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# Algebra 2 Properties

### Ch.1 Properties

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

Definition of Subtraction | a - b = a + (-b) |

Definition of Division | a ÷ b = a/b = a ∙ 1/b, b≠0 |

Distributive Property for Subtraction | a(b - c) = ab - ac |

Multiplication by 0 | 0 ∙ a = -a |

Multiplication by -1 | -1 ∙ a = -a |

Opposite of a Sum | -(a + b) = -a + (-b) |

Opposite of a Difference | -(a -b) = b-a |

Opposite of a Product | -(ab) = -a ∙ b = a ∙(-b) |

Opposite of an Opposite | -(-a) = a |

Reflexive Property of Equality | a = a |

Symmetric Property of Equality | If a = b, then b = a |

Transitive Property of Equality | If a = b and b = c, then a = c |

Addition Property of Equality | If a = b, then a + c = b + c |

Subtraction Property of Equality | If a = b, then a - c = b - c |

Multiplication Property of Equality | If a = b, then ac = bc |

Division Property of Equality | If a = b and c ≠ 0, then a/c = b/c |

Substitution Property of Equality | If a = b, then b may be substituted for a in any expression to obtain an equivalent expression |

Transitive Property of Inequality | If a ≤ b and b ≤ c, then a ≤ c |

Addition Property of Inequality | If a ≤ b, then a + c ≤ b + c |

Subtraction Property of Inequality | If a ≤ b, then a - c ≤ b - c |

Multiplication Property of Inequality | If a ≤ b and c > 0, then ac ≤ bc. If a ≤ b and c < 0, then ac ≥ bc. |

Division Property of Inequality | If a ≤ b and c > 0, then a/c ≤ b/c. If a ≤ b and c < 0, then a/c ≥ b/c. |

Closure of Addition | a + b is a real number |

Closure of Multiplication | ab is a real number |

Communtative of Addition | a + b = b + a |

Communtative of Multiplication | ab = ba |

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

Associative of Multiplication | (ab)c = a(bc)` |

Identity of Addition | a + 0 = a, 0 + a = a |

Identity of Multiplication | a ∙ 1 = a, 1∙ a = a |

Inverse of Addition | a + (-a) = 0 |

Inverse of Multiplication | a ∙ 1/a = 1, a ≠ 0 |

Distributive | a(b + c) = ab + ac |

Created by:
gnomealot