Controlliamo i millesimi mentre discutiamo la ripartizione delle spese.

Controlliamo is the 1st person plural form of controllare in the present tense.

So grammatically it can mean:

• we check
• we are checking
• and, depending on context, also let’s check

Italian often uses the same form for we do and let’s do.

It could be either in isolation, but in this sentence it most naturally sounds like we check / we are checking.

That is because the sentence has mentre discutiamo... = while we discuss..., which suggests two actions happening at the same time:

• Controlliamo i millesimi
• mentre discutiamo la ripartizione delle spese

So the overall feel is We’re checking the millesimi while we discuss the allocation of the expenses.

Still, in the right context, a speaker could also use it with a more practical Let’s check... sense.

Literally, millesimi means thousandths.

But in this kind of sentence, it usually refers to condominium ownership shares, often called millesimi condominiali in Italy. These are the fractions out of 1000 used to calculate things like:

• each owner’s share of common expenses
• voting weight in some condominium decisions

So this is not usually about abstract mathematics. It is a very common property / condo management term in Italian.

Because Italian normally uses an article here.

• i = the for a masculine plural noun
• millesimi is masculine plural

So:

• il millesimo = the thousandth / the thousandth share
• i millesimi = the thousandths / the thousandth shares

In this sentence, the speaker is referring to specific millesimi that the people involved already know about.

Mentre means while or as.

It links two actions that are happening at the same time:

• Controlliamo i millesimi
• mentre discutiamo la ripartizione delle spese

So mentre is the word that gives the sentence its simultaneous action meaning.

Because Italian commonly uses the present tense for actions happening right now or as part of a current situation.

Here:

• controlliamo = we check / we are checking
• discutiamo = we discuss / we are discussing

English often prefers the progressive form, but Italian uses the simple present much more broadly. So the Italian present can correspond to either:

• we check
• we are checking

depending on context.

Discutiamo is the 1st person plural present of discutere = to discuss.

Like controlliamo, it means:

• we discuss
• we are discussing

And like many noi forms, it can sometimes also serve as let’s discuss, though in this sentence it is best understood as ordinary present indicative because it is part of a mentre clause.

It breaks down like this:

• la ripartizione = the allocation / apportionment / distribution
• delle spese = of the expenses

And delle is a contraction:

• di + le = delle

So:

• la ripartizione delle spese = the apportionment of the expenses

This is fairly formal or administrative language. In a condo context, it means the way the shared costs are divided among the owners.

Because delle here is not really a vague partitive meaning like some. It is the normal prepositional form meaning of the:

• di
  • le = delle

So la ripartizione delle spese means the allocation of the expenses, usually referring to the specific expenses under discussion.

Also, Italian uses articles more often than English does, especially with nouns like spese in administrative phrases.

Because Italian usually leaves out subject pronouns when the verb ending already makes the subject clear.

Both verbs end in -iamo, which clearly tells you the subject is we:

• controlliamo = we check
• discutiamo = we discuss

So noi is unnecessary unless you want emphasis, contrast, or clarity.

For example:

• Noi controlliamo i millesimi, loro controllano i preventivi.
  = We check the millesimi, they check the estimates.

Yes, it is completely natural.

Italian word order is more flexible than English word order. Since the subject noi is omitted, starting directly with the verb is very common:

• Controlliamo i millesimi...

This sounds natural and efficient. English usually needs the subject:

• We check...
• We’re checking...

Italian does not.

It is quite specific to a condominium / property management / administrative context.

The key clue is i millesimi, which strongly suggests condo ownership shares. So this sentence would sound very natural in situations like:

• a condo meeting
• a discussion with a building administrator
• reviewing how shared building expenses are divided

Outside that context, millesimi might sound unusual or need explanation.