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**Properties of Real Numbers**

Commutative Property of Addition Commutative Property of Multiplication Associative Property of Addition Associative Property of Multiplication Additive Identity Property Multiplicative Identity Property Additive Inverse Property Multiplicative Inverse Property Distributive Property Zero Property

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**Subtraction is NOT Commutative Division is NOT Commutative**

Commutative Property of Addition When two numbers are added, the order can be switched and the sum will still be the same. Subtraction is NOT Commutative Commutative Property of Multiplication When two numbers are multiplied, the order can be switched and the product will still be the same. Division is NOT Commutative

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**Subtraction is NOT Associative Division is NOT Associative**

Associative Property of Addition When three or more numbers are added, any two or more can be grouped together and the sum will still be the same. Subtraction is NOT Associative Associative Property of Multiplication When three or more numbers are multiplied, any two or more can be grouped together and the product will still be the same. Division is NOT Associative

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**Additive Identity Property**

When zero is added to any number, the sum is the original number. Zero is the Identity Element of Addition Multiplicative Identity Property When any number is multiplied by one, the product is the original number. One is the Identity Element of Multiplication

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**Additive Inverse Property**

When the opposite of a number is added to it the sum is zero. Zero is the Identity Element of Addition Multiplicative Inverse Property When any number is multiplied by its reciprocal the product is one. One is the Identity Element of Multiplication

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**When any number is multiplied by zero the product is zero.**

Distributive Property Any number outside parenthesis can be distributed to the numbers inside the parenthesis. Zero Property When any number is multiplied by zero the product is zero.

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**Non-Zero Rational Numbers**

Binary Operations In a Binary Operation, two elements from a set are replaced by exactly one element from the same set. Property of Closure A set is Closed under a binary operation when every pair of elements from the set, under the given operation, yields an element from that set. The following sets of numbers are closed under the indicated operation. Division Addition Subtraction Multiplication Natural Numbers Natural Numbers Non-Zero Rational Numbers Integers Whole Numbers Rational Numbers Whole Numbers Integers Real Numbers Integers Non-Zero Real Numbers Rational Numbers Rational Numbers Real Numbers Real Numbers

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