Question

the denominator of fraction is 2 more than numerator. if 1 is subtracted from numerator and 1is added to denominator the fraction becomes 1/2 what is that fraction.​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, as per the provided question we are given that the denominator of fraction is 2 more than numerator. Also, if 1 is subtracted from numerator and 1is added to denominator the fraction becomes 1/2. We have to find the out original fraction.

We'll first assume the numerator and denominator as two variables, say x and y. After that, we'll form a linear equation and by solving that equation we'll find the numerator and the denominator.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Let,

$\maltese$ Numerator = x

$\maltese$ Denominator = y

$\bigstar \: \boxed{\sf { Fraction = \dfrac{x}{y} }}$

According to the question,

$\longrightarrow$ Denominator = 2 + Numerator

$\longrightarrow$ y = 2 + x

Let it be the equation (1).

Also, as per the question,

• If 1 is subtracted from numerator and 1 is added to denominator the fraction becomes 1/2 what is that fraction.

$\longrightarrow \sf { \dfrac{x-1}{y+1} = \dfrac{1}{2} }$

» Substituting the value of y from the equation (1).

$\longrightarrow \sf { \dfrac{x-1}{2 + x+1} = \dfrac{1}{2} }$

$\longrightarrow \sf { \dfrac{x-1}{3 + x} = \dfrac{1}{2} }$

By using cross multiplication method,

$\longrightarrow \sf { 2(x-1) = 1(3+x) }$

Using distributive property,

$\longrightarrow \sf { 2(x) + 2( -1) = 1(3) +1( x) }$

Performing multiplication,

$\longrightarrow \sf { 2x - 2= 3 +x }$

Transposing variables and constants,

$\longrightarrow \sf { 2x - x = 3 + 2 }$

Performing addition and subtraction,

$\longrightarrow \sf { x = 5 }$

$\star \large {\bf{ Numerator = 5}} \star$

Finding out the denominator :

From the equation (1), we have :

$\longrightarrow \sf { y = 2 + x }$

Substituting the value of x,

$\longrightarrow \sf { y = 2 + 5 }$

$\longrightarrow \sf { y = 7 }$

$\star \large {\bf{ Denominator = 7}} \star$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { Fraction = \dfrac{5}{7} }}$ ❞

Therefore, the fraction is $\pmb { \mathfrak \gray { \dfrac{5}{7} }}$.