Kakan er stór, svo ég borða bara hálfa.

Kaka means cake.

Kakan means the cake.

In Icelandic, the definite article is usually added to the end of the noun as a suffix. So:

• kaka = a cake / cake
• kakan = the cake

Here, the speaker is talking about a specific cake, so kakan is used.

Because stór is a predicate adjective here: it comes after er (is) and describes the subject.

In Icelandic, that is different from an adjective placed directly before a noun.

Compare:

• stóra kakan = the big cake
  
  • adjective directly attached to the noun
• kakan er stór = the cake is big
  
  • adjective comes after er

So in this sentence, stór is the correct form.

Here svo means so, therefore, or as a result.

So the logic is:

• Kakan er stór = The cake is big
• svo ég borða bara hálfa = so I only eat half

Be aware that svo can mean different things in other contexts, such as then, thus, or sometimes be part of other expressions. But in this sentence, it is simply linking the two clauses with the meaning so.

Because svo here is acting as a conjunction joining two clauses.

After this kind of conjunction, the new clause keeps normal main-clause order:

• ég borða = I eat

So:

• Kakan er stór, svo ég borða bara hálfa.

If you used a different expression such as þess vegna (therefore / for that reason), then inversion would happen:

• Kakan er stór, þess vegna borða ég bara hálfa.

So the word order in your sentence is natural and correct.

Bara here means only or just.

So:

• ég borða bara hálfa = I only eat half / I just eat half

It limits the amount: the speaker is not eating the whole cake, only half.

It stands for half of the cake.

Icelandic often leaves out a noun when it is obvious from context. Since the sentence has already mentioned kakan, the speaker does not need to repeat it.

So hálfa here means something like:

• half [of it]
• half [of the cake]

A fuller version could be:

• ég borða bara hálfa kökuna = I only eat half the cake

But the shorter version ég borða bara hálfa sounds natural when the noun is already clear.

Because hálfa is the form of hálfur (half) that matches what it refers to here.

It refers back to kaka, which is:

• feminine
• singular

And because it is the direct object of borða (eat), it appears in the accusative.

So hálfa is the correct feminine singular accusative form.

That is why you get:

• bara hálfa

and not, for example, hálf.

Yes.

• Ég borða bara hálfa. = I only eat half.
• Ég borða bara hálfa kökuna. = I only eat half the cake.

The second version is more explicit because it repeats the noun. The shorter version is more natural if everyone already knows you are talking about the cake.

Yes, but the structure changes a bit.

For example:

• Ég borða bara helminginn af kökunni. = I only eat half of the cake.

This is also correct and clear.

The version with hálfa is shorter and very natural in everyday speech when the noun is already understood:

• Ég borða bara hálfa.

So both are possible, but they are built differently.

Yes, it is normal.

The sentence contains two separate clauses:

• Kakan er stór
• ég borða bara hálfa

The comma helps separate them and makes the sentence easier to read. In standard written Icelandic, this punctuation is natural here.