Question

7. The numerator of a fraction is 2 less than the denominator. If 5 is added to both the
numerator and the denominator, the fraction becomes
3
Find the fraction.
​

Answer 1

${ \large{ \underline{ \boxed{ \red{\sf{Fraction = { \cfrac{ 1}{ 3} }}}}}}}$

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Correct Question :-

The numerator of a fraction is 2 less than the denominator. If 5 is added to both the numerator and the denominator, the fraction becomes 3 / 4. Find the fraction.

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Some Basics Terms related to the question :-

Fraction

• Fraction is part of the whole. For example :- An apple is cutted in total 8 slides. If 4 parts are removed then it will be 4 parts out of total 8 parts. By Mathematically it written as $\frac{4}{8}$ or $\frac{1}{2}$.
• Fraction has two parts which are Numerator and Denominator.

Numerator :-

• The Number which is above on the line is Numerator or Parts taken out from the whole.
• ${ \sf{ \boxed{ \frac{ 1 }{2} } \cfrac{\longrightarrow Numerator }{} }}$

Denominator:-

• The number which is below the line is Denominator or the whole is the Denominator.
• ${ \sf{ \boxed{ \cfrac{ 1 }{2}} \cfrac{}{ \longrightarrow Denominator} }}$

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Assumption :-

• Let x be the Denominator

Given :-

• We have given numerator of a fraction is 2 less than the denominator. So, Numerator is x - 2

• 5 is added to both of Numerator and Denominator.
• So, Numerator is x - 2 + 5
• And Denominator is x + 5

• Sum of the fraction is = 3/4

To find :-

• Fraction

Solution :-

Making the the given above data in equation from :-

$\sf{ \implies{ \cfrac{ Numerator }{ Denominator } }}$

${ \boxed{ \sf{ \implies{ \cfrac{ x - 2 + 5}{ x + 5} = \cfrac{3}{4} }}}}$

Further solving the equation :-

$\sf{ \implies{ \cfrac{ x - 2 + 5}{ x + 5} = \cfrac{3}{4} }}$

$\sf{ \implies{ \cfrac{ x + 3}{ x + 5} = \cfrac{3}{4} }}$

$\sf{ \implies{ {4( x + 3)} = {3}( { x + 5)}}}$

$\sf{ \implies{ 4x + 12 = 3x + 15}}$

$\sf{ \implies{4x - 3x = 15 - 12}}$

$\boxed{\sf{ \implies{x = 3}}}$

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Denominator of the fraction is :-

${ \large{\sf{\longmapsto{x = 3}}}} \\ \\ { \large{ \underline{ \boxed{\sf{{Denominator = 3}}}}}}$

Numerator of the fraction is :-

${ \large{\sf{\longmapsto{x-2}}}} \\ \\ { \large{\sf{\longmapsto{3-2}}}} \\ \\ { \large{ \underline{ \boxed{\sf{{Numerator = 1}}}}}}$

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Now fraction is :-

$\sf{ \implies{ \cfrac{ Numerator }{ Denominator } }}$

${ \large{ \underline{ \boxed{ \red{\sf{Fraction = { \cfrac{ 1}{ 3} }}}}}}}$