Jeg har en lille pumpe på bagagebæreren, hvis dækket mangler luft.

Because pumpe is a common-gender noun in Danish, so it takes en in the indefinite singular: en pumpe.

The adjective lille goes before the noun, so you get en lille pumpe.

Compare:

• en lille pumpe = a small pump
• et lille dæk = a small tire

So the article depends on the noun’s gender, not on the adjective.

Lille is a bit irregular. In attributive use before singular nouns, it stays lille for both common and neuter nouns.

So you say:

• en lille pumpe
• et lille dæk

But in the plural, Danish normally uses små:

• små pumper
• små dæk

In Danish, the definite article is usually attached to the end of the noun.

So:

• en bagagebærer = a luggage carrier / bike rack
• bagagebæreren = the luggage carrier / the bike rack

Here it refers to a specific one, most likely the rack on the bicycle.

It is a compound noun:

• bagage = luggage
• bærer = bearer / carrier

So bagagebærer literally means luggage carrier, and in everyday use it usually means the rack on a bicycle.

This is very typical Danish: several ideas are often joined into one compound word.

Because dækket is the definite form: the tire.

The noun is:

• et dæk = a tire
• dækket = the tire

So the -et ending shows that the noun is definite and neuter.

Because luft is being used as an uncountable noun, like air in English.

After a verb like mangle (to lack), Danish often uses the noun with no article:

• mangler luft = lacks air
• mangler penge = lacks money
• mangler tid = lacks time

So dækket mangler luft is perfectly normal Danish.

Here hvis means if.

It introduces a condition:

• hvis dækket mangler luft = if the tire needs air / if the tire is low on air

A learner may notice that hvis can also correspond to English whose in other contexts, but that is not what it means here. In this sentence, it is clearly the conjunction if.

Because hvis dækket mangler luft is a subordinate clause, and standard Danish spelling normally puts a comma before subordinate clauses.

So:

• Jeg har en lille pumpe på bagagebæreren, hvis dækket mangler luft.

This is very common in written Danish.

Because after hvis, you have a subordinate clause, and Danish subordinate clauses do not follow the main-clause verb-second pattern.

Here the order is:

• dækket = subject
• mangler = finite verb
• luft = object/complement

In this particular example, it looks similar to English. The difference becomes clearer when there is an adverb such as ikke:

• hvis dækket ikke mangler luft = if the tire does not lack air

That placement is typical of Danish subordinate clauses.

It suggests a physical location: the pump is on the luggage carrier, probably attached to it or kept there.

So på is literal here:

• på bagagebæreren = on the bike rack / on the luggage carrier

It does not just mean “with me” in an abstract sense; it points to where the pump is.

Here it is closer to I have / I keep / I carry than to a strong statement of ownership.

Because the sentence adds på bagagebæreren, it sounds like:

• I have a small pump on the bike rack
• I keep a small pump there
• I carry a small pump there

So har is about possession in the situation, not necessarily ownership as the main point.

Yes. It is a normal and understandable way to say that the tire needs air or is low on air.

Other natural Danish versions include:

• der mangler luft i dækket = there is air missing in the tire / the tire needs air
• dækket er fladt = the tire is flat

The difference is that mangler luft often suggests it needs more air, while er fladt can sound more like it is completely flat.

Yes, absolutely. That is also very natural Danish.

Compare:

• hvis dækket mangler luft
• hvis der mangler luft i dækket

Both mean roughly the same thing. The second version feels a little more explicit because it literally says if there is air missing in the tire.

A learner should understand both patterns.