Divine Fury static damage round up or down?

I have a new level 3 Zealot Barbarian and I am wondering about the wording of the feature Divine Fury.

Divine Fury (XGtE, page 11)

Starting when you choose this path at 3rd level, you can channel divine fury into your weapon strikes. While you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Would the static “half your barbarian level” round down as most things do that are not specified when at an odd level?

I suspect it does but I would like some clarification per RAW.