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# Carnegie Chapter 8

### carnegie math

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

sequence | A pattern involving an ordered arrangement of numbers, geometric figures, letters, or other objects. |

term | A number, a variable, or a product of numbers and variables. |

Commutative Property of Addition | This property states that changing the order of two or more terms in an addition problem does not change the sum. For any numbers a and b, then a + b = b + a. |

Commutative Property of Multiplication | This property states that changing the order of two or more factors in a multiplication problem does not change the product. For any numbers a and b, then a • b = b • a. |

Associative Property of Addition | This property states that changing the grouping of the terms in an addition problem does not change the sum. For any numbers a, b, and c, then (a + b) + c = a + (b + c). |

Associative Property of Multiplication | This property states that changing the grouping of the factors in a multiplication problem does not change the product. For any numbers a, b, and c, then (a • b) • c = a • (b • c). |

simplify | To use the rules of arithmetic and algebra to rewrite that expression with fewer terms. |

like terms | In an algebraic expression, two or more terms that have the same variable raised to the same power. |

Distributive Property of Multiplication over Addition | The property that states that if a, b, and c are real numbers and c does not equal zero, then a • (b + c) = a • b + a • c. |

Distributive Property of Multiplication over Subtraction | The property that states that if a, b, and c are real numbers, then a • (b - c) = a • b - a • c. |

Distributive Property of Division over Addition | The property that states that if a, b, and c are real numbers, then (a+b) / c = a/c + b/c. |

Distributive Property of Division over Subtraction | The property that states that if a, b, and c are real numbers and c does not equal zero, then (a - b) / c = a/c - b/c. |

equivalent expressions | Two algebraic expressions where when any values are substituted for the variables, the results are equal. |

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