Let the numerator be x and the denominator be y.

According to the given conditions:
x + y = 100
2y = 3x

From the second equation, we can rewrite it as:
y = (3/2)x

Substitute this into the first equation:
x + (3/2)x = 100
(5/2)x = 100
x = 40

Substitute x back into the equation y = (3/2)x:
y = (3/2)(40)
y = 60

Therefore, the fraction is 40/60 which simplifies to 2/3.