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Elementary and Intermediate Algebra
Mark Dugopolski, Southeastern Louisiana University

Real Numbers and Their Properties

Key Terms


absolute value  The magnitude of a number; the undirected distance from the point named by the number to the origin on the number line.

| -4 | = 4; | 3 | = 3.


additive identity  The number 0.
additive inverse  The opposite of a number.
algebraic expression  A meaningful combination of numbers and variables using the ordinary operations of arithmetic.
associative property of equality  When three or more numbers are added or multiplied, the operation can be performed in any order.
coefficient  A numeral or letter placed before an algebraic expression to indicate that the expression is to be multiplied by that factor.

In 3x, "3" is the coefficient of x.
commutative property of equality  The order in which two numbers are added or multiplied does not change the sum or product.
counting numbers  The numbers used for counting.
degree of a term  For a term with one variable, the degree is the value of the variable's exponent. For a term with two or more variables, the degree is the sum of the value of the exponents for all variables.
distributive property  Multiplication by a factor may be distributed over two or more addends.
equation  A mathematical statement that two expressions are equal.
equivalent equations  Equations that have the same solution.
exponent  A value that indicates the number of times a base is used as a factor.
integers  The set of positive and negative whole numbers including zero.
integral exponent  An exponent that is an integer.
irrational number  A number that cannot be expressed as a ratio of integers.
like terms  Terms that have the same variables with the same exponents.
multiplicative identity  The number 1.
natural numbers  The whole numbers used for counting, not including zero.

{1, 2, 3...}


null set  The empty set (the set containing no elements).
order of operations  The order in which operations are to be performed in the absence of grouping symbols.
rational number  A number that can be expressed as a quotient of two integers.
real numbers  The set of numbers made up of rational and irrational numbers.
term  An expression containing a number or the product of a number and one or more variables.
variable  A letter that is used to represent some numbers.
whole numbers  The numbers in the set {0, 1, 2, 3,...}.