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Properties

MTH005 Ch 1 Properties of Real Numbers

PropertyDescription
Commutative Property of Addition CHANGE ORDER. Addends may be added in any order and the sum of the addends is the same.
Commutitive Prpoerty of Multiplication CHANGE ORDER. Factors may be multiplied in any order and the product is the same.
Associative Property of Addition CHANGE GROUPING. For 3 or more addends, the grouping (not the order) may be changed and the sum of the addends is the same.
Associative Property of Multiplication CHANGE GROUPING. For 3 or more factors, the grouping (not the order) can be changed and the product is the same.
Property of the Opposite of the Opposite For any real number x, -(-x) = x. The oposite of the opposite is the original number.
Additive Identity Property Additive Identity is 0. Property: If 0 is added to any real number, the result is the original number.
Multiplicative Identity The multiplicative Identity is 1. Property: When any real number is multiplied by 1, the result is the original number.
Property of Additive Inverses Opposite = Inverse. Property: Every real number has a unique additive inverse and their sum is 0. a + (-a) = 0 The sum of any real number and its opposite is 0.
Property of Multiplicative Inverses Inverse = Reciprocal. Property: For any nonzero real number a, there is a unique real number 1/a such that their product is 1. a * 1/a = 1 Any real number multiplied by its reciprocal is 1.
Distributive Property MULTIPLY TO CONVERT a PRODUCT a(b + c) or a(b - c) into a SUM (ab + ac) or DIFFERENCE (ab - ac). FACTOR TO CONVERT a SUM (ab + ac) or DIFFERENCE (ab - ac) into a PRODUCT a(b + c) or a(b - c).
Other Properties Involvng 1 a/1 = a Any real number divided by 1 is the number. a/a = 1 Any real number divided by itself is 1. 1^n = 1 One raised to any natural number exponent is 1.
Other Properties Involving 0 0/a = a Zero divided by any nonzero real number is 0. 0^n = 0 Zero raised to any natural number exponent is 0.
Created by: powens