Question

Se consideră proporția x/y=7/9Feterminati următoarele rapoarte :
A)2x/x+y
B)y-x/2x
C)2y/x+y.

Answer 1

$\tfrac{x}{y} = \tfrac{7}{9} \implies x = \tfrac{7y}{9} \\ \\ \\ a) \: \frac{2 \times \frac{7y}{9} }{ \frac{7y}{9} + y } = \frac{ \frac{14y}{9} }{ \frac{7y}{9} + \frac{9y}{9} } = \frac{ \frac{14y}{9} }{ \frac{16y}{9} } = \tfrac{14y}{9} \times \tfrac{9}{16y} \\ = \tfrac{14y}{16y} = \color{magenta} \tfrac{7}{8} \\ \\ \\ b) \: \frac{y - \frac{7y}{9} }{2 \times \frac{7y}{9} } = \frac{ \frac{9y}{9} - \frac{7y}{9} }{ \frac{14y}{9} } = \tfrac{2y}{9} \times \tfrac{9}{14y} \\ = \tfrac{2y}{14y} =\color{magenta} \tfrac{1}{7} \\ \\ \\ c) \: \frac{2y}{ \frac{7y}{9} + y} = \frac{2y}{ \frac{7y}{9} + \frac{9y}{9} } = \small 2y \times \tfrac{9}{16y} = \color{magenta}\tfrac{9}{8}$