14 Тип 13 № 10003 Вычислите: \frac{65}{96} : (\frac{5}{16} - \frac{7}{12}) + 10 \frac{1}{3} : \frac{3}{20}.

Решим пример по действиям:

1) \(\frac{5}{16} - \frac{7}{12} = \frac{5 \cdot 3}{16 \cdot 3} - \frac{7 \cdot 4}{12 \cdot 4} = \frac{15}{48} - \frac{28}{48} = \frac{15 - 28}{48} = \frac{-13}{48}\)

2) \(\frac{65}{96} : \frac{-13}{48} = \frac{65}{96} \cdot \frac{48}{-13} = \frac{65 \cdot 48}{96 \cdot (-13)} = \frac{5 \cdot 1}{2 \cdot (-1)} = -\frac{5}{2} = -2.5\)

3) \(10 \frac{1}{3} : \frac{3}{20} = \frac{31}{3} : \frac{3}{20} = \frac{31}{3} \cdot \frac{20}{3} = \frac{31 \cdot 20}{3 \cdot 3} = \frac{620}{9} = 68 \frac{8}{9}\)

4) \(-2.5 + 68 \frac{8}{9} = -2 \frac{1}{2} + 68 \frac{8}{9} = -\frac{5}{2} + \frac{620}{9} = \frac{-5 \cdot 9}{2 \cdot 9} + \frac{620 \cdot 2}{9 \cdot 2} = \frac{-45}{18} + \frac{1240}{18} = \frac{1195}{18} = 66 \frac{7}{18}\)