"We eat half of the bread."
Translation:Vi spiser halvdelen af brødet.
Because "half" as a noun is "halvdel" in Danish (literally "half-part).
Since "halvdel" is a noun, it cannot stand alone like that. Either you make it definite (halvdelen), and talk about "that particular half of the bread", or you make it indefinite (en halvdel) and talk about some unspecified half of the bread.
"Vi spiste halvdelen af brødet" is the most common way to say "we ate half the bread". It technically means we ate "that specific half", and you can think of it as pointing implicitly to the specific half which is missing.
"Vi spiste en halvdel af brødet" just means we ate some half of the bread, and you won't hear people say it like that as often.