<< 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.

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.

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.

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.

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.

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 .

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

Practice set a

Perform the subtractions.

9 6

3

6 9

3

0 7

7

1 14

13

8 12

20

21 6

27

6 ( 4 )

2

8 ( 10 )

18

1 ( 12 )

13

86 ( 32 )

118

0 16

16

0 ( 16 )

16

0 ( 8 )

8

5 ( 5 )

10

24 ( ( 24 ) )

0

Exercises

For the following exercises, perform the indicated operations.

8 3

5

12 7

5 6

1

14 30

2 15

13

5 18

1 7

6

4 11

6 5

11

8 14

1 12

13

4 4

6 8

14

1 12

5 ( 3 )

2

11 ( 8 )

7 ( 12 )

5

2 ( 10 )

4 ( 15 )

11

11 ( 16 )

1 ( 6 )

5

8 ( 14 )

15 ( 10 )

5

11 ( 4 )

16 ( 8 )

8

12 ( 11 )

0 6

6

0 15

0 ( 7 )

7

0 ( 10 )

67 38

29

142 85

816 1140

324

105 421

550 ( 121 )

429

15.016 ( 4.001 )

26 + 7 52

71

15 21 ( 2 )

104 ( 216 ) ( 52 )

164

0.012 ( 0.111 ) ( 0.035 )

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

1

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

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

1

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

( 11 8 ) ( 1 6 )

8

( 5 12 ) ( 4 10 )

( 1 10 ) ( 2 15 )

4

( 0 8 ) ( 4 12 )

( 4 + 7 ) ( 2 5 )

6

( 6 + 2 ) ( 5 11 )

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

27

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

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

12

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

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

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

Exercises for review

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

20 x y + 44 x

( [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 .

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

11

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

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

3

Questions & Answers

how can chip be made from sand
Eke Reply
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 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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
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, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask