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- Fundamentals of mathematics
- Signed numbers
- Summary of key concepts
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module reviews the key concepts from the chapter "Signed Numbers."
Summary of key concepts
Variables and constants (
[link] )
A
variable is a letter or symbol that represents any member of a set of two or more numbers. A
constant is a letter or symbol that represents a specific number. For example, the Greek letter
(pi) represents the constant 3.14159 . . . .
The real number line (
[link] )
The
real number line allows us to visually display some of the numbers in which we are interested.
Coordinate and graph (
[link] )
The number associated with a point on the number line is called the
coordinate of the point. The point associated with a number is called the
graph of the number.
Real number (
[link] )
A
real number is any number that is the coordinate of a point on the real number line.
Types of real numbers (
[link] )
The set of
real numbers has many subsets. The ones of most interest to us are:
The
natural numbers : {1, 2, 3, 4, . . .}
The
whole numbers : {0, 1, 2, 3, 4, . . .}
The
integers : {. . . ,-3,-2,-1,0, 1, 2, 3, . . .}
The
rational numbers : {All numbers that can be expressed as the quotient of two integers.}
Positive and negative numbers (
[link] )
A number is denoted as
positive if it is directly preceded by a plus sign (+) or no sign at all. A number is denoted as
negative if it is directly preceded by a minus sign (–).
Opposites (
[link] )
Opposites are numbers that are the same distance from zero on the number line but have opposite signs. The numbers
and
are opposites.
Double-negative property (
[link] )
Absolute value (geometric) (
[link] )
The
absolute value of a number
, denoted
, is the distance from
to 0 on the number line.
Absolute value (algebraic) (
[link] )
Addition of signed numbers (
[link] )
To
add two numbers with
-
like signs , add the absolute values of the numbers and associate with the sum the common sign.
-
unlike signs , subtract the smaller absolute value from the larger absolute value and associate with the difference the sign of the larger absolute value.
Addition with zero (
[link] )
.
Additive identity (
[link] )
Since adding 0 to any real number leaves that number unchanged, 0 is called the
additive identity .
Definition of subtraction (
[link] )
Subtraction of signed numbers (
[link] )
To perform the
subtraction
, add the opposite of
to
, that is, change the sign of
and follow the addition rules (
[link] ).
Multiplication and division of signed numbers (
[link] )
Source:
OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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