Hun vælger en roligere baggrund, hvis børnene leger i stuen.

Because baggrund is a singular countable noun, and in Danish singular countable nouns normally take an article.

Also, baggrund is a common-gender noun, so its indefinite article is en, not et:

• en baggrund = a background
• baggrunden = the background

So en roligere baggrund is the normal way to say a calmer/quieter background.

Roligere is the comparative form of rolig.

• rolig = calm / quiet
• roligere = calmer / quieter

Danish often forms the comparative by adding -ere to the adjective.

In this sentence, roligere compares one background with another possible background. So it means she chooses a background that is more calm / less busy / quieter than some other option.

In Danish, the comparative form of an adjective usually stays the same regardless of the noun’s gender or number.

So you get:

• en roligere baggrund
• et roligere rum
• roligere farver

The comparative roligere does not need a different ending for en-words, et-words, or plural nouns in this kind of use.

Because barn is an irregular noun.

Its forms are:

• et barn = a child
• barnet = the child
• børn = children
• børnene = the children

So børnene is the definite plural form, meaning the children.

This is one of those noun patterns that just has to be learned as a set.

I stuen means in the living room, referring to a specific living room that is known from the context.

• en stue = a living room
• stuen = the living room

So:

• i en stue = in a living room, any living room
• i stuen = in the living room, the one we are talking about

Danish often uses the definite form when the place is understood to be specific.

Both are present tense forms:

• vælger = chooses / is choosing
• leger = play / are playing

A very important point for English speakers: Danish present tense often covers both the English simple present and present continuous.

So børnene leger can mean:

• the children play
• the children are playing

The context tells you which one sounds best in English.

After hvis, Danish uses subordinate clause word order, which is the normal subject + verb order:

• hvis børnene leger i stuen

That is:

• hvis = if
• børnene = the children
• leger = are playing / play

There is no inversion here.

In the main clause, the usual order is also subject + verb because the sentence starts with the main clause:

• Hun vælger en roligere baggrund

But if you move the hvis clause to the front, then the main clause changes word order:

• Hvis børnene leger i stuen, vælger hun en roligere baggrund.

Notice vælger hun, not hun vælger. That is the normal Danish verb-second pattern.

Hvis mainly means if.

It introduces a condition:

• Hun vælger en roligere baggrund, hvis børnene leger i stuen.
• She chooses a quieter background if the children are playing in the living room.

English sometimes uses when in situations that feel repeated or likely, but Danish usually keeps a distinction:

• hvis = if
• når = when

So if you wanted a clear when meaning, Danish would often prefer når instead.

Yes. You can put the hvis clause first:

• Hvis børnene leger i stuen, vælger hun en roligere baggrund.

This has the same basic meaning as:

• Hun vælger en roligere baggrund, hvis børnene leger i stuen.

The main difference is focus and word order:

• with the main clause first, the choice is introduced first
• with the hvis clause first, the condition is highlighted first

But the overall meaning stays the same.

Not necessarily.

In Danish, baggrund can refer to a literal background, but also to the general setting behind something, depending on context. In a sentence like this, it could mean:

• a visual background
• a backdrop
• a less distracting setting

So even if the basic meaning is already clear, it is useful to know that baggrund can be slightly broader than just a physical wall or scenery.