A gyerek orra piros, mert hideg a levegő.

Because Hungarian marks possession on the possessed noun.

• orr = nose
• orra = his/her/its nose or, in context, the child's nose

In a gyerek orra, the noun orr gets the possessive ending -a because the possessor is a third-person singular noun: a gyerek = the child.

So:

• orr = nose
• a gyerek orra = the child's nose

Also, orr already ends in double r, so orra is simply orr + a.

Hungarian expresses this kind of possession differently from English.

The usual pattern is:

possessor + possessed noun with a possessive ending

So:

• a gyerek = the child
• orra = his/her nose

Together:

• a gyerek orra = the child's nose

There is no separate word like of, and there is no apostrophe-s. The possessive relationship is mainly shown by the ending on the second noun.

A more explicit version is also possible:

• a gyereknek az orra

This also means the child's nose, but it sounds more marked or specific.

In Hungarian, the verb to be is usually omitted in the present tense, third person singular when the predicate is a noun or adjective.

So:

• A gyerek orra piros. = The child's nose is red.
• Hideg a levegő. = The air is cold.

This is completely normal Hungarian.

But in other persons or tenses, van or another form of to be appears:

• Piros vagyok. = I am red.
• Piros volt. = It was red.
• Hideg lesz. = It will be cold.

So the missing is is not an omission in the casual sense; it is the standard grammar.

Both are grammatical.

• Hideg a levegő.
• A levegő hideg.

The difference is mostly about word order and focus, not basic meaning.

In Hungarian, word order is flexible and often depends on what the speaker wants to emphasize. In this sentence, hideg comes first, which makes cold the more prominent idea: because the air is cold.

Very roughly:

• Hideg a levegő = The air is cold / It's the coldness of the air that matters here.
• A levegő hideg = The air is cold, with the air as the starting point/topic.

In many everyday contexts, the difference is subtle.

Because both nouns are definite here:

• a gyerek = the child
• a levegő = the air

Hungarian uses definite articles much like English the, although not always in exactly the same places.

Also, Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

So:

• a gyerek because gyerek starts with a consonant sound
• a levegő because levegő starts with l
• but az orr because orr starts with a vowel sound

Yes. mert means because.

It introduces a reason:

• A gyerek orra piros, mert hideg a levegő.
• The child's nose is red, because the air is cold.

This works very similarly to English. The clause after mert explains the reason for the first clause.

Because piros is a predicate adjective here: it describes the subject.

• A gyerek orra piros. = The child's nose is red.

In this use, Hungarian simply places the adjective as the predicate. No article is needed.

Compare:

• piros orr = a red nose
  
  • here piros is directly before the noun
• Az orr piros. = The nose is red
  
  • here piros is the predicate

So piros is bare because it is functioning as red in is red.

Yes. That is also correct.

• A gyerek orra piros.
• A gyereknek piros az orra.

Both mean basically The child's nose is red.

The second version uses a different possessive construction:

• a gyereknek = to the child / the child's
• az orra = his/her nose

This version can sound a bit more explicit or can place attention differently in the sentence. Hungarian often allows several natural ways to say the same thing with slightly different emphasis.

So as a learner, it is good to recognize both patterns.

The gy sound is one that English does not have exactly.

In gyerek, gy is a soft consonant, somewhat like the d in British English during for some speakers, or like a softened dy sound. It is not the same as English g in get.

A rough learner-friendly approximation is:

• gyerek ≈ dyeh-rek

But that is only approximate.

A few pronunciation notes:

• Hungarian stress is almost always on the first syllable
• so GYE-rek
• rr in orr is a trilled or tapped r, depending on speech style
• ő in levegő is a long rounded vowel; English has no exact equivalent

Yes, gyerek is a very common everyday word for child/kid.

• gyerek = child, kid
• gyermek = child, often a bit more formal, careful, or literary

In everyday speech, gyerek is extremely common and natural.

So this sentence sounds normal and idiomatic with gyerek.

Often, yes.

In this sentence, a levegő refers to the air in the situation around us, so the air is natural in Hungarian.

Hungarian can use the definite article with general or contextually understood things in ways that may feel slightly broader than English. Here, a levegő is simply the normal way to say the air in this statement.

So:

• hideg a levegő = the air is cold

This is a standard, natural expression.