Question

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

Answer 1

Answer :-

The required fraction is 3/7.

Solution :-

Let the denominator of a fraction be x

Numerator of a fraction = 4 less than numerator = x - 4

If 2 is added to numerator = (x - 4) + 2 = x - 2

Given

If 2 is added to the numerator fraction becomes 5/7

⇒ (x - 2)/x = 5/7

By cross multiplication

⇒ (x - 2)7 = 5x

⇒ 7x - 14 = 5x

⇒ 7x - 5x = 14

⇒ 2x = 14

⇒ x = 14/2

⇒ x = 7

Denominator of a fraction = x = 7

Numerator of a fraction = (x - 4) = (7 - 4) = 3

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

Therefore the required fraction is 3/7.

Answer 2

Answer :

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

Step-by-step explanation :

Given :

Numerator = 4 less than the denominator .

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

To Find :  

The Fraction.

Solution :

$\star\;\textbf{\underline{\underline{Consider as -}}}}$

Denominator as - x  

Numerator as - x - 4

It imples that :

$\bigstar\;\boxed{\sf{\red{\frac{(x - 4) + 2}{x} = \frac{5}{7}}}}$

Values in Equation :

$\tt\\ \\\implies \dfrac{(x - 4) + 2}{x} =  \dfrac{5}{7}\\ \\\implies 7(x - 4 + 2) = 5(x)\\ \\\implies 7x - 28+ 14= 5x\\ \\\implies - 28+ 14= 5x - 7x\\ \\\implies \cancel- 14= \cancel - 2x\\ \\\implies x = \dfrac{14}{2}\\ \\\implies x = 7\\ \\\rule{300}{1.5}$

★ Finding the Value of x - 4 :

$\tt\\\implies 7 - 4\\ \\\implies 3\\ \\Numerator = 3\\ \\Denominator = 7$

★ Hence, The required fraction is $\tt{\dfrac{3}{7}}$

$\rule{300}{1.5}$

$\bigstar\;\textbf{\underline{\underline{Verification :}}}}\\ \\\bigstar\;\textsf{\underline{\underline{As given in Question, that when 2 is added to the numerator.}}}}$

$\sf The\;Fraction\;should\;be\;\tt{\dfrac{5}{7}}\\ \\So,\\\sf \\ \implies \dfrac{3 + 2}{7} = \dfrac{5}{7}\\ \\\implies \dfrac{5}{7} = \dfrac{5}{7}\\ \\ \\\therefore The\;Fraction\; is\; \tt{\dfrac{3}{7}}$

$\rule{300}{1.5}$