# Why does bedmas/pedmas work?

#### kramer733

I've often wondered this myself. Is it just a convention? Is it because in a way, all the orders of operation are just "addition" ? addition is addition, subtraction is adding negative numbers, multiplying is addition, dividing is multiplying.

But then if this were true, it would only work depending on which number system you have right?

And if this was the convention, how did a middle eastern guy make this convention so widely known? Could somebody enlighten me on this question?

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#### rollcast

Theres no real reasoning behind why it is done in that order, although opposite functions eg. add. and sub., multply and divide, exponents and roots are performed consecutively.

Its just a convention which helps make everything we do in mathematics easier for anyone to read and understand.

#### micromass

Indeed, it is only a convention. Math wouldn't change one single bit if we would make another convention!! The only thing that we would change would be notational.

For example, if multiplication did not have precendence over addition, then we could note 2*3+5*6+6*7*8 as (2*3)+(5*6)+(6*7*8). We only need to add some extra brackets. That's the only thing that would ever change.

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