) \(\frac{3,1}{1,7} + \frac{6,7}{5,1} = \frac{31}{17} + \frac{67}{51} = \frac{31 \cdot 3}{17 \cdot 3} + \frac{67}{51} = \frac{93}{51} + \frac{67}{51} = \frac{93+67}{51} = \frac{160}{51} = 3 \frac{7}{51}\)

б) \(\frac{2,5}{4,4} + \frac{4,6}{13,2} = \frac{25}{44} + \frac{46}{132} = \frac{25 \cdot 3}{44 \cdot 3} + \frac{46}{132} = \frac{75}{132} + \frac{46}{132} = \frac{75+46}{132} = \frac{121}{132} = \frac{11}{12}\)

в) \(\frac{6,8}{7,2} - \frac{2,7}{3,6} = \frac{68}{72} - \frac{27}{36} = \frac{68}{72} - \frac{27 \cdot 2}{36 \cdot 2} = \frac{68}{72} - \frac{54}{72} = \frac{68-54}{72} = \frac{14}{72} = \frac{7}{36}\)

Ответ: а) \(3 \frac{7}{51}\); б) \(\frac{11}{12}\); в) \(\frac{7}{36}\)