Question

The numerator of a fraction is 4 less than iss denominacor. 1 is added to both the
numerator and the denominator, the fraction becomes 1/2
1. Find the fraction​

Answer 1

Step-by-step explanation:

(x-4)+1/x+1 = 1/2

(x-4+1)/x+1 = 1/2

x-3= 1/2(x+1)

x = 1/2x + 1/2 + 3

x -1/2x = 7/2

2(1/2x) = (7/2)(2)

x = 7

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

Answer 2

Answer:

$\bigstar{\bold{Fraction\:is\:\dfrac{3}{7} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• The numerator is 4 less than denominator
• If 1 is added to both numerator and denominator, the fraction becomes 1/2

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The fraction

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let the denominator be x. Hence numerator will be x-4

→ By the given data,

  $\dfrac{(x-4)+1}{x+1} \:=\:\dfrac{1}{2}$

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

→ Cross multiplying

   2 (x - 3) = x + 1

   2x - 6 = x + 1

   x = 7

   The denominator is 7

→ Numerator = x -4 = 7-4 = 3

$\boxed{\bold{The\:fraction\:is\:\dfrac{3}{7} }}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

→ Fraction is 3/7

→ Adding 1 on both numerator and denominator we get 4/8 which is equal to 1/2.

  Hence verified.