If We Add 1 to Both Numerator and Denominator It Becomes Equal to 1/2. Find the Fraction


Question: The numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator it becomes equal to 1/2. Find the fraction

The fraction is a part of a whole expressed as N/D.

Answer: The fraction whose numerator is 3 less than its denominator and if 1 is added to both numerator and denominator it becomes equal to 1/2  is 2/5.

Let's find out the fraction with the given conditions.

Explanation:

Let the denominator of the fraction be x.

Given that, the numerator of the fraction is 3 less than the denominator.

⇒ Numerator = x - 3

(x-3)/x is the fraction.

Given that, (N+1)/ (D+1) = 1/2

⇒ [(x -3) + 1] / [ x+ 1] = 1/2

⇒ [x - 2] / [ x+ 1] = 1/2

By cross-multiplication, we get:

2(x-2) = 1(x+1)

⇒ 2x - 4 = x + 1

⇒ 2x - x = 4 + 1

⇒ x = 5

⇒ Denominator = x = 5

Numerator = x - 3 = 5 - 3 = 2

Thus, the fraction is 2/5.