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Classifying Numbers

Classifying the different types of real numbers

QuestionAnswer
Real Numbers All numbers that we deal with in Algebra are real numbers.
Rational Numbers Rational numbers are any number that can be written as a fraction. It includes positive and negative numbers, and any decimal that either terminates or repeats. (Ex. -2, 3.232323..., 7/8)
Irrational Numbers Irrational numbers are decimals that do not terminate and do not repeat. (Ex. pi, 3.1289368342...)
Integers Integers include positive numbers, negative numbers, and zero. Integers do not have a fraction or decimal part. (Ex. -4, 0, 2, 5)
Whole Numbers Whole Numbers include the positive integers and zero. (Ex. 0, 1, 2, 3...)
Natural Numbers Natural Numbers (also known as Counting Numbers) include only the positive integers. (Ex. 1, 2, 3, 4...)
Identity Property of Addition Adding zero to any number return the same number. a + 0 = a The ADDITIVE IDENTITY is 0
Identity Property of Multiplication Multiplying any number by 1 returns the same number. a * 1 = a The MULTIPLICATIVE IDENTITY is 1
Inverse Property of Addition A number plus its opposite is 0. a + -a = 0
Inverse Property of Addition A number multiplied by its reciprocal is 1. a * (1/a) = 1
Commutative Property of Addition When adding, the order is not important. a + b = b + a
Commutative Property of Multiplication When multiplying, the order is not important. ab = ba
Associative Property of Addition When adding, the grouping is not important. a + (b + c) = (a + b) + c
Associative Property of Multiplication When multiplying, the order is not important. a(bc) = (ab)c
Created by: mburke79