Question

the sum of numerator and denominator of a fraction is 3 less than twice the denominator. if the numerator and denominator is decreased by 1 the fraction becomes 1 /2. find the fraction

Answer 1

Answer:

The fraction is  4 / 7.

Step-by-step explanation:

Let the fraction be a/b.

"sum of numerator and denominator is 3 less than twice the denominator"

=> a + b = 2b - 3

=> a = b - 3   ... (1)

"if the numerator and denominator are decreased by 1 the fraction is 1/2"

=> (a-1)/(b-1) = 1/2

=> 2 ( a - 1 ) = b - 1

=> 2a - 2 = b - 1

=> 2a = b + 1   ... (2)

Substituting equation (1) into equation (2):

2 ( b - 3 ) = b + 1

=> 2b - 6 = b + 1

=> b = 7

and a = b - 3 = 7 - 3 = 4.

So the fraction is 4/7.