<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses signed numbers. By the end of the module students be able to distinguish between positive and negative real numbers, be able to read signed numbers and understand the origin and use of the double-negative product property.

Section overview

  • Positive and Negative Numbers
  • Reading Signed Numbers
  • Opposites
  • The Double-Negative Property

Positive and negative numbers

Positive and negative numbers

Each real number other than zero has a sign associated with it. A real number is said to be a positive number if it is to the right of 0 on the number line and negative if it is to the left of 0 on the number line.

The notation of signed numbers

+ and - Notation

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.

Reading signed numbers

The plus and minus signs now have two meanings :

The plus sign can denote the operation of addition or a positive number.

The minus sign can denote the operation of subtraction or a negative number.

To avoid any confusion between "sign" and "operation," it is preferable to read the sign of a number as "positive" or "negative." When "+" is used as an operation sign, it is read as "plus." When " - " is used as an operation sign, it is read as "minus."

Sample set a

Read each expression so as to avoid confusion between "operation" and "sign."

- 8 should be read as "negative eight" rather than "minus eight."

Got questions? Get instant answers now!

4 + ( - 2 ) size 12{"4 "+ \( "–2" \) } {} should be read as "four plus negative two" rather than "four plus minus two."

Got questions? Get instant answers now!

- 6 + ( - 3 ) size 12{"–6 "+ \( "–3" \) } {} should be read as "negative six plus negative three" rather than "minus six plus minus three."

Got questions? Get instant answers now!

- 15 - ( - 6 ) size 12{"–15 – " \( "–6" \) } {} should be read as "negative fifteen minus negative six" rather than "minus fifteen minus minus six."

Got questions? Get instant answers now!

- 5 + 7 size 12{"–5 "+" 7"} {} should be read as "negative five plus seven" rather than "minus five plus seven."

Got questions? Get instant answers now!

0 - 2 size 12{"0 – 2"} {} should be read as "zero minus two."

Got questions? Get instant answers now!

Practice set a

Write each expression in words.

6 + 1 size 12{"6 "+" 1"} {}

six plus one

Got questions? Get instant answers now!

2 + ( - 8 ) size 12{2+ \( "–8" \) } {}

two plus negative eight

Got questions? Get instant answers now!

- 7 + 5 size 12{"–7"+5} {}

negative seven plus five

Got questions? Get instant answers now!

- 10 - ( + 3 ) size 12{"–10 – " \( +3 \) } {}

negative ten minus three

Got questions? Get instant answers now!

- 1 - ( - 8 ) size 12{"–1 –" \( "–8" \) } {}

negative one minus negative eight

Got questions? Get instant answers now!

0 + ( - 11 ) size 12{"0 "+ \( "–11" \) } {}

zero plus negative eleven

Got questions? Get instant answers now!

Opposites

Opposites

On the number line, each real number, other than zero, has an image on the opposite side of 0. For this reason, we say that each real number has an opposite. Opposites are the same distance from zero but have opposite signs.

The opposite of a real number is denoted by placing a negative sign directly in front of the number. Thus, if a size 12{a} {} is any real number, then a size 12{ - a} {} is its opposite.

The letter " a size 12{a} {} " is a variable. Thus, " a size 12{a} {} " need not be positive, and " - a size 12{–a} {} " need not be negative.

If a size 12{a} {} is any real number, a size 12{ - a} {} is opposite a size 12{a} {} on the number line.

Two number lines. One number line with hash marks from left to right, -a, 0, and a. This number line is titled a positive.  A second number line with hash marks from left to right, a, 0, and -a. This number line is titled a negative.

The double-negative property

The number a size 12{a} {} is opposite a size 12{ - a} {} on the number line. Therefore, ( a ) size 12{ - \( - a \) } {} is opposite a size 12{ - a} {} on the number line. This means that

( a ) = a size 12{ - \( - a \) =a} {}

From this property of opposites, we can suggest the double-negative property for real numbers.

Double-negative property: ( a ) = a size 12{ - \( - a \) =a} {}

If a size 12{a} {} is a real number, then
( a ) = a size 12{ - \( - a \) =a} {}

Sample set b

Find the opposite of each number.

If a = 2 size 12{"a "=" 2"} {} , then - a = - 2 size 12{"–a "=" –2"} {} . Also, ( a ) = ( 2 ) = 2 size 12{ - \( - a \) = - \( - 2 \) =2} {} .

A number line with hash marks from left to right, -2, 0, and 2. Below the -2 is -a, and below the 2 is a, or -(-a).

Got questions? Get instant answers now!

If a = - 4 size 12{"a "=" –4"} {} , then - a = - ( - 4 ) = 4 size 12{"–a "="– " \( "–4" \) =" 4"} {} . Also, - ( - a ) = a = - 4 size 12{– \( "–a" \) =" a "= – " 4"} {} .

A number line with hash marks from left to right, -4, 0, and 4. Below the -4 is a, or -(-a), and below the 2 is -a.

Got questions? Get instant answers now!

Practice set b

Find the opposite of each number.

Suppose a size 12{a} {} is a positive number. Is a size 12{ - a} {} positive or negative?

a size 12{ - a} {} is negative

Got questions? Get instant answers now!

Suppose a size 12{a} {} is a negative number. Is a size 12{ - a} {} positive or negative?

a size 12{ - a} {} is positive

Got questions? Get instant answers now!

Suppose we do not know the sign of the number k size 12{k} {} . Is k size 12{ - k} {} positive, negative, or do we not know?

We must say that we do not know.

Got questions? Get instant answers now!

Exercises

A number is denoted as positive if it is directly preceded by .

+ (or no sign)

Got questions? Get instant answers now!

A number is denoted as negative if it is directly preceded by .

Got questions? Get instant answers now!

How should the number in the following 6 problems be read? (Write in words.)

7 size 12{-7} {}

negative seven

Got questions? Get instant answers now!

15 size 12{"15"} {}

fifteen

Got questions? Get instant answers now!

1 size 12{- left (-1 right )} {}

negative negative one, or opposite negative one

Got questions? Get instant answers now!

5 size 12{- left (-5 right )} {}

Got questions? Get instant answers now!

For the following 6 problems, write each expression in words.

5 + 3 size 12{5+3} {}

five plus three

Got questions? Get instant answers now!

15 + 3 size 12{"15"+ left (-3 right )} {}

fifteen plus negative three

Got questions? Get instant answers now!

1 + 9 size 12{1+ left (-9 right )} {}

Got questions? Get instant answers now!

7 2 size 12{-7- left (-2 right )} {}

negative seven minus negative two

Got questions? Get instant answers now!

0 12 size 12{0- left (-"12" right )} {}

Got questions? Get instant answers now!

For the following 6 problems, rewrite each number in simpler form.

2 size 12{- left (-2 right )} {}

2

Got questions? Get instant answers now!

16 size 12{- left (-"16" right )} {}

Got questions? Get instant answers now!

8 size 12{- left [- left (-8 right ) right ]} {}

-8

Got questions? Get instant answers now!

20 size 12{- left [- left (-"20" right ) right ]} {}

Got questions? Get instant answers now!

7 3 size 12{7- left (-3 right )} {}

7 + 3 = 10 size 12{7+3="10"} {}

Got questions? Get instant answers now!

6 4 size 12{6- left (-4 right )} {}

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the quotient; 8 ÷ 27 size 12{8÷"27"} {} .

0 . 296 ¯ size 12{0 "." {overline {"296"}} } {}

Got questions? Get instant answers now!

( [link] ) Solve the proportion: 5 9 = 60 x size 12{ { {5} over {9} } = { {"60"} over {x} } } {}

Got questions? Get instant answers now!

( [link] ) Use the method of rounding to estimate the sum: 5829 + 8767 size 12{"5829"+"8767"} {}

6, 000 + 9, 000 = 15 , 000   ( 5, 829 + 8, 767 = 14 , 59 6 )   or 5, 800 + 8, 800 = 14 , 600 size 12{6,"000"+9,"000"="15","000" \( 5,"829"+8,"767"="14","59"6 \) " or 5,""800"+8,"800"="14","600"} {}

Got questions? Get instant answers now!

( [link] ) Use a unit fraction to convert 4 yd to feet.

Got questions? Get instant answers now!

( [link] ) Convert 25 cm to hm.

0.0025 hm

Got questions? Get instant answers now!

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
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 is the latest information on a no technology how can I find it
William
currently
William
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
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

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask