Answer:
The fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is
increased by 25% and its denominator is increased by 20%.
Step-by-step explanation:
- Let 'd' be the denominator
As
[tex]100\%\mathrm{\:in\:fractions}=\:1[/tex]
[tex]25\%\mathrm{\:in\:fractions}=\:\frac{1}{4}[/tex]
[tex]20\%\mathrm{\:in\:fractions}=\frac{1}{5}[/tex]
so
Increase in 25% means
[tex]100\%\:+25\%\:=\frac{5}{4}[/tex]
Increase in 20% means
[tex]100\%\:+20\%\:=\frac{6}{5}[/tex]
Thus the fraction becomes
[tex]\:\frac{\frac{5}{4}\times \:n}{\frac{6}{5}\times \:d}[/tex]
[tex]=\frac{\frac{5}{4}n}{\frac{6d}{5}}[/tex]
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\times \:d}{b\times \:c}[/tex]
[tex]=\frac{5n\times \:5}{4\times \:6d}[/tex]
[tex]=\frac{25n}{24d}[/tex]
[tex]=1.0417\left(\frac{n}{d}\right)[/tex]
[tex]=1\left(\frac{n}{d}\right)+0.047\left(\frac{n}{d}\right)[/tex]
As
[tex]0.047=4.7\:\%[/tex]
Therefore, the fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is
increased by 25% and its denominator is increased by 20%.
