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# Stack #122090

### AG1 BM 21-22 Properties of Real Numbers

PropertyDefinition 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
additive identity If you add zero to any quantity, the resulting quantity remains the same. Ex: a + 0 = a
additive inverse The opposite of a number. When a number is added to its additive inverse, the sum is zero. Ex: a + -a = 0
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)
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
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
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 )
multiplicative identity If you multiply any quantity by one, the resulting quantity remains the same. Ex: a ( 1 )=a
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 .
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
symmetric property If if a = b then b = a. This is one of the equivalence properties of equality.
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.
Created by: wzwells