the denominator of fraction is 2 more than numerator. if 1 is subtracted from numerator and 1is added to denominator the fraction

1 thought on “the denominator of fraction is 2 more than numerator. if 1 is subtracted from numerator and 1is added to denominator the fraction”

1. [tex] \Large {\underline { \sf \orange{Clarification :}}}[/tex]

   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.

   [tex] \Large {\underline { \sf \orange{Explication \: of \: Steps :}}}[/tex]

   Let,

   [tex] \maltese [/tex] Numerator = x

   [tex] \maltese [/tex] Denominator = y

   [tex]\bigstar \: \boxed{\sf { Fraction = \dfrac{x}{y} }} \\ [/tex]

   According to the question,

   [tex] \longrightarrow [/tex] Denominator = 2 + Numerator

   [tex] \longrightarrow [/tex] 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.

   [tex] \longrightarrow \sf { \dfrac{x-1}{y+1} = \dfrac{1}{2} } [/tex]

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

   [tex] \longrightarrow \sf { \dfrac{x-1}{2 + x+1} = \dfrac{1}{2} } [/tex]

   [tex] \longrightarrow \sf { \dfrac{x-1}{3 + x} = \dfrac{1}{2} } [/tex]

   By using cross multiplication method,

   [tex] \longrightarrow \sf { 2(x-1) = 1(3+x) } [/tex]

   Using distributive property,

   [tex] \longrightarrow \sf { 2(x) + 2( -1) = 1(3) +1( x) } [/tex]

   Performing multiplication,

   [tex] \longrightarrow \sf { 2x – 2= 3 +x } [/tex]

   Transposing variables and constants,

   [tex] \longrightarrow \sf { 2x – x = 3 + 2 } [/tex]

   Performing addition and subtraction,

   [tex] \longrightarrow \sf { x = 5 } [/tex]

   [tex] \star \large {\bf{ Numerator = 5}} \star[/tex]

   Finding out the denominator :

   From the equation (1), we have :

   [tex] \longrightarrow \sf { y = 2 + x } [/tex]

   Substituting the value of x,

   [tex] \longrightarrow \sf { y = 2 + 5 } [/tex]

   [tex] \longrightarrow \sf { y = 7 } [/tex]

   [tex] \star \large {\bf{ Denominator = 7}} \star[/tex]

   [tex] \longrightarrow \\ [/tex] ❝ [tex] \boxed{ \sf \orange { Fraction = \dfrac{5}{7} }} \\[/tex] ❞

   Therefore, the fraction is [tex] \pmb { \mathfrak \gray { \dfrac{5}{7} }} [/tex].

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