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# algebra prop

### properties of algebra

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

commutative property | Arithmetic: 5+3=3+5 or 5(3)=3(5) Algebraic: x+y=y+x or ab=ba |

additive identity | arithmetic: 5+0=5, anything added to 0 is itself Algebraic: x+0=x, abc+0=abc |

associative property | arithmetic: (5+2)+3=5+(2+3) Algebraic: (mn)z=m(nz) |

multiplicative property of zero | arithmetic: 6*0=0, any numbwer times 0=0 Algebraic: ab*0=0 |

multiplicative identity | arithmetic: a*1=a, any number times 1=the number Algebraic: xy*1=xy |

distributive property | arithmetic: 5(7+3)=5(7)+5(3) Algebraic: x(y+z)=x(y)+x(z) |

additive inverse | arithmetic: 5-9=5+(-9) or -3-9=-3+(-9) Algebraic: a-b=a+(-b) |

comparison property | algebraic: given any two numbers a and b, either a>b, a |

density property | algebraic: the number line is forever dense. there are infinate numbers between any two numbers |

reflexive property | algebraic: x=x, 5=5, 2x-3=2x-3 |

symetric property | arithmetic: if 5+2=7 then 7=5+2 Algebraic: if a=b then b=a, if 2x+3=13 then 13=2x+3 |

transitive property | arithmetic: if 5+3=8 and 8=4*2, then 5+3=4*2 Algebraic: if a=b and b |

transitive property of order | algebraic: if a>b and b>c, then a>c |

substitution property | arithmetic: if a=b, then b may replace a Algebraic: 5(2)+3=10+3 |

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