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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

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
In the number 779,844,205 how many ten millions are there?
TELLY Reply
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
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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