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# Adding & Multiplying

### Additive and Multiplicative Properties

Question | Answer |
---|---|

Commutativity of Addition | a+b=b+a |

Associativity of Addition | a+(b+c)=(a+b)+c |

Zero Is the Identity for Addition | 0+a=a and a+0=a |

Existence of Additive Inverses | For each number a, there is another number, denoted -a, such that a+-a=0 and -a+a=o. Each of a and -a is the additive inverse of the other. |

Commutativity of Multiplication | a⋅b=b⋅a |

Associativity of Multiplication | a⋅(b⋅c)=(a⋅b)⋅c |

One Is the Identity for Mulitplication | 1⋅a=a and a⋅1=a for any number a. |

Existence of Multiplicative Inverses | For each nonzero number a, there is another number b, such that a⋅b=1 and b⋅a=1. Multiplicative inverses are also reciprocals. |

Distributive Property | a⋅(b+c)=(a⋅b)+(a⋅c) and (b+c)⋅a=(b⋅a)+(c⋅a) for any numbers a, b, and c. |

Unnamed Additive Property of Equalities | If a=b, then a+c=b+c |

Unnamed Subtractive Property of Equalities | If a=b, then a-c=b-c |

Unnamed Multiplicative Property of Equalities | If a=b, then a⋅c=b⋅c |

Unnamed Divisive Property of Equalities | If a=b, then a÷c=a÷b |

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clearviewregional