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### Properties

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Date: 10/15/97 at 22:46:41
From: Lynne McGraw
Subject: The name of problems

My daughter's homework asks: Which property is being shown?

COMMUTATIVE,   ASSOCIATIVE,    IDENTITY

19.  6 + 4 = 10   4 + 6 = 10 ____________

20. 34 + 0 = 0 _____________

21. 17 + 3 = 20      3 + 17 = 20 _____________

22. (17 + 25) + 5 = 47    17 + (25 + 5) = 47 ______________

23. 729 + 0 = 0 ________________

She is pretty sure numbers 20 and 23 are IDENTITY.

Thank you.
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Date: 10/16/97 at 18:01:56
From: Doctor Terrel
Subject: Re: The name of problems

Dear Lynne,

The commutative property is involved when the "order" of the elements
produces no change in the outcome.  For example:

7 + 3 is the same as 3 + 7; both are 10.

5 * 6 is the same as 6 * 5; both are 30.

But subtraction is NOT commutative: 9 - 2 = 7, while 2 - 9 = -7.
Similarly with division: 8 / 4 = 2, while 4 / 8 = 0.5 (or one-half).

So, 19 and 21 are commutative.

The associative property says: (a + b) + c = a + (b + c).  In other
words, you can "associate" two elements differently with no change.

Example:   (3 + 8) + 2  =  3 +  (8 + 2)
11   + 2  =  3 +    10
13  = 13

So, 22 is associative.

But I think there has been a misprint in the remaining two items.

34 + 0 = 0  and  729 + 0 = 0  aren't even true. Perhaps what was
intended was 34 + 0 = 34  and 729 + 0 = 729, in which case the
leaves the original or other item "identical," or unchanged. In
multiplication, the number "1" plays a similar role, as in

45 * 1 = 45.

I hope this helps.  If you need more help, write to me again.

-Doctor Terrel,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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