Question

the numerator of a fraction is 6 less than its denominator.If 3 is added to the numerator, the fraction is equal to 2/3, Find the original fraction

Answer 1

let denominator be x. So numerator is x-6&fraction is x-6/x.
3 is added to numerator.
x-6+3/x=2/3
x-3/x=2/3
therefore x=9&fraction =9-6/9=3/9

Answer 2

Let the numerator be n and denominator be d
n = d-6 ------------(1)
(n+3)/d = 2/3 ----------- (2)
Now by putting the value of 'n' from equation (1) to equation (2) we get
(d-6+3)/d = 2/3
(d-3)/d = 2/3
Now by cross-multiplying,
3*(d-3) = 2*d
3*d - 9 = 2*d
3*d - 2*d = 9
d = 9
Now by putting the value of 'd' into equation (1)
n = 9 - 6 = 3
Original fraction is 3/9.