Gummihandskerne er våde, så jeg hænger dem ved siden af vasken.

Danish, like English, often makes compound nouns, but Danish usually writes them as one word.

So:

• gummi = rubber
• handsker = gloves
• gummihandsker = rubber gloves

Then the definite ending is added:

• gummihandskerne = the rubber gloves

This is very normal in Danish.

The ending -ne marks the definite plural.

Here is the pattern:

• en gummihandske = a rubber glove
• gummihandsker = rubber gloves
• gummihandskerne = the rubber gloves

So -ne here means the for a plural noun.

Because gummihandskerne is plural, the adjective also has to match.

• våd = wet, used with some singular forms
• våde = wet, plural/definite form

So:

• Handsken er våd = The glove is wet
• Handskerne er våde = The gloves are wet

That is why the sentence uses våde.

Because dem is the object form of they.

In English, compare:

• they hang there
• I hang them

In Danish:

• de = they
• dem = them

So in jeg hænger dem, dem is correct because it is the thing being hung.

For the same reason English says them rather than they after the verb.

The structure is:

• jeg = I
• hænger = hang
• dem = them

So dem is the direct object. Danish distinguishes between subject and object pronouns here.

Because hænger is the present tense form.

• at hænge = to hang
• hænger = hang / am hanging

So:

• jeg hænger dem = I hang them / I am hanging them

Danish present tense usually ends in -r.

It can mean either, depending on context.

Danish present tense often covers both:

• I hang them
• I am hanging them

In this sentence, English would probably most naturally say I’m hanging them or I hang them up because it describes what the speaker does as a result of the gloves being wet.

Here så means so in the sense of therefore / as a result.

So the sentence is structured like this:

• Gummihandskerne er våde = The rubber gloves are wet
• så = so
• jeg hænger dem ved siden af vasken = I hang them beside the sink

It links cause and result.

Because this så is being used as a coordinating conjunction meaning so.

After that kind of så, Danish often keeps normal main-clause order:

• jeg hænger dem

So the structure is:

• statement
• så
• another statement

If så meant something more like then at the beginning of a clause, you could get inversion:

• Så hænger jeg dem = Then I hang them / So I hang them

But in your sentence, så jeg hænger dem is the natural pattern for ..., so I hang them.

Ved siden af means beside or next to.

It is a fixed expression:

• ved = by / at
• siden = side
• af = of

Together: ved siden af = next to / beside

So:

• ved siden af vasken = beside the sink

It is best to learn ved siden af as one whole phrase.

Because vasken is the definite singular form: the sink.

The noun pattern is:

• en vask = a sink
• vasken = the sink

In Danish, definiteness is often shown by an ending on the noun instead of a separate word like the.

In this sentence, vasken most naturally means the sink.

Depending on context, vask can relate to washing or a washbasin/sink, but here ved siden af vasken clearly means beside the sink.

Because Danish usually puts definiteness at the end of the noun.

So instead of a separate the, Danish often uses endings:

• handskerne = the gloves
• vasken = the sink

This is one of the big differences from English.

Usually, no. The normal idiomatic phrase is ved siden af.

So you should learn:

• ved siden af noget = next to something

Using på siden af would usually sound wrong or at least unnatural in this context.

Because våde is a predicate adjective after the verb er.

This works like English:

• The gloves are wet

In Danish:

• Gummihandskerne er våde

So the pattern is:

• subject + er
  • adjective

Most likely a single action in the present situation.

Because the first clause says the gloves are wet, the second clause sounds like the speaker is responding right now:

• The rubber gloves are wet, so I’m hanging them beside the sink.

But grammatically, the present tense in Danish can also express a general habit if the context supports that. The sentence itself does not force only one interpretation, though the immediate-situation reading is the most natural.

A singular version would be:

• Gummihandsken er våd, så jeg hænger den ved siden af vasken.

Notice the changes:

• gummihandskerne → gummihandsken
• våde → våd
• dem → den

That shows how Danish changes nouns, adjectives, and pronouns to match singular vs. plural.