Hún borðar gulrót með kvöldmatnum og biður svo um smáköku með teinu.

Icelandic does not have an indefinite article like English a/an. So a bare noun can often mean a carrot, a cookie, and so on.

• gulrót = a carrot
• smáköku = a cookie in this sentence

The idea of indefiniteness is simply understood from context.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word.

So:

• kvöldmatnum = the dinner / the evening meal in the form required here
• teinu = the tea in the form required here

This is one of the biggest differences from English. Instead of a separate the, Icelandic often uses a noun ending.

Because the preposition með takes the dative case.

So after með, the nouns must appear in dative form:

• kvöldmatur → kvöldmatnum
• te → teinu

So með kvöldmatnum means with the dinner, and með teinu means with the tea, with both nouns in the dative because of með.

Because the expression biðja um takes the accusative case.

The base form is:

• smákaka = nominative singular

But after um in biðja um, it becomes:

• smáköku = accusative singular

So:

• biður um smáköku = asks for a cookie

Because gulrót is one of those nouns whose nominative and accusative singular are the same in form.

So even though it is the direct object of borðar, it still appears as:

• gulrót

That is very common in Icelandic, especially with many feminine nouns.

Because Icelandic can omit the subject in a coordinated clause when it is clearly the same subject as before.

So:

• Hún borðar ... og biður ...

means:

• She eats ... and asks ...

The second she is understood automatically. English often does the same thing.

This is related to Icelandic word order. Icelandic main clauses usually follow a verb-second pattern, and in a clause like this the finite verb comes early.

So:

• og biður svo um smáköku

is a natural order meaning and then asks for a cookie

Here svo is an adverb meaning then / afterwards, and it comes after the finite verb biður in this structure.

biðja um means to ask for or to request something.

So:

• biður um smáköku = asks for a cookie

The preposition um is part of the normal pattern here. Icelandic often uses a verb + preposition combination where English might use just a verb plus object.

A useful thing to remember is:

• biðja um hjálp = ask for help
• biðja um vatn = ask for water

Both are present tense, third person singular forms.

• borðar = eats
• biður = asks

Because the subject is hún (she), English uses eats and asks, and Icelandic uses borðar and biður.

Also, Icelandic verbs do not change for gender here:

• hann borðar = he eats
• hún borðar = she eats
• það borðar = it eats

The verb form stays the same.

A few useful pronunciation points:

• ú in hún is roughly like oo in food
• ð in borðar, biður, and með is like th in this, though it can sound quite light
• ö in smáköku is like German ö or the vowel in French peur
• ei in teinu is roughly like ay in say

So even if the spelling looks unfamiliar, the sounds become much easier once you learn a few Icelandic letter patterns.