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# Algebraic Properties

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

Transitive Property of Equality | If a=b and b=c then a=c Ex.) If x+5 = 9 and 9 = 4+5 then x+5 = 4+5 Ex.) If a<b and b<7 then a<7. |

Symmetric Property of Equality | If a=b then b=a Ex.) If 2x+9 = 12 then 12 = 2x+9 Ex.) If x+6 = 5 then 5 = x+6 |

Reflexive Property of Equality | For all real numbers a, a = a Ex.) 8x = 8x Ex.) x-3 = x-3 |

Addition Property of Equality /Inequality | If the same number is added to both sides of an equation, the two sides remain equal. That is if x = y, then x+z = y+z In an inequality,the number does not change the inequality. if x>y, then x+z > y+z, and if x<y, then x+z < y+z |

Substitution Property | If a = b then a can be substituted for b in any equation or inequality. |

Commutative Property | The order of adding does not change the sum or product. Ex.) 5x+3y = 3y+5x (Addition) Ex.) 7x(2) = 2(7x) (Multiplication) |

Associative Property | Grouping numbers differently does not change the sum or product. Ex.) 5x+(6x + 3) = (5x + 6x)+3 ( + ) Ex.) 9*(10 * 3) = (9 * 10)*3 ( * ) |

Identity Property | Adding zero to a number does not change its value. Ex.) 6xy+0 = 6xy Multiplying a number by one does not change its value. Ex.) 18a(1) = 18a ( Multiplication ) |

Additive Inverse /Multiplicative Inverse Property | The sum of opposites equals zero. ( + ) Ex.) 8x+( -8x ) = 0 A number times its reciprocal equals one. ( * ) Ex.) 2 * 1/2 = 1 |

Multiplication Property of Zero or (The Zero Property) | Zero times any number equals zero. Ex.) 3*0 = 0 |

The Distributive Property | a( b + c) = a*b + a*c or (b + c)a = a( b + c) = a*b + a*c Rainbow method. |

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