



This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of x. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and reallife examples.Objectives of this module: understand the definition of subtraction, be able to subtract signed numbers.
Overview
 Definition of Subtraction
 Subtraction of Signed Numbers
Definition of subtraction
We know from our experience with arithmetic that the subtraction
$52$ produces 3, that is,
$52=3$ . Illustrating this process on the number line suggests a rule for subtracting signed numbers.
We begin at 0, the origin.
Since 5 is positive, we move 5 units to the right.
Then, we move
2 units to the left to get to 3. (This reminds us of addition with a negative number.)
This illustration suggests that
$52$ is the same as
$5+(2)$ .
This leads us directly to the definition of subtraction.
Definition of subtraction
If
$a$ and
$b$ are real numbers,
$ab$ is the same as
$a+(b)$ , where
$b$ is the opposite of
$b$ .
Subtraction of signed numbers
The preceding definition suggests the rule for subtracting signed numbers.
Subtraction of signed numbers
To perform the subtraction
$ab$ , add the opposite of
$b$ to
$a$ , that is, change the sign of
$b$ and add.
Sample set a
Perform the subtractions.
The high temperature today in Lake Tahoe was
${26}^{\circ}\text{F}$ . The low temperature tonight is expected to be
${7}^{\circ}\text{F}$ . How many degrees is the temperature expected to drop?
We need to find the difference between 26 and
$7$ .
$26(7)=26+7=33$
Thus, the expected temperature drop is
${33}^{\circ}\text{F}$ .
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$\begin{array}{lll}6(5)10\hfill & =\hfill & 6+5+(10)\hfill \\ \hfill & =\hfill & (6+5)+(10)\hfill \\ \hfill & =\hfill & 1+(10)\hfill \\ \hfill & =\hfill & 11\hfill \end{array}$
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Practice set a
Perform the subtractions.
Exercises
For the following exercises, perform the indicated operations.
When a particular machine is operating properly, its meter will read 34. If a broken bearing in the machine causes the meter reading to drop by 45 units, what is the meter reading?
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Exercises for review
Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
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?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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