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# Properties and More

### Expressions and Equations vocabulary for 6th grade math

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

Addition Property of Equality | If you add the same number to each side of an equation, the two sides remain equal. For any numbers a, b, and c, if a = b, then a + c = b + c. Example: If x = 3, then x + 5 = 3 + 5. |

*Associative Property | The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. Example:: (2 + 3) + 4 = 2 + (3 + 4) or (2 x 3) x 5 = 2 x (3 x 5) |

coefficient | The numerical factor of a term. |

*Division Property of Equality | If you divide each side of an equation by the same nonzero number, the two sides remain equal. |

Division Property of Inequality | When you divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true. |

equation | A mathematical sentence stating that two expressions are equal. Example: 3 x (7 + 8) = 9 x 5 |

*equivalent equation | Equations that have the same solution. |

Inequality | An open sentence that uses symbols to compare two expressions with less than, greater than, less than or equal to, greater than or equal to. |

*Multiplicative Property of Equality | If you multiply each side of an equation by the same nonzero number, the two sides remain equal. For any numbers a, b, and c, if a = b, then a(c) = b(c). Example: If x = 3, then 5x = 3(5). |

solution | A replacement value for the variable in an open sentence. A value for the variable that makes an equation true. Example: The solution of 12 = x + 7 is 5. |

Subtraction Property of Equality | If you subtract the same nonzero number from each side of an equation, the two sides remain equal. For any numbers a, b, and c, if a = b, then a - c = b - c. Example: if x = 3, then x - 2 = 3 - 2. |

Multiplicative Property of Inequality | When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true. |

Addition Property of Inequality | If you add the same number to each side of an inequality, the inequality remains true. |

two-step equation | An equation having two operations. |

two-step inequality | An inequality that contains two operations. |

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