Is the Order of Operations Always Clear-Cut in Math?

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Discussion Overview

The discussion centers around the expression 48/2(9+3) and whether the order of operations in mathematics leads to a clear-cut answer. Participants explore different interpretations of the expression, examining how rearranging it can yield different results, specifically 2 or 288. The scope includes mathematical reasoning and debate over the clarity of operational rules.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that rearranging 48/2(9+3) can lead to different results, specifically 288, by following certain steps.
  • Others assert that if 48/2(9+3) equals 2, then it leads to a contradiction with the derived statement 24=0.1666..., questioning the validity of that interpretation.
  • One participant points out that the same expression can be parsed differently, leading to different conclusions, highlighting the ambiguity in the order of operations.
  • A later reply critiques the logic of a previous claim, suggesting that it fails to follow the left-to-right rule for multiplication and division.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the interpretation of the expression and the application of the order of operations.

Contextual Notes

The discussion highlights limitations in the clarity of mathematical expressions and the potential for different interpretations based on the order of operations. There are unresolved mathematical steps and assumptions about how to handle the expression.

Corosus
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If you take 48/2(9+3) = 288 and re arrange it like so:

48/2(12 )= 288
48/2(12)/12 = 288
48/2 = 288/12
24 = 24
See, legitimate

But if you rearrange 48/2(9+3) = 2
48/2(12) = 2
48/2(12)/12 = 2/12
48/2 = 2/12
24 = 0.1666...
So why would anyone even say 2 or is this just completely stupid and just doesn't work?
 
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This is a true statement: if 48/2(9+3) = 2, then 24=0.1666 ...

The statement A implies B is true unless A is true and B is false. In this case, A is not true. You cannot conclude from this (true) statement that the conclusion, 24=0.1666 is true.
 
So why would anyone even say 2

[tex]\frac{48}{2(9+3)}= 2[/tex]

but

[tex]\frac{48(9+3)}{2}=288[/tex]

The same expression was parsed differently by different people.
 
Corosus said:
If you take 48/2(9+3) = 288 and re arrange it like so:

48/2(12 )= 288
48/2(12)/12 = 288
48/2 = 288/12
24 = 24
See, legitimate

Um you forgot to divide both sides by 12 in the second line. More amusingly, you're committing the same logic as proponents of 48/2(9+3) = 2 in your derivation, i.e., you do not perform multiplication/division from left to right.

Also guys go solve the problems I posted https://www.physicsforums.com/showthread.php?t=71315&page=16"
 
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