let

x = the original fraction's denominator, x<>0

y = the original fraction's numerator

y/x = the original fraction

A non-zero fraction's denominator is increased by 1 and its numerator is decreased by 50% and the resulting fraction is 1/3 of the original fraction:

y(1 - 0.50)/(x + 1) = (1/3)(y/x)

by solving we find:

x = 2

click here to see the step by step solution of the equation:

the original fraction's denominator is 2.