Risene koger i gryden, mens jeg skærer en agurk.

Risene is the definite form here: it refers to a specific batch of rice, not rice in general.

A learner-friendly way to think about it is:

• ris = rice, rice as a substance/general idea
• risene = the rice / the grains of rice

Even though English usually just says the rice, Danish may use risene when talking about the rice that is currently being cooked or discussed.

Koger is the present tense of koge.

Here it means something like:

• is boiling
• is cooking

So Risene koger means the rice is in the process of being cooked by boiling. Danish often uses one present-tense form where English might use either boils or is boiling, depending on context.

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

So:

• gryde = pot
• gryden = the pot

This is very common in Danish:

• bog → bogen = book → the book
• stol → stolen = chair → the chair
• gryde → gryden = pot → the pot

So i gryden literally means in-the-pot, but naturally in English we say in the pot.

Mens means while.

It connects two actions that happen at the same time:

• Risene koger i gryden
• mens jeg skærer en agurk

So the idea is: one thing is happening at the same time as another.

The comma marks the boundary between the two clauses:

• Risene koger i gryden
• mens jeg skærer en agurk

In Danish, commas are often used before subordinate clauses like the one introduced by mens. You may also notice some variation in real-life writing because Danish comma conventions allow a little flexibility depending on the system being used, but the comma here is completely normal.

Because mens introduces a subordinate clause, and subordinate clauses normally keep the order:

• subject + verb

So:

• mens jeg skærer en agurk

not

• mens skærer jeg en agurk

Compare that with a main clause, where Danish often has verb-second word order.

A useful comparison:

• Jeg skærer en agurk. = main clause
• ..., mens jeg skærer en agurk. = subordinate clause

Because agurk is a common-gender noun in Danish, so it takes en.

• en agurk = a cucumber
• agurken = the cucumber

In Danish, nouns are usually either:

• common gender → en
• neuter → et

So this is something you mainly have to learn with each noun.

Yes. Danish present tense often covers both ideas.

So:

• koger can mean boils or is boiling
• skærer can mean cut or am cutting

In this sentence, because the actions are clearly happening right now and at the same time, English naturally uses the progressive:

• the rice is cooking
• I am cutting a cucumber

Yes, absolutely.

You can say:

• Mens jeg skærer en agurk, koger risene i gryden.

When the mens-clause comes first, the main clause then shows the usual Danish inversion:

• ..., koger risene ...

not

• ..., risene koger ...

So the two versions are both correct:

• Risene koger i gryden, mens jeg skærer en agurk.
• Mens jeg skærer en agurk, koger risene i gryden.

Skærer is the present tense of skære, which is a general verb meaning to cut.

Depending on context, it can be translated as:

• cut
• slice

Here, with en agurk, English would often naturally say I am slicing a cucumber or I am cutting a cucumber. Danish skære is broader than any one English verb, so the exact translation depends on the situation.