<< Chapter < Page Chapter >> Page >
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 real-life 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 5 2 produces 3, that is, 5 2 = 3 . Illustrating this process on the number line suggests a rule for subtracting signed numbers.

A number line with arrows on each end, labeled from negative one to seven in increments of one. There is a curved arrow starting from zero, and pointing towards five. There is another curved arrow starting from five, and pointing towards three.

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 5 2 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, a b 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 a b , add the opposite of b to a , that is, change the sign of b and add.

Sample set a

Perform the subtractions.

5 3 = 5 + ( 3 ) = 2

A number line with arrows on each end, labeled from negative three to six in increments of one. There is a curved arrow starting from zero, and pointing towards five. There is another curved arrow starting from five, and pointing towards two.

Got questions? Get instant answers now!

4 9 = 4 + ( 9 ) = 5

A number line with arrows on each end, labeled from negative six to six in increments of one. There is a curved arrow starting from zero, and pointing towards four. There is another curved arrow starting from four, and pointing towards negative five.

Got questions? Get instant answers now!

4 6 = 4 + ( 6 ) = 10

A number line with arrows on each end, labeled from negative twelve to three in increments of one. There is curved arrow starting from zero, and pointing towards negative four. There is another curved arrow starting from negative four, and pointing towards negative ten.

Got questions? Get instant answers now!

3 ( 12 ) = 3 + 12 = 9

A number line with arrows on each end, labeled from negative five to twelve in increments of one. There is a curved arrow starting from zero, and pointing towards negative three. There is another curved arrow starting from negative three, and pointing towards nine.

Got questions? Get instant answers now!

0 ( 15 ) = 0 + 15 = 15

A number line with arrows on each end, labeled from negative two to eighteen in increments of one. There is a curved arrow starting from zero, and pointing towards fifteen.

Got questions? Get instant answers now!

The high temperature today in Lake Tahoe was 26 F . The low temperature tonight is expected to be 7 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 F .

Got questions? Get instant answers now!

6 ( 5 ) 10 = 6 + 5 + ( 10 ) = ( 6 + 5 ) + ( 10 ) = 1 + ( 10 ) = 11

Got questions? Get instant answers now!

Practice set a

Perform the subtractions.

6 ( 4 )

2

Got questions? Get instant answers now!

24 ( ( 24 ) )

0

Got questions? Get instant answers now!

Exercises

For the following exercises, perform the indicated operations.

5 ( 3 )

2

Got questions? Get instant answers now!

15 ( 10 )

5

Got questions? Get instant answers now!

16 ( 8 )

8

Got questions? Get instant answers now!

550 ( 121 )

429

Got questions? Get instant answers now!

15.016 ( 4.001 )

Got questions? Get instant answers now!

26 + 7 52

71

Got questions? Get instant answers now!

15 21 ( 2 )

Got questions? Get instant answers now!

104 ( 216 ) ( 52 )

164

Got questions? Get instant answers now!

0.012 ( 0.111 ) ( 0.035 )

Got questions? Get instant answers now!

[ 5 + ( 6 ) ] [ 2 + ( 4 ) ]

1

Got questions? Get instant answers now!

[ 2 + ( 8 ) ] [ 5 + ( 7 ) ]

Got questions? Get instant answers now!

[ 4 + ( 11 ) ] [ 2 + ( 10 ) ]

1

Got questions? Get instant answers now!

[ 9 + ( 6 ) ] [ 4 + ( 12 ) ]

Got questions? Get instant answers now!

( 11 8 ) ( 1 6 )

8

Got questions? Get instant answers now!

( 5 12 ) ( 4 10 )

Got questions? Get instant answers now!

( 1 10 ) ( 2 15 )

4

Got questions? Get instant answers now!

( 0 8 ) ( 4 12 )

Got questions? Get instant answers now!

( 4 + 7 ) ( 2 5 )

6

Got questions? Get instant answers now!

( 6 + 2 ) ( 5 11 )

Got questions? Get instant answers now!

[ 8 + ( 5 + 3 ) ] [ 9 ( 3 5 ) ]

27

Got questions? Get instant answers now!

[ 4 + ( 1 + 6 ) ] [ 7 ( 6 1 ) ]

Got questions? Get instant answers now!

[ 2 ( 6 + 10 ) ] [ 1 ( 2 11 ) ]

12

Got questions? Get instant answers now!

[ 5 ( 2 5 ) ] [ 2 ( 1 4 ) ]

Got questions? Get instant answers now!

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?

11

Got questions? Get instant answers now!

The low temperature today in Denver was 4 F and the high was 42 F . What is the temperature difference?

Got questions? Get instant answers now!

Exercises for review

( [link] ) Use the distributive property to expand 4 x ( 5 y + 11 ) .

20 x y + 44 x

Got questions? Get instant answers now!

( [link] ) Simplify 2 ( 3 x 2 y 2 ) 3 ( 2 x 4 y 3 ) 0 27 x 4 y 3 . Assume x 0 , y 0 .

Got questions? Get instant answers now!

( [link] ) Simplify | ( 4 2 + 2 2 3 2 ) | .

11

Got questions? Get instant answers now!

( [link] ) Find the sum. 8 + ( 14 ) .

Got questions? Get instant answers now!

( [link] ) Find the sum. 3 + ( 6 ) .

3

Got questions? Get instant answers now!

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask