Hvis der ligger støv på gulvet, fejer jeg det op med kosten.

Here der is a dummy subject, like there in English there is / there are.

So:

• der ligger støv på gulvet = literally something like there lies dust on the floor
• natural English meaning = there is dust on the floor

This der does not mean a physical place like over there. It is just there because Danish often needs a subject in this kind of sentence.

Danish often uses ligge for things that are lying/resting somewhere, especially on a surface.

So der ligger støv på gulvet suggests that dust is lying on the floor.

This is very natural in Danish, even though English would usually just say there is dust on the floor.

A useful way to think about it:

• er focuses on existence: there is
• ligger focuses on position: is lying/is sitting there

Yes, absolutely.

Both are natural, but they are slightly different in feel:

• der er støv på gulvet = there is dust on the floor
• der ligger støv på gulvet = dust is lying on the floor

The version with ligger is a bit more visual and concrete. It makes you picture the dust on the surface.

Hvis means if, so it introduces a condition.

• Hvis der ligger støv på gulvet, fejer jeg det op = If there is dust on the floor, I sweep it up

If you used når, it would mean when or whenever, which sounds more like something expected or habitual:

• Når der ligger støv på gulvet, fejer jeg det op = When/whenever there is dust on the floor, I sweep it up

So:

• hvis = conditional, maybe maybe not
• når = when/whenever, more factual or routine-like

In this sentence, hvis is completely fine.

This is because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

The first position here is occupied by the whole if-clause:

• Hvis der ligger støv på gulvet = first element

So the main clause must begin with the verb:

• fejer = second position
• jeg = comes after the verb

That is why you get:

• Hvis der ligger støv på gulvet, fejer jeg det op med kosten.

If the sentence started directly with jeg, then you would say:

• Jeg fejer det op med kosten, hvis der ligger støv på gulvet.

Det refers back to støv.

So:

• støv = dust
• det = it

Even though dust is uncountable in English, Danish still treats støv as a singular noun here, so using det is normal.

You could think of it as:

• If there is dust on the floor, I sweep it up.

Because feje op works like a verb + particle combination, meaning to sweep up.

In Danish main clauses, the particle op often comes later, and an object pronoun like det usually goes before the particle:

• fejer det op

So the order is:

• verb: fejer
• object pronoun: det
• particle: op

This is very similar to English sweep it up, where it also goes between the verb and the particle.

Compare:

• Jeg fejer støvet op. = I sweep the dust up.
• Jeg fejer det op. = I sweep it up.

It is best understood as a verb plus particle:

• feje = to sweep
• op = up

Together, feje op means to sweep up.

In Danish, these combinations are often split in normal sentences:

• Jeg fejer det op.

But you still learn them as a unit because the meaning belongs together.

Med kosten means with the broom.

Danish often uses the definite form when talking about a familiar, relevant object in the situation. If you are cleaning a floor, the broom is a natural, identifiable tool.

So:

• med kosten = with the broom
• med en kost = with a broom

Both are possible, but they feel slightly different:

• med kosten sounds like the known or expected broom
• med en kost introduces it more as one broom among others

Gulvet is the definite form of gulv, so it means the floor.

In this sentence, we are talking about a specific floor, presumably the floor in the room or place being discussed. That is why Danish uses the definite form:

• på gulvet = on the floor

If you said på et gulv, that would mean on a floor, which is more indefinite and less natural here.

In Danish, the present tense is often used for:

• general truths
• habits
• repeated actions
• normal procedures

So this sentence is not necessarily about one specific moment. It can mean something like a regular habit:

• If there is dust on the floor, I sweep it up with the broom.

That is why ligger and fejer are both in the present tense.

Because the first part is a subordinate clause introduced by hvis, and Danish normally separates that clause from the main clause with a comma.

So:

• Hvis der ligger støv på gulvet, fejer jeg det op med kosten.

The comma helps show the boundary between:

• the condition: Hvis der ligger støv på gulvet
• the main statement: fejer jeg det op med kosten

A rough breakdown is:

• Hvis = if
• der = there
• ligger = lies / is lying
• støv = dust
• på gulvet = on the floor
• fejer = sweep
• jeg = I
• det = it
• op = up
• med kosten = with the broom

So the structure is:

• If there lies dust on the floor, sweep I it up with the broom

That is not good English, but it helps show how the Danish sentence is built.