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Carnegie Chapter 8

carnegie math

QuestionAnswer
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.
Created by: molnarmath