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Operation sequence

Mathematical operations must be performed in a fixed order, that is

A calculator also works according to these rules.



The rules have been laid down by mathematicians to avoid confusion. They have no special meaning, but are well choosen. And you have to stick to them if you want to join the rest of the world.



Nothing is said about the use of brackets, which play a special role.


Example 1

The rules force a particular syntax, such as in

6 + 3 × 5  = 21

and so it is not


Sometimes it has advantages to use brackets, if only for readability, because at

all is clear.


Example 2

In the calculation of

you must first perform the exponentiation, and only then take the square root. Thus


is completely wrong. The brackets must be solved from inside to outside, so


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