On the other hand (til gengæld, derudover, blandt andet)

Connecting your arguments

B1 Danish is about saying why, comparing, and adding a point. These connectors do that work:

DanishEnglish
til gengældon the other hand; in return
omvendtthe other way round
derudoverin addition, furthermore
genereltgenerally
først og fremmestfirst and foremost

When one of them opens the sentence, it takes the first place, so the verb comes second and the subject after it — the same inversion as after i dag or derfor:

Furthermore, she speaks three languages.
Derudover taler hun tre sprog.
First and foremost, I want to say thank you.
Først og fremmest vil jeg sige tak.

Til gengæld often follows a drawback: something is bad — til gengæld something else is good.

The apartment is small. On the other hand, it is in the middle of town.
Lejligheden er lille. Til gengæld ligger den midt i byen.

Giving an example, saying it another way

DanishEnglishshort form
for eksempelfor examplef.eks.
blandt andetamong other thingsbl.a.
det vil sigethat is (to say)dvs.
med andre ordin other wordsm.a.o.

You will see the short forms in texts; say the whole phrase aloud.

We talked about work and family, among other things.
Vi talte blandt andet om arbejde og familie.
See you on Friday, that is in three days.
Vi ses på fredag, det vil sige om tre dage.
In other words, we do not have enough money.
Med andre ord har vi ikke penge nok.

med hensyn til (as regards) is common in more formal speech and writing; i sig selv (in itself) is everyday:

The idea is good in itself.
Ideen er god i sig selv.

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