Question

if numerator is increase by 8 and denominator is double them the resulting fraction is 1by2​

Answer 1

$\huge\mathcal{\fcolorbox{pink}{black}{\blue{Good\: Morning}}}$

Let,

• Numerator of a fraction be x.

• Denominator of the fraction be y.

$;\longrightarrow\:\tt{Fraction\:=\:\dfrac{x}{y}\:}$

According to the question,

• Numerator is increased by 8.

$;\longrightarrow\:\tt{Numerator\:=\:x\:+\:8\:}$

And,

• Denominator is doubled.

$;\longrightarrow\:\tt{Denominator\:=\:2y\:}$

$;\implies\:\tt{New\:fraction\:=\:\dfrac{x\:+\:8}{2y}\:}$

Where,

• New fraction = $\bf{\dfrac{1}{2}}$

$;\implies\:\tt{\dfrac{1}{2}\:=\:\dfrac{x\:+\:8}{2y}\:}$

$;\implies\:\tt{2y\:=\:(x\:+\:8)\times{2}\:}$

$;\implies\:\tt{2y\:=\:2x\:+\:16\:}$

$;\implies\:\bf\pink{2y\:-\:2x\:=\:16\:}$

Answer 2

Answer:

Let,

Numerator of a fraction be x.

Denominator of the fraction be y.

\begin{gathered};\longrightarrow\:\tt{Fraction\:=\:\dfrac{x}{y}\:} \\ \end{gathered}

;⟶Fraction=

y

x

According to the question,

Numerator is increased by 8.

\begin{gathered};\longrightarrow\:\tt{Numerator\:=\:x\:+\:8\:} \\ \end{gathered}

;⟶Numerator=x+8

And,

Denominator is doubled.

\begin{gathered};\longrightarrow\:\tt{Denominator\:=\:2y\:} \\ \end{gathered}

;⟶Denominator=2y

\begin{gathered};\implies\:\tt{New\:fraction\:=\:\dfrac{x\:+\:8}{2y}\:} \\ \end{gathered}

;⟹Newfraction=

2y

x+8

Where,

New fraction = \begin{gathered}\bf{\dfrac{1}{2}} \\ \end{gathered}

2

1

\begin{gathered};\implies\:\tt{\dfrac{1}{2}\:=\:\dfrac{x\:+\:8}{2y}\:} \\ \end{gathered}

;⟹

2

1

=

2y

x+8

\begin{gathered};\implies\:\tt{2y\:=\:(x\:+\:8)\times{2}\:} \\ \end{gathered}

;⟹2y=(x+8)×2

\begin{gathered};\implies\:\tt{2y\:=\:2x\:+\:16\:} \\ \end{gathered}

;⟹2y=2x+16

\begin{gathered};\implies\:\bf\pink{2y\:-\:2x\:=\:16\:} \\ \end{gathered}

;⟹2y−2x=16