Hvis suppen er gammel, kaster jeg den ud.

Hvis means if in the sense of a condition.

Here it introduces a conditional clause:

• Hvis suppen er gammel = If the soup is old

A learner may confuse hvis with:

• om = whether / if in indirect questions
  
  • Jeg ved ikke, om suppen er gammel = I don’t know whether the soup is old
• når = when for something expected or repeated
  
  • Når suppen er klar, spiser vi = When the soup is ready, we eat

So in this sentence, hvis is correct because the speaker means under that condition.

Suppen is the definite form of suppe.

In Danish, a noun often gets definiteness by adding it to the end of the word:

• en suppe = a soup
• suppen = the soup

So Hvis suppen er gammel means If the soup is old, referring to a specific soup already known from the context.

Using just suppe here would not be natural as a normal singular noun phrase.

The adjective matches the noun.

Suppe is a common-gender noun, an en-word, so in the singular the predicate adjective takes the basic form:

• en suppe er gammel
• et hus er gammelt
• flere ting er gamle

Since suppen is singular and common gender, gammel is the right form.

Also, because the adjective comes after er, it is a predicate adjective, not one directly before the noun. So Danish does not use the definite adjective form here.

Because suppe is an en-word.

In Danish, pronouns usually match the grammatical gender of the noun:

• en suppe → den
• et bord → det

So:

• Jeg kaster den ud = I throw it out

If the noun were neuter, you would use det instead.

This is because Danish main clauses normally follow the verb-second rule, often called V2.

The first part of the sentence is a subordinate clause:

• Hvis suppen er gammel

When that whole clause comes first, it fills the first position in the main sentence. Then the finite verb of the main clause must come next:

• Hvis suppen er gammel, kaster jeg den ud

So the pattern is:

• subordinate clause
• finite verb
• subject

That is why you get kaster jeg instead of jeg kaster.

Compare:

• Jeg kaster den ud, hvis suppen er gammel
• Hvis suppen er gammel, kaster jeg den ud

Both are correct, but the word order changes because of V2.

Because kaste ud is a verb + particle combination, similar to English throw out.

In Danish main clauses, the particle often comes later in the sentence:

• Jeg kaster den ud
• Han smider det ud

This is especially common when there is an object pronoun like den.

So:

• kaster = throw
• ud = out
• kaster den ud = throw it out

This is very similar to English, where we usually say throw it out, not throw out it.

Yes, but it depends on what exactly you mean.

Gammel literally means old, and with food it can mean something like:

• old
• not fresh
• too old
• gone bad, depending on context

In real everyday Danish, people might also say:

• Hvis suppen er dårlig, kaster jeg den ud = If the soup is bad, I throw it out
• Hvis suppen er for gammel, kaster jeg den ud = If the soup is too old, I throw it out

So the sentence is understandable and grammatically fine, but another adjective might sound more natural in some situations.

Yes. You can say:

• Hvis suppen er gammel, så kaster jeg den ud.

The så is optional here. It can make the conditional relationship feel a little clearer or more conversational.

So both are correct:

• Hvis suppen er gammel, kaster jeg den ud.
• Hvis suppen er gammel, så kaster jeg den ud.

Yes, in standard writing you normally put a comma after the initial hvis-clause:

• Hvis suppen er gammel, kaster jeg den ud.

The comma marks the boundary between the subordinate clause and the main clause. It helps readability and is the expected written form here.