Properties of Whole Number Addition by Wk87dH9l

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```									                    Properties of Whole Number Addition

1. Commutative Property of Addition: No matter what order numbers are added they
always have the same sum.

a + b = b + a

Example:    2 + 3 = 3 + 2

2. Associative Property of Addition: No matter how you group addends the sum will
remain the same.

a + (b + c) = (a + b) + c

Example:    5 + (2 + 3) = (5 + 2) + 3

3. Identity Element for Addition: The number that when added to any number gives the
number itself back. The identity element is zero.

a + 0 = a

Example:    9 + 0 = 9

4. Additive Inverse: The number, the opposite, which when added to the number
produces the identity element for addition. This property shows us that subtraction is the
inverse operation for addition, since adding an opposite is how subtraction is defined.

a + -a = 0

Example:    12 + -12 = 0

5. Closure: If two numbers are in a set of numbers, then their sum is also in the set.

Let a € X and b € X

The sum a + b is closed because a + b € X

Example: The set X = {2, 4, 6, 8, …} is CLOSED under addition

(i.e. 2 + 4 = 6)

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