Hvis vi tager en omvej, viser navigationen en kortere vej uden vejarbejde.

Hvis means if and introduces a conditional subordinate clause.

So:

• Hvis vi tager en omvej = If we take a detour

Because it is a subordinate clause, Danish does not use normal main-clause word order there. The subject stays before the verb:

• vi tager
• not tager vi

That is normal after hvis.

This is because Danish main clauses usually follow the verb-second (V2) rule.

The first part of the sentence is the subordinate clause:

• Hvis vi tager en omvej

After that comes the main clause. In a Danish main clause, the finite verb must come in the second position, so you get:

• viser navigationen en kortere vej uden vejarbejde

Even though navigationen is the subject, the verb comes first here because something else has already been placed before the main clause.

A more basic main clause would be:

• Navigationen viser en kortere vej uden vejarbejde.

But after the opening hvis-clause, inversion happens:

• Hvis ..., viser navigationen ...

Navigationen literally means the navigation, but in natural English this often corresponds to:

• the GPS
• the navigation system
• the map app
• the satnav

So in this sentence, it probably refers to whatever system is giving route directions.

The ending -en is the definite article attached to the noun.

In Danish, instead of putting a separate word like the before the noun, you usually add the definite ending to the noun itself.

So:

• en navigation = a navigation system / a GPS
• navigationen = the navigation system / the GPS

This is very common in Danish:

• en vej = a road / way
• vejen = the road / the way

Vej means road, way, or route, depending on context.

Omvej is a compound word:

• om- = around
• vej = way/road

So en omvej means a detour or literally a way around.

In the sentence:

• tager en omvej = take a detour
• en kortere vej = a shorter route

Even though both contain the idea of way/road, they are used a bit differently.

Because both omvej and vej are common gender nouns, and the indefinite article for common gender nouns is en.

So:

• en omvej
• en vej
• en kortere vej

The word kortere does not change the article. It just modifies the noun.

Kortere is the comparative form of kort.

• kort = short
• kortere = shorter

So:

• en kortere vej = a shorter route

This works much like English short → shorter.

In this sentence, kortere compares the route to some other route, even if that comparison is only implied.

Because vej is a common gender noun, so it takes en.

Also, adjectives in Danish agree with the noun in some situations, but here the comparative form kortere stays the same. The important thing is the noun’s article:

• en vej
• therefore en kortere vej

If the noun were a neuter noun, the article might be et, but vej is not neuter.

After uden (without), Danish often uses a noun without an article, especially when talking about something in a general sense.

So:

• uden vejarbejde = without roadwork / without roadworks

This does not necessarily mean just one specific piece of roadwork. It means the route is free of roadwork in general.

This is very natural in Danish.

Vejarbejde is a compound noun, which is extremely common in Danish.

It is made from:

• vej = road
• arbejde = work

So vejarbejde means roadwork or roadworks.

Danish usually writes such combinations as one word, unlike English, which may write them as one word, two words, or a plural form depending on style.

Danish often uses the present tense for real or likely conditions, just like English often does:

• Hvis vi tager en omvej, viser navigationen ...
• If we take a detour, the GPS shows ...

This suggests a normal, realistic situation.

If the speaker wanted to talk about something more hypothetical or unreal, Danish could use other structures, but for everyday statements like this, present tense is completely normal.

Because Hvis vi tager en omvej is a subordinate clause, and it is followed by the main clause.

In standard Danish writing, a subordinate clause is typically separated from the main clause by a comma:

• Hvis vi tager en omvej, viser navigationen ...

So the comma helps show the boundary between:

1. the condition
2. the main statement

Yes. In this sentence, vej is best understood as route.

Literally, vej often means road or way, but with navigation and directions, English usually prefers:

• route
• sometimes way

So:

• en kortere vej is most naturally a shorter route

This is a good example of how the most literal translation is not always the most natural one.