Penser que, croire que = To think that, to believe that

Look at these sentences:

Vous pensez qu'elle chante bien.You think (that) she sings well.

Elle croit que les anges existent.She believes (that) angels exist.

Nous pensons que c'est une bonne idée.We think it's a good idea.

Ils croient que tu caches quelque chose.They believe you're hiding something.


ATTENTION 
When using verbs of opinions such as penser (to think) and croire (to believe) to say 'I believe that / I think that' in French, you always need to put que ('that') after them, whereas in English you can sometimes omit it.

For example: In French, you can NEVER say ''Vous pensez elle chante bien.'' or ''Elle croit les anges existent.''

 

See also the more advanced Using 'trouver' to express 'to find' and opinions  and Using Le Subjonctif after penser, trouver. savoir, croire, prétendre + que in the negative

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Examples and resources

Elle croit que les anges existent.She believes (that) angels exist.
Je pense que tu es gentil.I think you're kind.
Vous pensez qu'elle chante bien.You think (that) she sings well.
Ils croient que tu caches quelque chose.They believe you're hiding something.
Je crois que mon ami a raison.I believe my friend is right.
Nous pensons que c'est une bonne idée.We think it's a good idea.
Let me take a look at that...