48. Найдите значения выражений: a) \(\frac{1,4}{5-\frac{1}{3}}\) б) \(\frac{2,6}{3-\frac{1}{9}}\) в) \(\frac{0,13}{1+\frac{4}{9}}\) г) \(\(\frac{0,17}{4+\frac{6}{7}}\) )

Решение:

а) \(\frac{1,4}{5-\frac{1}{3}} = \frac{1,4}{\frac{15-1}{3}} = \frac{1,4}{\frac{14}{3}} = \frac{\frac{14}{10}}{\frac{14}{3}} = \frac{14}{10} \cdot \frac{3}{14} = \frac{3}{10} = 0,3\)

б) \(\frac{2,6}{3-\frac{1}{9}} = \frac{2,6}{\frac{27-1}{9}} = \frac{2,6}{\frac{26}{9}} = \frac{\frac{26}{10}}{\frac{26}{9}} = \frac{26}{10} \cdot \frac{9}{26} = \frac{9}{10} = 0,9\)

в) \(\frac{0,13}{1+\frac{4}{9}} = \frac{0,13}{\frac{9+4}{9}} = \frac{0,13}{\frac{13}{9}} = \frac{\frac{13}{100}}{\frac{13}{9}} = \frac{13}{100} \cdot \frac{9}{13} = \frac{9}{100} = 0,09\)

г) \(\frac{0,17}{4+\frac{6}{7}} = \frac{0,17}{\frac{28+6}{7}} = \frac{0,17}{\frac{34}{7}} = \frac{\frac{17}{100}}{\frac{34}{7}} = \frac{17}{100} \cdot \frac{7}{34} = \frac{1}{100} \cdot \frac{7}{2} = \frac{7}{200} = 0,035\)

Ответ:

• а) 0,3
• б) 0,9
• в) 0,09
• г) 0,035