What times of games utilize fractions in them?

3 answers

What TIMES or what KINDS?

Halftimes (football), quarters (NBA basketball) and thirds (hockey).
By the way, fractions are also a great part of standard music notation. You need to know fractions to read musical notes.
Betting odds are really fractions. If a horse has 3:2 odds, for example, it means that 3/2 of the bet (PLUS the original bet), will be returned if the bettor wins.