Question

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

Answer 1

Answer:

80% increase

Step-by-step explanation:

let the given fraction $f=\frac{x}{y}$

numerator=$x$

denominator=$y$

Given

• numerator decreased by 10%
• denominator decreased by 50%

let new numerator$=x_{new}=x-\frac{10}{100} x=\frac{9}{10} x$

let new denominator$=y_{new}=y-\frac{50}{100} y=\frac{1}{2} y$

Therefore new fraction,  $f_{new}=\frac{x_{new} }{y_{new} }=\frac{\frac{9}{10}x}{\frac{1}{2}y }=\frac{9\times2}{10} \frac{x}{y}=\frac{9}{5} \frac{x}{y}$

Percentage increase  $=\frac{f_{new} -f}{f} \times 100=\frac{\frac{9}{5} \frac{x}{y} -\frac{x}{y} }{\frac{x}{y} }\times 100=\frac{4}{5} \times100= 80$

⇒ Percentage increase of function $f$ = 80%