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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

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
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
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
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
How can I make nanorobot?
Lily
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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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