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Properties of Algebra By: Will Bienkowski

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**Commutative Property Explanation Examples**

The commutative property works for multiplication and addition. It states that switching the order of the numbers and variables will not change the sum or product. 6+3=3+6 is for addition. 8·6=6·8 is for multiplication

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**Associative Property Explanation Examples**

The associative property works for multiplication and addition. It states that that if you switch the grouping of numbers or variables the sum or product will stay the same. 7+(6+2)=15 6+(7+2)=15 8(2·4)=64 2(8·4)=64

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**Identity Property Explanation Example**

The identity property works for multiplication and addition. It states that anything added to zero or multiplied by one the result is that number. 9+0=9 6·1=6

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**Distributive Property**

Explanation Examples The distributive property states that you can make hard and long problems easy and short. 8·104 8·100=800 8·4= =832

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**Equality Property Explanation Example**

The equality property states that if you add or take away numbers from one side of the =,< or > you have to add or take the same number away from the other side. 3+b< b<6

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**Inverse Property Explanation Example**

It states that addition and subtraction can undo each other and multiplication and division can undo each other. a-a=0 and a+(-a)=0 a\a=1 and a·(-a)=1

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