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Properties
MTH005 Ch 1 Properties of Real Numbers
| Property | Description |
|---|---|
| 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
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