The denominator of a fraction is 4 more than its numerator. when 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fraction and its numerator is 1 more than its denominator. what is the numerator of the original fraction?

5

Let n represent the numerator of the original fraction, which is n/(n+4). After adding 1/2, the value is (2(n+4)+1)/(2(n+4)), so we have ...

  n/(n+4) + 1/2 = (2(n+4)+1)/(2(n+4))

Simplifying gives ...

... (2n +(n+4))/(2(n+4)) = (2n +9)/(2(n+4))

Since the denominators are the same, we can work only with the numerators.

  3n +4 = 2n +9

  n = 5 . . . . . . . . . . . subtract 2n+4

Check

The original fraction is 5/(5+4) = 5/9. Adding 1/2 gives ...

  5/9 + 1/2 = 10/18 + 9/18 = 19/18

Note the numerator of this last fraction is 1 more than the denominator, which is twice the original denominator.