“une moitié de...” VS “la moitié de...”

Question

A quiz question was as follows:Je te donne ________ de mon salaire. ——> I give you half my salary.I answered “une moitié”,  but the correct answer was “la moitié”.Why is this the case? I understood from the lesson that these two are interchangeable. Even if they are not interchangeable, I would think:-  “une moitié de mon salaire” ——> one half of my salaryWhereas:-  “La moitié de mon salaire” ——> the half of my salaryThanks

Accepted Answer

I give you half of my salary. -- Je te donne la moitié de mon salaire.
Without specifying "one half", you go with the definite article.

Answer

Is that distinction really maintained in real life? In English , the 'one' or 'a' half of is understood. is that not so in French?