What Fraction Of A Year Is 120 Days?

It depends.
There are various definitions for a year, depending on what you need it for. A regular calendar non-leap year has 365 days, so the fraction is 120/365 = 24/73.

A leap year has 366 days, so the fraction is 120/366 = 20/61.
An average year in a series of 4 years has 365.25 days, so the fraction is 120/365.25 = 160/487
An average year in a series of 400 years has 365.2425 days, so the fraction is
  120/365.2475 = 16,000/48,699
A year used for computing accrued interest may be 365 days (see above for the fraction), or it may be 360 days. 120/360 = 1/3