Does Associative Property Apply to Subtraction and Division Too?

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Discussion Overview

The discussion centers around the applicability of the associative property to subtraction and division, contrasting it with addition and multiplication. Participants explore examples and reasoning related to these operations.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant presents the associative property for addition and multiplication, questioning its applicability to subtraction and division.
  • Another participant provides specific examples to illustrate the differences in outcomes when applying operations in different orders for subtraction and division.
  • A third participant confirms the non-applicability of the associative property to subtraction and division through additional examples, showing that the results differ based on the grouping of operations.
  • Another participant argues that the lack of associative property in subtraction and division is why these operations are not treated as separate from addition and multiplication, suggesting they can be expressed in terms of their inverses.

Areas of Agreement / Disagreement

Participants generally agree that the associative property does not apply to subtraction and division, but the discussion includes varying perspectives on the implications of this observation.

Contextual Notes

Some examples provided may depend on specific interpretations of operations, and the discussion does not resolve whether the definitions of subtraction and division as inverses are universally accepted.

Who May Find This Useful

Readers interested in mathematical properties, particularly in the context of operations and their relationships, may find this discussion relevant.

bballwaterboy
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I show that the assoc. property applies to addition and multiplication in my book:

(a+b)+c = a+(b+c)
(ab)c = a(bc)

But what about subtraction and division?
 
Mathematics news on Phys.org
What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?
 
##0-(0-1) = 1 \neq -1 = (0-0)-1##.
##1/(1/2) = 2 \neq \frac12 = (1/1)/2##.
 
jbriggs444 said:
What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?

:-p Got it! Answer = No, Associative Property does not apply to subtraction and division.
 
It is precisely because the associative law does not apply to subtraction and division that we do NOT think of them as separate operations. Instead "a subtract b" is "a plus the additive inverse of a" and "a divided by b" is "a times the multiplicative inverse of b".
 

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