Hvis vejen er glat, kører jeg forsigtigt.

Because Danish usually puts the definite article at the end of the noun.

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

So vejen literally contains both road and the.

You can also see den vej, but that usually means that road, or it is used when there is an adjective before the noun:

• den glatte vej = the slippery road

So in this sentence, vejen is the normal way to say the road.

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

In a simple statement, you get:

• Jeg kører forsigtigt. = I drive carefully.

But when another element comes first, the finite verb must still stay in the second position. Here, the whole hvis-clause comes first:

• Hvis vejen er glat, kører jeg forsigtigt.

So the structure is:

1. Hvis vejen er glat
2. kører
3. jeg forsigtigt

That is why kører comes before jeg.

Because after hvis, Danish uses normal subordinate clause word order.

So:

• Hvis vejen er glat = If the road is slippery

Here the subject comes before the verb:

• vejen = subject
• er = verb

The form Er vejen glat? would be a direct question:

• Er vejen glat? = Is the road slippery?

So in the sentence you gave, vejen er glat is correct because it is part of an if-clause, not a question.

In this sentence, hvis is the correct word because it introduces a condition:

• Hvis vejen er glat, kører jeg forsigtigt.
• If the road is slippery, I drive carefully.

Om is usually used for whether / if in indirect questions, not for normal conditional sentences:

• Jeg ved ikke, om vejen er glat. = I don’t know if/whether the road is slippery.

So a useful distinction is:

• hvis = if, in a condition
• om = whether / if, in an indirect question

Yes, but the meaning changes slightly.

• Hvis = if
  This presents it as a condition or possibility.
• Når = when / whenever
  This sounds more like something that happens and, whenever it happens, the result follows.

So:

• Hvis vejen er glat, kører jeg forsigtigt.
  = If the road is slippery, I drive carefully.
• Når vejen er glat, kører jeg forsigtigt.
  = When/whenever the road is slippery, I drive carefully.

In many real-life situations, both are possible, but hvis is the closer match to English if.

Forsigtigt is an adverb here, and it means carefully.

It comes from the adjective forsigtig = careful.

• en forsigtig chauffør = a careful driver
• jeg kører forsigtigt = I drive carefully

A very common pattern in Danish is that an adjective gets -t when it is used adverbially:

• hurtig → hurtigt
• langsom → langsomt
• forsigtig → forsigtigt

So in this sentence, forsigtigt describes how I drive.

Because glat is the correct form here for a singular predicate adjective.

In vejen er glat, the adjective comes after er, so it is a predicate adjective. Danish adjectives still agree, and here the subject is singular.

Compare:

• vejen er glat = the road is slippery
• vejene er glatte = the roads are slippery
• den glatte vej = the slippery road

So glatte would be used for plural, or in certain definite adjective phrases, but not here.

A small extra point: glat already ends in -t, so some of the usual adjective differences are not visible in this word as clearly as they are with other adjectives.

Because Danish often uses the present tense for general truths, habits, and normal future meaning when the context is clear.

So:

• Hvis vejen er glat, kører jeg forsigtigt.

means something like:

• If the road is slippery, I drive carefully
• If the road is slippery, I will drive carefully

English often uses present tense too in the if-clause, but learners sometimes expect a future form somewhere. Danish does not need one here.

If you wanted to make the future more explicit, you could say:

• Hvis vejen er glat, vil jeg køre forsigtigt.

But the original sentence sounds very natural.

Because the sentence starts with a subordinate clause, and the comma marks the boundary before the main clause.

• Hvis vejen er glat, = subordinate clause
• kører jeg forsigtigt. = main clause

So the comma helps show where the first clause ends and the main statement begins.

It is a bit broader than English drive.

In this sentence, kører jeg clearly means I drive because the context is about a road and careful driving.

But køre can also be used more widely in Danish for movement or transport involving vehicles:

• Bussen kører klokken otte. = The bus leaves/runs at eight.
• Vi kører til Aarhus. = We’re driving/going to Aarhus.

So køre often covers ideas that English may express with drive, go by vehicle, run, or operate.

The letter ø has no exact English equivalent.

A good comparison is:

• German ö
• French eu in deux

So kører has a rounded vowel that English does not normally use.

A rough guide is:

• kører ≈ KØ-er

with the stress on the first syllable.

The important thing is not to pronounce ø like ordinary English o. If you know German or French vowel sounds, that can help a lot.