Part of an ongoing series of 5e Rules notes.
So this one is short and sweet, but an important guideline to remember. It shows up in multiple 5e rulebooks, including the introductory material to the Players Handbook [PHB 7], repeated for emphasis in Xanathar’s and Tasha’s (emphasis mine):
Whenever you divide a number in the game, Round Down if you end up with a fraction, even if the fraction is one-half or greater.
That is, for those of you with an Excel frame of mind, always use TRUNC(), rather than ROUND() or CEILING().
A common example of this is with damage Resistance, which some monsters have. Resistance to a type of damage means it’s halved. If you do 15 points of fire damage to a creature with Resistance to Fire, they only take 7 points (15 / 2 = 7½, Round Down to 7).
Is there some deep, important, mystical and/or pragmatic reason to Round Down by default? No. I suspect things would all balance out decently enough if we handled rounding in a different fashion. But it is important that there be a rule so that one isn’t having to look up every case where fractions show up, seeing how the rounding should work for each. Consistency makes for faster, easier, less contentious gameplay.
Of course, as the preceding general rule in the PHB says, exceptions beat general rules, and there are places where there are specific exceptions to Rounding Down called out — either specifically changing how things should be rounded, or more often providing a minimum. For example, you regain half of your maximum Hit Dice used after a Long Rest, but the rules note a minimum of 1 Hit Die is recovered (otherwise 1st level characters would get nothing, as 1 HD / 2 = ½ HD, rounded down is 0 HD).
But unless an exception is called out, the general rule is always to Round Down.