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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Signed Numbers" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise supplement

Variables, constants, and real numbers ( [link] )

For problems 1-5, next to each real number, note all subsets of the real numbers to which it belongs by writing N for natural numbers, W for whole numbers, or Z for integers. Some numbers may belong to more than one subset.

14 size 12{-"14"} {}

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Write all the integers that are strictly between 4 size 12{-4} {} and 3

3, 2, 1, 0, 1, 2 size 12{ left lbrace -3,-2,-1, 0, 1, 2 right rbrace } {}

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Write all the integers that are between and including 6 size 12{-6} {} and 1 size 12{-1} {}

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For each pair of numbers in problems 7-10, write the appropriate symbol (<,>, =) in place of the □.

For problems 11-15, what numbers can replace x so that each statement is true?

5 x 1 size 12{-5<= x<= -1} {} , x is an integer

5, 4, 3, 2, 1 size 12{ left lbrace -5,-4,-3,-2,-1 right rbrace } {}

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10 < x 0 size 12{-"10"<x<= 0} {} , x is a whole number.

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0 x < 5 size 12{0<= x<5} {} , x is a natural number.

1, 2, 3, 4 size 12{ left lbrace 1, 2, 3, 4 right rbrace } {}

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3 < x < 3 size 12{-3<x<3} {} , x is a natural number

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8 < x 2 size 12{-8<x<= -2} {} , x is a whole number.

none

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For problems 16-20, how many units are there between the given pair of numbers?

1 size 12{-1} {} and 3

4

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7 size 12{-7} {} and 4 size 12{-4} {}

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6 size 12{-6} {} and 0

6

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1 and 1 size 12{-"1 and 1"} {}

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A number is positive if it is directly preceded by a sign or no sign at all.

+ (plus)

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A number is negative if it is directly preceded by a sign.

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Signed numbers ( [link] )

For problems 23-26, how should each number be read?

8 size 12{-8} {}

negative eight

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

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

negative negative one or opposite negative one

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For problems 27-31, write each expression in words.

1 + 7 size 12{1+ left (-7 right )} {}

one plus negative seven

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2 6 size 12{-2- left (-6 right )} {}

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1 + 4 size 12{-1- left (+4 right )} {}

negative one minus four

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

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0 11 size 12{0- left (-"11" right )} {}

zero minus negative eleven

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For problems 32-36, rewrite each expression in simpler form.

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

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

15

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7 size 12{- left [- left (-7 right ) right ]} {}

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1 18 size 12{1- left (-"18" right )} {}

19 or 1 + 18 size 12{1+"18"} {}

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0 1 size 12{0- left (-1 right )} {}

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Absolute value ( [link] )

For problems 37-52, determine each value.

9 size 12{ lline 9 rline } {}

9

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16 size 12{ lline "16" rline } {}

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5 size 12{ lline -5 rline } {}

5

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8 size 12{ lline -8 rline } {}

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2 size 12{- lline -2 rline } {}

2 size 12{-2} {}

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1 size 12{- lline -1 rline } {}

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12 size 12{- left (- lline "12" rline right )} {}

12

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90 size 12{- left (- lline "90" rline right )} {}

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

16

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0 size 12{- left (- lline 0 rline right )} {}

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4 2 size 12{ lline -4 rline rSup { size 8{2} } } {}

16

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5 2 size 12{ lline -5 rline rSup { size 8{2} } } {}

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2 3 size 12{ lline -2 rline rSup { size 8{3} } } {}

8

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3 4 size 12{ lline - left (3 cdot 4 right ) rline } {}

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5 + 2 size 12{ lline -5 rline + lline -2 rline } {}

7

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7 10 size 12{ lline -7 rline - lline -"10" rline } {}

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Addition, subtraction, multiplication and division of signed numbers ( [link] , [link] , [link] )

For problems 53-71, perform each operation.

6 + 4 size 12{-6+4} {}

2 size 12{-2} {}

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10 + 8 size 12{-"10"+8} {}

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1 6 size 12{-1-6} {}

7 size 12{-7} {}

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8 12 size 12{8-"12"} {}

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0 14 size 12{0-"14"} {}

14 size 12{-"14"} {}

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5 2 size 12{5 cdot left (-2 right )} {}

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8 6 size 12{-8 cdot left (-6 right )} {}

48

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3 9 size 12{ left (-3 right ) cdot left (-9 right )} {}

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14 3 size 12{"14" cdot left (-3 right )} {}

42 size 12{-"42"} {}

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5 70 size 12{5 cdot left (-"70" right )} {}

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- 18 ÷ - 6 size 12{–"18""÷–"6} {}

3

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72 ÷ - 12 size 12{"72""÷–""12"} {}

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16 ÷ - 16 size 12{–"16""÷–""16"} {}

1

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0 ÷ - 8 size 12{0"÷–"8} {}

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- 5 ÷ 0 size 12{–5÷0} {}

not defined

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15 3 size 12{ { {-"15"} over {-3} } } {}

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28 7 size 12{ { {-"28"} over {7} } } {}

4 size 12{-4} {}

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120 2 size 12{ { {-"120"} over {- lline 2 rline } } } {}

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66 3 size 12{ { { lline -"66" rline } over {- lline -3 rline } } } {}

22 size 12{-"22"} {}

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Questions & Answers

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
Rethabile Reply
we're do you find electromagnetism past papers
Ntombifuthi
what a normal force
Tholulwazi Reply
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
Anna Reply
how to calculate coefficient of static friction
Lisa Reply
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
Anna Reply
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
Amahle Reply
How is energy being used in bonding?
Raymond Reply
what is acceleration
Syamthanda Reply
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
hi
Leago
use fnet method. how many obects are being calculated ?
Khuthadzo
khuthadzo hii
Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
Mulaudzi Reply
how to calculate normal force
Mulaudzi
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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