Date: 01/26/98 at 21:30:47 From: Leslie Seagle Subject: Number Properties My daughter is trying to learn about number properties, and is having an extremely difficult time understanding the definitions of: closure for addition, commutative for addition, associative for addition, identity for addition, and so on all the way through multiplication. What we are looking for are very distinct definitions for these terms, in order for her to create her own examples based on the definitions. Could you please help with this? Anything you could provide would be great. Thanks a million, Leslie and Amanda
Date: 01/27/98 at 09:18:11 From: Doctor Anthony Subject: Re: Number Properties ADDITION -------- (1) Closure for addition of integers This means that if you add two integers (whole numbers), you get another integer. So, as long as you start with two integers you will always end with an integer. You don't move outside integers into fractions or square roots or whatever. You are 'enclosed' in a universe of integers. (2) Commutative property for addition This means that the order you write down the two numbers does not affect the answer. So 3 + 7 = 7 + 3 Both give the same answer: 10. (3) Associative property for addition If we have three numbers to add, say 3 + 9 + 4, we can proceed in two ways. (3 + 9) + 4 = 12 + 4 = 16 or 3 + (9 + 4) = 3 + 13 = 16 In the first situation we first 'associated' the 3 and the 9. In the second situation we first 'associated' the 9 and the 4. (4) Identity element for addition The identity element leaves any other element unchanged if added. Clearly 0 is the identity element for addition: 5 + 0 = 5 MULTIPLICATION -------------- (1) Closure for multiplication of integers Yes, if you multiply two integers you get an integer. (2) Commutative property for multiplication Yes: 3 x 4 = 4 x 3 Both = 12 (3) Associative property for multiplication Yes: (3 x 4) x 5 = 3 x (4 x 5) 12 x 5 = 3 x 20 60 = 60 (4) Identity element for multiplication Clearly the identity element for multiplication is 1: 5 x 1 = 5 and so on. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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