By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?

Answer:80% increaseStep-by-step explanation:let the given fraction [tex]f=\frac{x}{y}[/tex]numerator=[tex]x[/tex]denominator=[tex]y[/tex]Givennumerator decreased by 10%denominator decreased by 50%let new numerator[tex]=x_{new}=x-\frac{10}{100} x=\frac{9}{10} x[/tex]let new denominator[tex]=y_{new}=y-\frac{50}{100} y=\frac{1}{2} y[/tex]Therefore new fraction,  [tex]f_{new}=\frac{x_{new} }{y_{new} }=\frac{\frac{9}{10}x}{\frac{1}{2}y }=\frac{9\times2}{10} \frac{x}{y}=\frac{9}{5} \frac{x}{y}[/tex]Percentage increase  [tex]=\frac{f_{new} -f}{f} \times 100=\frac{\frac{9}{5} \frac{x}{y} -\frac{x}{y} }{\frac{x}{y} }\times 100=\frac{4}{5} \times100= 80[/tex]⇒ Percentage increase of function [tex]f[/tex] = 80%