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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.

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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.

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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.

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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.

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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.

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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 .

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

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Practice set a

Perform the subtractions.

6 ( 4 )

2

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24 ( ( 24 ) )

0

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Exercises

For the following exercises, perform the indicated operations.

5 ( 3 )

2

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15 ( 10 )

5

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16 ( 8 )

8

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550 ( 121 )

429

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15.016 ( 4.001 )

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26 + 7 52

71

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15 21 ( 2 )

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104 ( 216 ) ( 52 )

164

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0.012 ( 0.111 ) ( 0.035 )

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

1

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

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

1

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

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( 11 8 ) ( 1 6 )

8

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( 5 12 ) ( 4 10 )

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( 1 10 ) ( 2 15 )

4

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( 0 8 ) ( 4 12 )

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( 4 + 7 ) ( 2 5 )

6

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( 6 + 2 ) ( 5 11 )

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

27

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

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

12

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

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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

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

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Exercises for review

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

20 x y + 44 x

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( [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 .

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

11

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

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

3

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Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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