Vi kæmper med problemet.

In Danish, the definite article is usually attached to the end of the noun instead of being a separate word.

• et problem = a problem
• problemet = the problem

So problemet is made from:

• problem = problem
• -et = the definite ending for many neuter nouns

You normally use det separately only in certain cases, such as when there is an adjective:

• problemet = the problem
• det store problem = the big problem

Because problem is a neuter noun in Danish, so its indefinite form is et problem.

For neuter nouns, the definite singular ending is often -et:

• et hus → huset
• et problem → problemet

So the ending tells you both that the noun is singular and that it means the problem.

The base form, or infinitive, is kæmpe.

Here is the pattern:

• at kæmpe = to fight / to struggle
• kæmper = fight / fights / am fighting / are fighting / is fighting

In this sentence, kæmper is present tense.

It can mean both, depending on context.

Kæmpe often has the idea of fighting, battling, or struggling. In a sentence like Vi kæmper med problemet, English will often translate it more naturally as:

• We are struggling with the problem
• We are battling with the problem

So the exact English word depends on the situation, but the Danish verb is the same.

Danish does not usually use a separate verb like English am/is/are to make the present continuous.

English says:

• We fight
• We are fighting

Danish often uses just the simple present for both ideas:

• Vi kæmper

So Vi kæmper med problemet can mean either:

• We fight with the problem
• We are struggling with the problem

The context tells you which English translation sounds best.

The verb kæmpe is commonly used with med when talking about struggling with something.

• kæmpe med noget = to struggle with something

So:

• Vi kæmper med problemet = We are struggling with the problem

You should learn this as a common verb + preposition combination. Prepositions often do not match English exactly, so it is best to remember the whole phrase kæmpe med.

Usually, med is the natural choice here.

There is a difference:

• kæmpe med noget = struggle with something, deal with something difficult
• kæmpe mod noget/nogen = fight against something/someone

So:

• Vi kæmper med problemet = We are struggling with the problem
• Vi kæmper mod problemet = We are fighting against the problem

The second version is possible, but it sounds more like the problem is an opponent. Med is the more normal choice for everyday language in this sentence.

Vi means we.

In Danish, subjects are normally stated clearly, just as in English, so vi is necessary here. You cannot usually leave it out in a full sentence.

• Vi kæmper med problemet = We are struggling with the problem

This sentence has the normal word order for a main clause with the subject first:

• Vi = subject
• kæmper = verb
• med problemet = prepositional phrase

So the structure is basically:

Subject + verb + rest

That is the most straightforward Danish word order.

If another element comes first, Danish often uses verb-second word order, for example:

• I dag kæmper vi med problemet.
  = Today we are struggling with the problem.

Notice that kæmper stays in second position.

A rough guide for English speakers is:

• kæm- has a vowel somewhat like the a in cat, but it is not exactly the same
• -per is said quickly, with a soft Danish r

A practical approximation is something like KEM-buh or KEM-per, but that is only approximate.

The letter æ is important here. It is a very common Danish vowel, and English speakers usually need practice to hear and pronounce it well.

Because Danish verbs do not change form according to the subject the way English verbs sometimes do.

In English:

• I fight
• he fights
• we fight

In Danish, the present tense form stays the same:

• jeg kæmper
• han kæmper
• vi kæmper

So kæmper works with I, you, he/she/it, we, and they.

Use et problem when you mean a problem, not a specific known problem.

• Vi har et problem. = We have a problem.
• Vi kæmper med problemet. = We are struggling with the problem.

So et problem introduces a problem in a general or indefinite way, while problemet refers to a specific problem that is already known from the context.

Yes. It is a very useful verb.

Some common patterns are:

• kæmpe med noget = struggle with something
• kæmpe for noget = fight for something
• kæmpe mod noget/nogen = fight against something/someone

Examples:

• Hun kæmper med lektierne. = She is struggling with the homework.
• De kæmper for frihed. = They are fighting for freedom.
• Vi kæmper mod tiden. = We are fighting against time.

So the preposition changes the meaning or nuance.