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HHS-Prop. of Real #s

Commutative, Associative, Inverse, Identity, Distributive

QuestionAnswer
Associative Property of Addition For this property, the order of the numbers stays the same and the parentheses move. EX: 2 + ( 3 + 4 ) = ( 2 + 3 ) + 4
Associative Property of Multiplication For this property, the order of the numbers stays the same and the parentheses move. EX: 2 ( 3 x 4 ) = ( 2 x 3 ) x 4
Commutative Property of Addition For this property you add two numbers together and then reverse the order on the other side. EX: 4 + 6 = 6 + 4
Commutative Property of Multiplication For this property you multiply numbers together and reverse the order of these numbers on the other side. EX: 2 + ( 3 x 5 ) = 2 + ( 5 x 3 )
Identity Property of Addition For this property you must start and end with the same number and the operation must be addition. EX: 5 + 0 = 5
Identity Property of Multiplication For this property you must start and end with the same number and the operation must be multiplication. EX: 4 x 1 = 4
Inverse Property of Addition For this property you must add the opposite of the term and the sum equals zero. EX: 5x + ( - 5x ) = 0
Inverse Property of Multiplication For this property you must divide or multiply by the reciprocal of the first term to come up with a value of one. EX: (4/3)x(3/4)=1
Distributive Property When you multiply a term through a set of parentheses. EX: 4(x-1) = 4x-4
Natural Numbers The set of all counting numbers. {1, 2, 3, 4, 5, ...}
Whole Numbers The set of all counting numbers with 0 also included. {0, 1, 2, 3, 4, ...}
Integers The set of all whole numbers including the negative of these numbers. These are the positive and negative "nice" numbers.
Rational Numbers The set of all fractions, repeating decimals, and terminating decimals. EX: 2/3, 1.7777..., 4.9
Irrational Numbers The set of all non-terminating AND non-repeating decimals. This set includes the square roots that cannot be simplified down to whole numbers.