Let's start with the easiest one of the three verbs:
Glauben means to believe, examples: ich glaube an Gottt - I believe in God; ich glaube, er hat recht - I believe that he is right. The verb "glauben" expresses that you are convinced of something.
Meinen means to opine, to favor one or another opinion without really being sure which one is right.
Denken means to think. It is used the same way as "to think" is used in English.
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Let's start with the easiest one of the three verbs:
Glauben means to believe, examples: ich glaube an Gottt - I believe in God; ich glaube, er hat recht - I believe that he is right. The verb "glauben" expresses that you are convinced of something.
Meinen means to opine, to favor one or another opinion without really being sure which one is right.
Denken means to think. It is used the same way as "to think" is used in English.
Ufff...that's a hard question, you know that? =P
1. denken = to think
2. glauben = to believe
3. meinen = to mean
These are the LITERAL translations.
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You can use "denken" when you think or believe something.
A: What are you thinking about? = Worüber denkst du nach?
B: I am thinking about the math problem = Ich denke über die Matheaufgabe nach.
A: What do you think about religion? = Was denkst du über Religion?
B: I believe that...I think that....= Ich glaube....Ich denke, dass
You can use "denken" when you think about something such as a math problem or when you give an opinion on something.
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"Glauben" is pretty much the same as "denken".
It only includes the belief into something. Such as religion.
A: Do you believe in God? = Glaubst du an Gott?
B: hmmmm....
A: What is your definition of society? = Wie lautet deine Definition für Gesellschaft?
B: I believe that society is divided into two categories = Ich glaube, dass die Gesellschaft in zwei Kategorein unterteilt wird.
or when someone asks you something but you're not sure if your given answer is correct!
A: How much is 1+1? = Wieviel ist 1+1?
B: I think/believe...2 = Ich glaube 2! (You wouldn't use "denken" here)
A: You believe only? Or are you sure the result is 2? = Du glaubst nur? Oder bist du dir sicher, dass das Ergebnis 2 ist?
B: errrrr.....
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"meinen". I think "meinen" is the one which is less common than the other two.
The person A is asking for an opinion. "Denken" is also fine here.
A: What do you think? = Was meinst du?
You also use it in that context:
A: How do you mean? I don't get you! = Was meinst du? Ich verstehe dich nicht.
These are the only examplesI can think of...there are more but I don't really know how to explain those =P
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Hope it helps =)