Learn Italian: Aveva pagato la metà del conto. - She had paid half of the bill.

Unlike English where we often just say "half", Italian treats metà as a regular noun meaning "the half". Therefore, it generally requires the definite article la when you are specifying what it is half of.

Why use aveva pagato instead of ha pagato?

Aveva pagato is the trapassato prossimo (past perfect) tense, which translates to "she had paid". You use this tense to talk about an action in the past that happened before another past action. Ha pagato would just mean "she paid" or "she has paid".

Where is the word for "she" in this sentence?

It is omitted, which is standard in Italian. The verb form aveva tells us the subject is third-person singular. Without a wider context, this sentence could just as easily mean "He had paid" or "You (formal) had paid". The translation assumes we already know from context that we are talking about a woman.

Why is it del conto rather than just di conto?

To say "half of the bill", you need to combine the preposition di (of) with the definite article il (the) for the masculine noun conto. In Italian, di + il always merges to form the articulated preposition del.