Question

when the numerator of a fraction is increased by 4, the fraction increases by 2/3. what is the denominator of the fraction. ​

Answer 1

$\LARGE{\textbf{Explanation}}$

[tex]\large{\sf{Let\:the\:numerator\:and}}[/tex]

$\large{\textbf{denominator\:be\:y\: respectively}}$

$\Large{\textbf{ATQ,}}$

$\large{\textsf{ \dfrac{x+4}{y}\:=\:\dfrac{x}{y}\:+\:\dfrac{2}{3} }}$

$\textbf{Taking\:the\:LCM}$

$\Large{\textbf{of\:RHS,\:LCM\:is\:3}}$

$\large{\textsf{ \dfrac{x+4}{y}\:=\:\dfrac{3\timesx\:+\:2\timesy}{3y} }}$

$\large{\textsf{ \dfrac{x+4}{y}\:=\:\dfrac{3x+2y}{3y} }}$

$\Large{\textbf{Cross\: Multiplying\:LHS\:and\:RHS}}$

$\large{\textsf{ 3y\times(x+4)\:=\:y\times(3x+2y) }}$

$\large{\textsf{3xy+12y\:=\:3xy+ 2y^2 }}$

$\Large{\textbf{Cancelling\:3xy\: from\:LHS\:and\:RHS}}$

$\large{\textsf{12y\:=\: 2y^2 }}$

$\Large{\textbf{Sending\:12y\:to\:RHS}}$

$\large{\textsf{ 2y^2-12y=0}}$

$\Large{\textbf{Taking\:2y\:as\:common}}$

$\large{\textsf{2y(y-6)=0}}$

$\large{\textsf{y-6=0}}$

$\Large{\textbf{Sending\:-6\:to\:RHS}}$

$\large{\textsf{y=6}}$

$\LARGE{\textbf{Denominator\:=\:6}}$