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### Number Properties

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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
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.
great.

Thanks a million,
Leslie and Amanda
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```
Date: 01/27/98 at 09:18:11
From: Doctor Anthony
Subject: Re: Number Properties

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(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.

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.

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.

The identity element leaves any other element unchanged if added.

Clearly 0 is the identity element for addition:  5 + 0 = 5

MULTIPLICATION
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(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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