Min datter blev jaloux, da hendes bror fik en større portion dessert.

Because datter is a common gender noun in Danish, so the singular possessive is min.

• min = for common gender singular nouns
• mit = for neuter singular nouns
• mine = for plural nouns

Also, when you use a possessive like min, you do not add a separate article. So:

• min datter = my daughter
• not min datteren

The possessive already fills the role that the or a/an would fill in English.

Blev is the past tense of blive, which often means become.

So blev jaloux means became jealous. It shows a change of state: she was not jealous before, and then she became jealous.

If you said var jaloux, that would mean was jealous, which describes a state without focusing on the change into that state.

So:

• blev jaloux = became jealous
• var jaloux = was jealous

Yes, jaloux does mean jealous, and it is very natural in everyday Danish.

A learner may notice that in English, this situation can sound more like envious than jealous, because the daughter wants what her brother got. Danish also has misundelig, which is often closer to envious.

Very roughly:

• jaloux = jealous
• misundelig = envious

But in real everyday Danish, people often use jaloux in situations like this too. So the sentence sounds normal.

Here da means when, referring to a specific event in the past.

So:

• da = when, for a particular past event
• når = when, for repeated events, general truths, or the future
• fordi = because

This sentence is about one completed past situation, so da fits well:

• Min datter blev jaloux, da hendes bror fik ...
  = My daughter became jealous when her brother got ...

If you used når, it would sound more like a general pattern:

• Min datter bliver jaloux, når hendes bror får ...
  = My daughter gets jealous when her brother gets ...

If you used fordi, the focus would become cause rather than time:

• Min datter blev jaloux, fordi hendes bror fik ...
  = My daughter became jealous because her brother got ...

That version is possible, but it is slightly different in meaning.

This is a very important Danish grammar point.

Sin/sit/sine is a reflexive possessive, and it refers back to the subject of its own clause.

In the clause da hendes bror fik en større portion dessert, the subject is hendes bror.

So if you used sin bror there, sin would try to refer back to bror, not to datter. That is not what you want.

You want to say her brother, referring to the daughter, so Danish uses hendes.

Compare:

• Hun så sin bror.
  = She saw her own brother.
  Here the subject is hun, so sin can refer back to her.

But in your sentence, inside the da-clause, the subject is no longer hun or min datter. It is hendes bror, so sin would not work the way English speakers might expect.

Because da hendes bror fik ... is a subordinate clause, and subordinate clauses do not use the usual Danish main-clause inversion pattern.

In Danish main clauses, the finite verb often comes in second position. But after a subordinating conjunction like da, the clause usually keeps normal subject-verb order:

• da hendes bror fik ...

So:

• hendes bror = subject
• fik = finite verb

That is the expected order after da.

Fik is the past tense of få, which often means get or receive.

So here:

• hendes bror fik en større portion dessert
  = her brother got / received a larger portion of dessert

This is a very common verb in Danish, and it has several uses in other contexts too, but here the meaning is simply got.

Større is the comparative form of stor, so it means larger or bigger.

Danish, like English, can use a comparative without stating the full comparison if it is obvious from the context.

So en større portion dessert means:

• a larger portion of dessert

The sentence does not need to say exactly larger than what. The comparison is understood, usually:

• larger than someone else’s portion
• larger than the daughter’s portion
• larger than expected

This works just like English a bigger piece or a larger portion, even when the comparison is left unstated.

In en større portion dessert, the word dessert is being used like a mass noun, similar to coffee, water, or rice.

Danish often says:

• en kop kaffe = a cup of coffee
• et glas vand = a glass of water
• en portion dessert = a portion of dessert

So dessert does not need its own article here.

If you wanted to refer to a specific dessert already known in the conversation, you could say something like:

• en større portion af desserten

But in the original sentence, the simpler form en større portion dessert is very natural.

Yes, there are other possible ways to express similar ideas, but the original sentence is natural as it stands.

For example:

• Min datter blev jaloux, da hendes bror fik mere dessert.
  = My daughter became jealous when her brother got more dessert.

This is a bit simpler and focuses on more dessert rather than a larger portion.

But en større portion dessert is perfectly good Danish and sounds a little more concrete: it emphasizes the visible size of the serving.

So the original sentence is grammatically normal and stylistically natural.