This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret.Objectives of this module: understand the closure, commutative, associative, and distributive properties, understand the identity and inverse properties.
Overview
- The Closure Properties
- The Commutative Properties
- The Associative Properties
- The Distributive Properties
- The Identity Properties
- The Inverse Properties
Property
A
property of a collection of objects is a characteristic that describes the collection. We shall now examine some of the properties of the collection of real numbers. The properties we will examine are expressed in terms of addition and multiplication.
The closure properties
The closure properties
If
and
are real numbers, then
is a unique real number, and
is a unique real number.
For example, 3 and 11 are real numbers;
and
and both 14 and 33 are real numbers. Although this property seems obvious, some collections are not closed under certain operations. For example,
The commutative properties
Let
and
represent real numbers.
The commutative properties
The commutative properties tell us that two numbers can be added or multiplied in any order without affecting the result.
Sample set a
The following are examples of the commutative properties.
Practice set a
Fill in the
with the proper number or letter so as to make the statement true. Use the commutative properties.
The associative properties
Let
and
represent real numbers.
The associative properties
The associative properties tell us that we may group together the quantities as we please without affecting the result.
Sample set b
The following examples show how the associative properties can be used.