denken
to think
To engage in mental activity; to occupy one's mind with something, have an opinion, or imagine something.
Ich denke, dass es morgen regnen wird.
I think that it will rain tomorrow.

to think
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to think
To engage in mental activity; to occupy one's mind with something, have an opinion, or imagine something.
Ich denke, dass es morgen regnen wird.
I think that it will rain tomorrow.

'Denken' (to think) uses different prepositions for different meanings. 'Denken an (+ accusative)' directs one's thoughts toward something, while 'denken von (+ dative)' asks for an opinion.
Ich denke an die schöne Zeit am Meer.
I think of the lovely time by the sea.
'Denken' (to think) is the basis for a large word family. Important related words are the noun 'der Gedanke' (thought) and the separable verb 'nachdenken' (to reflect on something).
Dieser Gedanke gefällt mir.
I like that thought.
To express an opinion or assumption, 'denken' (to think) is very often used with a subordinate clause that begins with 'dass' (that). The conjugated verb of the subordinate clause comes at the end.
Ich denke, dass wir auf dem richtigen Weg sind.
I think that we are on the right path.
When your thoughts are directed toward a person or thing, always use the preposition 'an' followed by the accusative.
Er denkt jeden Tag an seine Familie in der Heimat.
He thinks every day of his family back home.
When you ask for an opinion about someone or something, or express an opinion, use the preposition 'von' followed by the dative.
Ich weiß nicht, was ich von der Situation denken soll.
I don't know what to think of the situation.
The reflexive expression 'sich etwas denken' means that one assumes something or comes to a conclusion. The pronoun is in the dative (mir, dir, sich...).
Ich kann mir schon denken, was jetzt passiert.
I can already figure out what will happen now.
to know
'wissen' and 'denken' both have to do with the mind and with information. The important difference is certainty. You use 'wissen' when you have information for sure or consider it certain. You use 'denken' when you express an opinion, assumption, or idea. Learners often confuse the words because in both cases you are talking about something in your head. A practical tip: If you are certain, say 'ich weiß' (I know). If you only have an opinion or assumption, say 'ich denke' (I think).

Nach der Nachricht denkt sie, dass der Termin später beginnt.
After the message, she thinks that the appointment starts later.
Für das Projekt weiß der Verkäufer den genauen Preis des Geräts.
For the project, the salesperson knows the exact price of the device.