Does Associative Property Apply to Subtraction and Division Too?

[bballwaterboy]

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?

 

[jbriggs444]

What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?

 

[economicsnerd]

$0-(0-1) = 1 \neq -1 = (0-0)-1$.
$1/(1/2) = 2 \neq \frac12 = (1/1)/2$.

 

[bballwaterboy]

What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?

Got it! Answer = No, Associative Property does not apply to subtraction and division.

 

[HallsofIvy]

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".