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 |
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. |