# 10.7 Summary of key concepts

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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."

## 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 $\pi$ (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 are numbers that are the same distance from zero on the number line but have opposite signs. The numbers $a$ and $-a$ are opposites.

## Double-negative property ( [link] )

$-\left(-a\right)=a$

## Absolute value (geometric) ( [link] )

The absolute value of a number $a$ , denoted $\mid a\mid$ , is the distance from $a$ to 0 on the number line.

## Absolute value (algebraic) ( [link] )

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.

$\text{0}+\left(\text{any number}\right)=\text{that particular number}$ .

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

## Definition of subtraction ( [link] )

$a-b=a+\left(-b\right)$

## Subtraction of signed numbers ( [link] )

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

## Multiplication and division of signed numbers ( [link] )

$\left(+\right)\left(+\right)=\left(+\right)$ $\frac{\left(+\right)}{\left(+\right)}=\left(+\right)$ $\frac{\left(+\right)}{\left(-\right)}=\left(-\right)$
$\left(-\right)\left(-\right)=\left(+\right)$
$\left(+\right)\left(-\right)=\left(-\right)$ $\frac{\left(-\right)}{\left(-\right)}=\left(+\right)$ $\frac{\left(-\right)}{\left(+\right)}=\left(-\right)$
$\left(-\right)\left(+\right)=\left(-\right)$

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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