Why does multiplication precede addition?

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Discussion Overview

The discussion revolves around the order of operations in mathematics, specifically why multiplication is prioritized over addition in expressions. Participants explore the implications of this convention and its historical reasoning, touching on both theoretical and conceptual aspects.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants reference the acronym BEDMAS, questioning the rationale behind the established order of operations.
  • One participant suggests that the order is purely a convention that simplifies the interpretation of mathematical expressions.
  • Another participant expresses a preference for the current order, arguing that it is more convenient to work with sums of products rather than products of sums.
  • A participant challenges the use of the term "convection," clarifying that the correct term is "convention" and emphasizing the importance of adhering to these conventions to arrive at correct answers.
  • There is a playful remark about the acronym BEDMAS potentially being rearranged, indicating a light-hearted exploration of the topic.

Areas of Agreement / Disagreement

Participants generally agree that multiplication precedes addition according to established conventions, but there is no consensus on the reasons for this order or its implications. The discussion includes both supportive and questioning perspectives.

Contextual Notes

Some assumptions about the clarity and necessity of the order of operations are present, but these are not explicitly stated or universally accepted among participants.

Howers
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We all know BEDMAS from grade school: brackets, exponents, division, multiplication, addition, subtraction. My question is, why does multiplication precede addition, and likewise their inverse operations?
 
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So you would suggest that we make the multiplication before addition, and the inverses of these behind each operation respectively?

How would you pronounce BEASMD?
 
Thats what we already have, multiplication before addition. I'm not proposing anything, I'm just curious as to why it was decided to be that way.
 
It purely convention - useful to the reduce work one has to put in the make any expression have only one interpretation.

Further, I'd rather have things this way. I think it's handier to deal with sums of products than products of sums. The latter are rarer (except in some trivial sense); they mean an expression is factorizable into smaller parts.
 
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just wondering if you say that's convection, then how come if you don't do BEDMAS properly you do not get the right answer?.
 


He said "convention", not "convection".

And you would get the wrong answer because you would be doing the wrong thing!

That's what "convention" means. If some one asked you what 3+ 4 was and you answered "12" because you thought "+" meant multiplication, you would have given the wrong answer because you were wrong about the convention that "+" means addition, not multiplication.
 


Anyway, BEDMAS is the same as BEDMSA! But it doesn't sound good...
 

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