Treba mi pola kilograma sira.

Treba mi means I need.

Literally, Serbian expresses this idea a bit differently from English. It is closer to It is needed to me:

• treba = is needed / is necessary
• mi = to me

So Treba mi pola kilograma sira is the natural Serbian way to say I need half a kilo of cheese.

Because Serbian often uses trebati impersonally in this meaning.

So instead of matching the verb directly to I, Serbian commonly says:

• Treba mi... = I need...
• Treba ti... = you need...
• Treba mu/joj... = he/she needs...

The verb stays in the neutral-looking 3rd person singular form treba, and the person is shown by the dative pronoun:

• mi = to me
• ti = to you
• mu = to him
• joj = to her

This is one of the most important patterns to learn for everyday Serbian.

Mi is the dative clitic form of ja.

Here it means to me.

Compare:

• ja = I
• meni = to me
• mi = to me, but in short clitic form

In this sentence, Serbian normally uses the short form:

• Treba mi pola kilograma sira.

If you use meni, it usually adds emphasis:

• Meni treba pola kilograma sira. = I need half a kilo of cheese.

Pola means half.

In Serbian, pola is used very often in quantity expressions:

• pola sata = half an hour
• pola hleba = half a loaf of bread
• pola kilograma sira = half a kilogram of cheese

A key thing to remember is that pola is followed by the genitive.

Because pola requires the genitive, and kilograma is the genitive singular of kilogram.

So:

• dictionary form: kilogram
• after pola: kilograma

That gives:

• pola kilograma = half a kilogram

This is a very common Serbian pattern after quantity words.

Because sir also appears in the genitive here.

The structure is basically:

• pola of kilograma
• kilograma of sira

So both nouns after the quantity idea end up in genitive forms:

• kilograma = of a kilogram
• sira = of cheese

This is normal with measurements and amounts in Serbian.

Compare:

• kilogram sira = a kilogram of cheese
• pola kilograma sira = half a kilogram of cheese

The dictionary form is sir, meaning cheese.

Here are the two forms:

• sir = nominative singular
• sira = genitive singular

You learn nouns in the dictionary form, but in real sentences Serbian changes them depending on case.

A learner should usually stick with Treba mi pola kilograma sira.

That is the safest and most standard everyday Serbian way to say I need half a kilo of cheese.

You may hear forms like trebam in some regional or neighboring varieties, but for standard Serbian, especially as a learner, Treba mi... is the best pattern to use.

Yes, Serbian word order is flexible, but not completely free.

The neutral word order here is:

• Treba mi pola kilograma sira.

You may also hear:

• Pola kilograma sira mi treba.

That shifts the focus more onto half a kilo of cheese.

One important point: mi is a clitic, so it usually goes near the beginning of the sentence, often in the second position area. That is why Treba mi... sounds very natural.

As a beginner, it is best to keep the original order until you feel comfortable with clitics and emphasis.

Because Serbian has no articles.

So sir can mean:

• cheese
• the cheese
• a cheese

The exact meaning depends on context.

In Treba mi pola kilograma sira, the sense is simply some cheese / half a kilo of cheese. English needs an article or a slightly different structure, but Serbian does not.

Yes, it is natural and understandable.

If you are in a shop or at a market, Treba mi pola kilograma sira sounds fine.

But Serbian speakers also often use shorter or more directly request-like phrases, such as:

• Pola kilograma sira, molim. = Half a kilo of cheese, please.
• Dajte mi pola kilograma sira. = Give me half a kilo of cheese.
• Molim vas, pola kilograma sira. = Half a kilo of cheese, please.

So your sentence is correct, but in a real buying situation, many people would use one of these slightly more practical request forms.

Yes, in everyday speech you may hear more colloquial versions with kila instead of kilogram.

So:

• pola kilograma sira = more standard / full form
• pola kile sira = more colloquial, very common in speech

As a learner, it is good to know both, but the sentence you were given is a very good standard model.

The most useful things to notice are:

1. Treba mi = a very common Serbian pattern for I need
2. mi is dative = to me
3. pola is followed by the genitive
4. quantity expressions often cause genitive on the following noun
5. Serbian has no articles

So this one sentence teaches several important everyday grammar patterns at once.