Question

the numerator of a fraction is 4 less than its denominator. if 2 is added to the numerator than then the fraction becomes 5/7. find the fraction .​

Answer 1

$\mathfrak{\large{\underline{\underline{\pink{Answer :-}}}}}$

The Fraction is $\tt{\dfrac{3}{7}}$

$\mathfrak{\large{\underline{\underline{\pink{Explanation :-}}}}}$

Given :

Numerator = 4 less than the denominator

If 2 added to the numerator = Fraction turns $\tt{\dfrac{5}{7}}$

To Find :

The Fraction

Solution :

Consider the Denominator as x

Numerator = x - 4

★ $\boxed{\sf{\purple{\frac{(x - 4) + 2}{x} = \frac{5}{7}}}}$

$\sf{\implies} \: \dfrac{(x - 4) + 2}{x} = \dfrac{5}{7}$

$\sf{\implies} \: 7(x - 4 + 2) = 5(x)$

$\sf{\implies} \: 7x - 28+ 14= 5x$

$\sf{\implies} \: - 28+ 14= 5x - 7x$

$\sf{\implies} \: \cancel- 14= \cancel - 2x$

$\sf{\implies} \:x = \dfrac{14}{2}$

$\sf{\implies}\red{ \: x = 7}$

$\rule{300}{1.5}$

★ Value of x - 4

$\sf{\implies} \: 7 - 4$

$\sf{\implies} \: 3$

Numerator = 3

Denominator = 7

$\therefore$ The Fraction is $\tt{\dfrac{3}{7}}$

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{\pink{Verification :-}}}}}$

As it is given in the Question, the Fraction should be $\tt{\dfrac{5}{7}}$ when 2 is added to the numerator.

$\sf{\implies} \: \dfrac{3 + 2}{7} = \dfrac{5}{7}$

$\sf{\implies} \: \dfrac{5}{7} = \dfrac{5}{7}$

$\therefore$ The Fraction is $\tt{\dfrac{3}{7}}$

Answer 2

$\bf{\large{\underline{\underline{Answer:-}}}}$

Required fraction is $\bold{ \dfrac{3}{7} }$

$\bf{\large{\underline{\underline{Explanation:-}}}}$

Given :-

Numerator of a fraction less than its denominator by 4. If 2 is added to the numerator than fraction becomes 5/7.

To find :- Required fraction

Solution :-

Let the denominator of the fraction be x

Numerator of the fraction = 4 less than its denominator = (x - 4)

Given that when 2 added to the fraction the fraction becomes 5/7

In this case numerator becomes [(x - 4) - 4] and denominator is x

According to the question :-

Equation formed :-

$\tt{ \dfrac{(x - 4) + 2}{x} = \dfrac{5}{7} }$

$\tt{ \dfrac{x - 4 + 2}{x} = \dfrac{5}{7} }$

By Cross multiplication :-

$\tt{(x - 4 + 2)7 = 5 \times x}$

$\tt{7x - 28 + 14 = 5x}$

$\tt{7x - 14 = 5x}$

$\tt{7x - 5x = 14}$

$\tt{2x = 14}$

$\tt{x = \dfrac{14}{2} }$

$\tt{x = 7}$

So, Denominator of the fraction = x = 7

To find the value of numerator sustitute value of x in (x - 4)

(x - 4) = (7 - 4) = 3

So, Numerator of the fraction = 3

Therefore the fraction is $\bold{ \dfrac{3}{7} }$

$\bf{\large{\underline{\underline{Verification:-}}}}$

To check whether the answer is correct or not subtitute the fraction in the equation that is formed to solve.

$\tt{ \dfrac{3 + 2}{7} = \dfrac{5}{7}}$

$\tt{\dfrac{5}{7} = \dfrac{5}{7} }$

Therefore the fraction is $\bold{ \dfrac{3}{7} }$