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AG1 BM 21-22 Properties of Real Numbers

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Property
Definition and Example
addition property of equality   that allows one to add the same quantity to both sides of an equation. Ex: If a = b, then a + c = b + c  
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additive identity   If you add zero to any quantity, the resulting quantity remains the same. Ex: a + 0 = a  
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additive inverse   The opposite of a number. When a number is added to its additive inverse, the sum is zero. Ex: a + -a = 0  
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associative property of addition   The sum stays the same when the grouping of addends or factors is changed. Ex: ( a + b ) + c = a + ( b + c) or (a b) c = a (b c)  
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commutative property   The sum stays the same when the order of the addends or factors is changed Ex: a + b = b + a or ab =ba  
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distributive property   The product of a number and the sum or difference of two numbers is equal to the sum or difference of the two products. Ex: c ( a + b) = ac + bc  
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multiplication property of equality   If two numbers are equal then the product of these two numbers and another number is also equal. Ex: If a = b, then c ( a )= c ( b )  
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multiplicative identity   If you multiply any quantity by one, the resulting quantity remains the same. Ex: a ( 1 )=a  
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multiplicative inverse   Reciprocal of a number. When a number is multiplied by its multiliped by its multiplicative inverse , the products is always one. The reciprocal of a/b is b/a .  
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substitution property   if a = b, then a can be substituted for b in any equation or inequality. Ex: If c = a + 2, then c = b + 2  
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symmetric property   If if a = b then b = a. This is one of the equivalence properties of equality.  
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zero product property   if the product of two factors is zero, then at least one of the factors must be zero. Ex: If ab = 0, then a = 0 or b = 0.  
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