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# Properties Organizer

### Pre-Algebra

Term | Definition |
---|---|

Commutative Property | Order of values does not matter! Operations: Addition & Multiplication a+b=b+a a*b=b*a |

Associative Property | Grouping of values does not matter! Operations: Addition & Multiplication (a+b)+c=a+(b+c) (a*b)*c=a*(b*c) |

Identity Property | Stays the same! Operations: Addition & Multiplication Addition: a+0=a (Zero) Multiplication: a*1=a (One) |

Inverse Property | Using opposites to "cancel" a value! Operations: Addition & Multiplication Addition: a+(-a)=0 Multiplication: a*(1/a)=1 |

Zero Product Property | Multiplying by zero always equals zero! a*0=0 |

Distributive Property *A way of simplifying an expression! | Multiplying a value to an expression inside parenthesis (). a(b-3)=ab-3b |

Reflexive Property | A value always equals itself! 7x=7x 16=16 *Note: This is important whenever you are solving equations with a variable on both sides. |

Symmetric Property | If a=b, then b=a Example1: If x=3, then 3=x Example2: If 5x=30, then 30=5x Note: This is important whenever you are solving equations. |

Transitive Property | If a=b and b=c, Then a=c Example: If 5+3=8 and 8=4*2, then 5+3=4*2 |