
kauen
to chew
To break down food with the teeth before swallowing it.
Man sollte jeden Bissen gut kauen, um die Verdauung zu erleichtern.
You should chew every bite well to make digestion easier.
to chew
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to chew
To break down food with the teeth before swallowing it.
Man sollte jeden Bissen gut kauen, um die Verdauung zu erleichtern.
You should chew every bite well to make digestion easier.

to struggle with
To have to deal with a problem, defeat, or difficult task for a long time and very intensely.
An dieser unerwarteten Niederlage wird die Mannschaft noch eine Weile zu kauen haben.
The team will have to struggle with this unexpected defeat for quite a while.
The literal meaning (breaking down food) is often used without a preposition or with 'auf'. The figurative meaning (having a problem to deal with) always appears in the fixed expression 'an etwas (Dativ) zu kauen haben' (to have something to chew on/to struggle with something).
Er kaute nachdenklich auf seinem Stift.
He thoughtfully chewed on his pen.
When you want to say what someone is chewing on, you use the preposition 'auf' followed by the dative.
Das Kind kaut auf seinem Spielzeug.
The child is chewing on his toy.
Common things people chew are 'Kaugummi kauen' (to chew gum) or, out of nervousness, 'Fingernägel kauen' (to bite/chew one's fingernails). When eating, people often emphasize that you should chew 'gut' (well) or 'gründlich' (thoroughly).
Hör bitte auf, an deinen Fingernägeln zu kauen.
Please stop chewing your fingernails.
The idiom 'an etwas zu kauen haben' (to have something to chew on/to struggle with something) is a fixed structure. The 'etwas' is in the dative and describes the problem that occupies someone mentally or emotionally.
Der Sportler hatte an der Kritik der Presse schwer zu kauen.
The athlete struggled a lot with the criticism from the press.
to nibble
Kauen means breaking food down in the mouth. Knabbern, by contrast, emphasizes repeatedly biting off small pieces of something, usually something hard. After biting off the pieces, you can then chew them.

Sie kaut das Stück Karotte gründlich, bevor sie es schluckt.
She chews the piece of carrot thoroughly before swallowing it.
Sie knabbert kleine Stücke von der harten Karotte ab.
She nibbles small pieces off the hard carrot.