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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 π (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.

A number line with hash marks from -3 to 3.

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 a size 12{a} {} and a size 12{ - a} {} are opposites.

Double-negative property ( [link] )

( a ) = a size 12{ - \( - a \) =a} {}

Absolute value (geometric) ( [link] )

The absolute value of a number a size 12{a} {} , denoted a size 12{ lline a rline } {} , is the distance from a size 12{a} {} to 0 on the number line.

Absolute value (algebraic) ( [link] )

| a | = a , if  a 0 - a , if  a < 0

Addition of signed numbers ( [link] )

To add two numbers with
  1. like signs , add the absolute values of the numbers and associate with the sum the common sign.
  2. 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] )

0 + ( any number ) = that particular number size 12{"0 "+ \( "any number" \) =" that particular number"} {} .

Additive identity ( [link] )

Since adding 0 to any real number leaves that number unchanged, 0 is called the additive identity .

Definition of subtraction ( [link] )

a b = a + ( b ) size 12{a - b=a+ \( - b \) } {}

Subtraction of signed numbers ( [link] )

To perform the subtraction a b size 12{a - b} {} , add the opposite of b size 12{b} {} to a size 12{a} {} , that is, change the sign of b size 12{b} {} and follow the addition rules ( [link] ).

Multiplication and division of signed numbers ( [link] )

+ + = + size 12{ left (+{} right ) left (+{} right )= left (+{} right )} {} + + = + size 12{ { { left (+{} right )} over { left (+{} right )} } = left (+{} right )} {} + = size 12{ { { left (+{} right )} over { left ( - {} right )} } = left ( - {} right )} {}
= + size 12{ left ( - {} right ) left ( - {} right )= left (+{} right )} {}
+ = size 12{ left (+{} right ) left ( - {} right )= left ( - {} right )} {} = + size 12{ { { left ( - {} right )} over { left ( - {} right )} } = left (+{} right )} {} + = size 12{ { { left ( - {} right )} over { left (+{} right )} } = left ( - {} right )} {}
+ = size 12{ left ( - {} right ) left (+{} right )= left ( - {} right )} {}

Questions & Answers

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Mueller Reply
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Tanis Reply

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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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