PropertiesDate: 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. 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 "additive identity property of zero" was used. You see, "adding 0" 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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