Ég borða bara hálfa köku.

Because both words have changed form to match their role in the sentence.

• kaka is the dictionary form, meaning cake
• Here it is the direct object of borða (to eat), so it goes into the accusative singular
• kaka → köku

The adjective hálfur (half) must agree with the noun in:

• gender
• number
• case

Since kaka is:

• feminine
• singular
• accusative

the adjective becomes hálfa.

So:

• hálfur kaka = incorrect
• hálfa köku = correct

Icelandic does not have an indefinite article like English a/an.

So where English says:

• a cake

Icelandic simply says:

• kaka / köku

Whether English translates it as a cake, cake, or something similar depends on context.

So hálfa köku literally looks like half cake, but in natural English it is half a cake.

This is part of the noun’s declension pattern.

The noun is:

• kaka = nominative singular

But in the accusative singular it becomes:

• köku

This vowel change is normal for this word and must simply be learned as part of its forms.

A useful mini-paradigm:

• (nom.) kaka
• (acc.) köku
• (dat.) köku
• (gen.) köku

So in this sentence, borða takes an accusative object, which is why you get köku.

Bara usually means only, just, or sometimes simply, depending on context.

In this sentence, it means something like:

• only
• just

So it limits what is being eaten: the speaker is not eating more than half a cake.

Position matters a little. In Ég borða bara hálfa köku, bara naturally modifies the phrase that follows, especially hálfa köku.

So the sense is:

• I eat only half a cake
• or I’m just eating half a cake

depending on context.

Yes, sometimes word order can shift, but the nuance may change slightly.

For example:

• Ég borða bara hálfa köku.
  = I only eat half a cake / I’m just eating half a cake.

You may also see other placements in Icelandic, but this version is very natural and straightforward.

For learners, the safest pattern is:

• subject + verb + bara + the thing being limited

So in this sentence, bara comes after the verb and before the object phrase.

Yes.

Borða here is the 1st person singular present tense of borða (to eat):

• ég borða = I eat / I am eating

Icelandic often uses the simple present where English might use either:

• the simple present: I eat
• the present progressive: I am eating

Context tells you which is meant.

So this sentence could be understood as:

• a general statement: I only eat half a cake
• something happening now: I’m only eating half a cake

Usually, no. Icelandic normally does not drop subject pronouns the way some languages do.

So you usually say:

• Ég borða = I eat

not just:

• Borða on its own to mean I eat

The verb ending does give some information, but Icelandic still normally uses the pronoun.

So ég is there because Icelandic sentences usually need an explicit subject.

The dictionary form is:

• hálfur = half

But adjectives in Icelandic change form to match the noun they describe.

Since köku is:

• feminine
• singular
• accusative

the adjective becomes:

• hálfa

So:

• hálfur = base form
• hálfa = the form used here

This is a very common feature of Icelandic adjectives.

Literally, Icelandic does not need a separate word for of here.

So hálfa köku corresponds to natural English:

• half a cake
• half of a cake

In ordinary usage, it means one half of a whole cake, not a special type of cake called a half-cake.

English needs a or of a, but Icelandic expresses that idea just with the adjective + noun phrase.

Not exactly by itself.

hálfa köku is indefinite, so it is more like:

• half a cake

If you wanted half the cake, you would normally make the noun definite, for example with the suffixed definite article:

• hálfa kökuna = half the cake

So:

• hálfa köku = half a cake
• hálfa kökuna = half the cake

That distinction is important in Icelandic.

A rough English-friendly approximation is:

• yeg BOR-tha BA-ra HOWL-va KOE-ku

A few notes:

• Ég starts with a sound somewhat like yeg
• ð in borða is like the th in this
• á is a clear long vowel, roughly ow as in cow but steadier
• ö in köku does not exist exactly in English; it is somewhat like the vowel in some pronunciations of bird, but with rounded lips

This is only approximate, but it can help you get started.

No, but it is the most common and beginner-friendly choice.

You may also come across words like:

• aðeins = only, just, merely

In many everyday sentences, bara is extremely common and natural.

So for a learner, Ég borða bara hálfa köku is a very normal sentence.

This sentence is a great example of several basic Icelandic patterns:

1. Subject pronoun + present tense verb

   • Ég borða

2. No indefinite article

   • no separate word for a

3. Accusative object after the verb

   • köku

4. Adjective agreement

   • hálfa matches köku

5. Common adverb placement

   • bara after the verb

So if you understand why hálfa köku is in that form, you are already learning one of the most important parts of Icelandic grammar.