Does Associative Property Apply to Subtraction and Division Too?

In summary, the associative property does not apply to subtraction and division, as they are not considered separate operations but rather as inverse operations of addition and multiplication, respectively. This is due to the fact that (a-b)-c is not equal to a-(b-c) and (a/b)/c is not equal to a/(b/c).
  • #1
bballwaterboy
85
3
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?
 
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  • #2
What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?
 
  • #3
##0-(0-1) = 1 \neq -1 = (0-0)-1##.
##1/(1/2) = 2 \neq \frac12 = (1/1)/2##.
 
  • #4
jbriggs444 said:
What is (3-2)-1? What is 3-(2-1)?
What is (2/1)/2? What is 2/(1/2)?

:tongue: Got it! Answer = No, Associative Property does not apply to subtraction and division.
 
  • #5
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".
 

1. What is the associative property?

The associative property is a mathematical rule that states that when performing a series of operations on a set of numbers, the grouping or order in which the operations are performed does not affect the result.

2. Does the associative property apply to subtraction?

Yes, the associative property applies to subtraction. This means that when subtracting a series of numbers, the grouping or order in which the subtractions are performed does not affect the result.

3. Does the associative property apply to division?

Yes, the associative property applies to division. This means that when dividing a series of numbers, the grouping or order in which the divisions are performed does not affect the result.

4. Can the associative property be applied to both subtraction and division at the same time?

Yes, the associative property can be applied to both subtraction and division at the same time. This means that when performing a series of operations that includes both subtraction and division, the grouping or order in which these operations are performed does not affect the result.

5. Are there any exceptions to the associative property?

Yes, there are some operations that do not follow the associative property. For example, the order in which exponents are evaluated does affect the result. Additionally, the associative property does not apply to operations involving non-associative elements, such as vector addition.

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