The fraction decreases by 20% ,after the 40% decrease in numerator and 25% decrease in denominator.
What is percentage change?
Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent or value.
Formula for calculating percentage decrease and percentage increase:
% decrease = [tex]\frac{original number - new number}{original number}[/tex] × 100
% increase = [tex]\frac{New number - original number}{original number}[/tex]× 100
Let the fraction be [tex]\frac{x}{y}[/tex].
According to the given question
Numerator is decreased by 40% and denominator is decreased by 25%.
Therefore
New Numerator = [tex]x-\frac{40}{100}x[/tex] =[tex]\frac{60}{100}x[/tex]
New Denominator = [tex]y -\frac{25}{100} y =\frac{75}{100}y[/tex]
New fraction = [tex]\frac{\frac{60}{100} x}{\frac{75}{100} y}[/tex] [tex]=\frac{4x}{5y}[/tex]
So, the new fraction is less than the initial fraction by = [tex]\frac{x}{y} -\frac{4x}{5y} = \frac{5x-4x}{5y} =\frac{x}{5y}[/tex]
Thus, in percent = [tex]\frac{\frac{x}{5y} }{\frac{x}{y} }[/tex]× 100 = 20%
Hence, the fraction will decrease by 20% ,after the 40% decrease in numerator and 25% decrease in denominator.
Learn more about the percentage change here:https://brainly.com/question/13450942
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