Question

The numerator of a fraction is 4 less than the denominator. If one is added to both its numerator and denominator, it becomes 1/ 2 Find the fraction​

Answer 1

Answer:

hope this will help you..........

Answer 2

Answer:

Given :-

• The numerator of a fraction is 4 less than the denominator. If one is added to both its numerator and denominator it becomes 1/2.

To Find :-

• What is the fraction.

Solution :-

Let, the denominator be x

And, the numerator will be x - 4

Hence, the fraction will be $\sf\dfrac{x - 4}{x}$

According to the question,

⇒ $\sf\dfrac{x - 4 + 1}{x + 1} =\: \dfrac{1}{2}$

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

By doing cross multiplication we get,

⇒ 2(x - 3) = x + 1

⇒ 2x - 6 = x + 1

⇒ 2x - x = 1 + 6

➠ x = 7

Hence, the required fraction will be,

↦ $\sf\dfrac{x - 4}{x}$

↦ $\sf\dfrac{7 - 4}{7}$

➦ $\sf\dfrac{3}{7}$

$\therefore$ The fraction is $\sf\boxed{\bold{\large{\dfrac{3}{7}}}}$.

Let's Verify :

↦ $\sf\dfrac{x - 4 + 1}{x + 1} =\: \dfrac{1}{2}$

Put x = 7 we get,

↦ $\sf\dfrac{7 - 4 + 1}{7 + 1} =\: \dfrac{1}{2}$

↦ $\sf\dfrac{4}{8} =\: \dfrac{1}{2}$

↦ $\sf\dfrac{\cancel{4}}{\cancel{8}} =\: \dfrac{1}{2}$

↦ $\sf\dfrac{1}{2} =\: \dfrac{1}{2}$

➠ LHS= RHS

Hence, Verified ✔