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# Properties

Example | Property Name |
---|---|

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

a+b=b+a | Commutative property of Addition |

0+a = a+0 = a | Additive identity |

a+(-a)= 0 and (-a)+a = 0 | Additive Inverse |

If a = b, then a+c = b+c | Addition property of equality |

(ab)c = a(bc) | Associative property of multiplication |

ab = ba | Commutative property of multiplication |

a . 1 = a and 1 . a = a | multiplicative identity |

a . (1/a) = 1 and (1/a) . a = 1 | multiplicative inverse |

if a = b, then ac = bc | multiplication property of equality |

a(b+c) = ab + ac and (b+c)a = ba + ca | distributive property |

a = a | Reflexive property of equality |

if a = b, then b = a | symmetric property of equality |

if a = b, and b = c, then a = c | transitive property of equality |

if a = b, and c = b, then a = c | substitution property of equality |

a(-1) = -a and (-1)a = -a | multiplicative property of -1 |

a . 0 = 0 and 0 . a = 0 | Multiplicative property of 0 |

a - b = a + (-b) | relationship between Addition and Subtraction |

(a/b) = a . (1/b) | relationship between Multiplication and Division |

1/ab = (1/a) . (1/b) | property of the reciprocal of a product |

(-a)b = -ab, a(-b) = -ab, (-a)(-b) = ab | property of negatives in products |

-(a+b) = -a + (-b) | property of negative of a sum |

Sum (or two differences) of 2 real numbers equals a real number product | Closure properties |

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