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# Stack #122585

### Properties of Real Numbers

Property | Definition/Example |
---|---|

addition property of equality | If you have an equation you can 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. |

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wzwells