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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

a - b = a + ( - b ) 5 - 3 = 5 + ( - 3 )

So, this means that subtraction is simply a short-cut for adding a negative number and instead of writing a + ( - b ) , 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.

Table of signs for multiplying or dividing two numbers.
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.

Table of signs for adding two numbers.
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,

- a + b = b - a - 5 + 10 = 10 + ( - 5 ) = 10 - 5 = 5

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.

- c - d = - ( c + d ) - 7 - 2 = - ( 7 + 2 ) = - 9

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

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 ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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.
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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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