# Review of past work  (Page 4/8)

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Subtraction is actually the same as adding a negative number .

In this example, $a$ and $b$ are positive numbers, but $-b$ is a negative number

$\begin{array}{c}\hfill a-b=a+\left(-b\right)\\ \hfill 5-3=5+\left(-3\right)\end{array}$

So, this means that subtraction is simply a short-cut for adding a negative number and instead of writing $a+\left(-b\right)$ , we write $a-b$ . This also means that $-b+a$ is the same as $a-b$ . Now, which do you find easier to work out?

Most people find that the first way is a bit more difficult to work out than the second way. For example, most people find $12-3$ a lot easier to work out than $-3+12$ , even though they are the same thing. So $a-b$ , which looks neater and requires less writing is the accepted way of writing subtractions.

[link] shows how to calculate the sign of the answer when you multiply two numbers together. The first column shows the sign of the firstnumber, the second column gives the sign of the second number and the third column shows what sign the answer will be.

 $a$ $b$ $a×b$ or $a÷b$ $+$ $+$ $+$ $+$ $-$ $-$ $-$ $+$ $-$ $-$ $-$ $+$

So multiplying or dividing a negative number by a positive number always gives you a negative number, whereas multiplying or dividing numbers which have thesame sign always gives a positive number. For example, $2×3=6$ and $-2×-3=6$ , but $-2×3=-6$ and $2×-3=-6$ .

Adding numbers works slightly differently (see [link] ). The first column shows the sign of the first number, the second column gives the sign of the second number and the third column showswhat sign the answer will be.

 $a$ $b$ $a+b$ $+$ $+$ $+$ $+$ $-$ ? $-$ $+$ ? $-$ $-$ $-$

If you add two positive numbers you will always get a positive number, but if you add two negative numbers you will always get a negative number. If thenumbers have a different sign, then the sign of the answer depends on which one isbigger.

## Living without the number line

The number line in [link] is a good way to visualise what negative numbers are, but it can get very inefficient to use it every timeyou want to add or subtract negative numbers. To keep things simple, we will write down three tips that you can use to make working with negative numbers alittle bit easier. These tips will let you work out what the answer is when you add or subtract numbers which may be negative, and will also help you keep yourwork tidy and easier to understand.

## Negative numbers tip 1

If you are given an expression like $-a+b$ , then it is easier to move the numbers around so that the expression looks easier. In this case, we have seen thatadding a negative number to a positive number is the same as subtracting the number from the positive number. So,

$\begin{array}{ccc}\hfill -a+b& =& b-a\hfill \\ \hfill -5+10& =& 10+\left(-5\right)\hfill \\ \hfill & =& 10-5\hfill \\ \hfill & =& 5\hfill \end{array}$

This makes the expression easier to understand. For example, a question like “What is $-7+11$ ?” looks a lot more complicated than “What is $11-7$ ?”, even though they are exactly the same question.

## Negative numbers tip 2

When you have two negative numbers like $-3-7$ , you can calculate the answer by simply adding together the numbers as if they were positive and then putting anegative sign in front.

$\begin{array}{ccc}\hfill -c-d& =& -\left(c+d\right)\hfill \\ \hfill -7-2& =& -\left(7+2\right)=-9\hfill \end{array}$

## Negative numbers tip 3

In [link] we saw that the sign of two numbers added together depends on which one is bigger. This tip tells us that all we need todo is take the smaller number away from the larger one and remember to give the answer the sign of the larger number. In this equation, $F$ is bigger than $e$ .

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
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
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?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
Got questions? Join the online conversation and get instant answers!
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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