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The sentence
Je me suis trompé dans mon calcul.
can be translated as
I've made a mistake in my calculation.
However, I don't understand the purpose of "me" in that sentence; for example,
je -> I
suis trompé -> have made
dans -> in
mon calcul -> my calculation
so if we didn't put "me" there, would the meaning change ?
You confusion is due to the fact the most idiomatic ways to express it differs between French and English. However there are alternative forms with a closer structure in both cases.
I've made a mistake in my calculation.
word by word translates to:
J'ai fait une erreur dans mon calcul.
while
Je me suis trompé dans mon calcul.
literally translates to:
I mislead myself in my computation.
This particular verb in French that means "to make an error", "to err", is a pronominal verb; it's just like that; you can use other verbs, but they are not heard so often and they are verbal locutions instead of simple one word terms: "commettre une erreur", "faire une erreur". In a pronominal verb, just as in English, you have to use the pronoun all the time; there is no way to omit it. This pronoun, moreover, has nothing to do with the possessive adjective "mon"; that word is in the noun group not the verb group: you can replace it by all of these words in turn and say something a little different each time without changing the verb;
ce, le, un, leur, ses, mes, tous ces, certains, etc. ("calcul" or "calculs" according to gender)
The conjugation is as follows ;
je me suis trompé
tu t'es trompé
il s'est trompé
nous nous sommes trompés
vous vous êtes trompés
ils se sont trompés
It's often not a good idea to translate word for word. You made a mistake when you said "suit trompe -> have made".
You should have included "a mistake", but also "me".
me suis trompé -> have made a mistake
In French, to make a mistake is se tromper. As Jlliagre said, it's reflexive because literally it means "to mislead oneself".
(It's a little more subtle than that, you should go see all the meanings of "tromper" and "se tromper".)
