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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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 ((Reference))

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.

Exercise 1

Exercise 2

1414 size 12{-"14"} {}

Exercise 3

Exercise 4

1

Exercise 5

Write all the integers that are strictly between 44 size 12{-4} {} and 3

Solution

3,2,1, 0, 1, 23,2,1, 0, 1, 2 size 12{ left lbrace -3,-2,-1, 0, 1, 2 right rbrace } {}

Exercise 6

Write all the integers that are between and including 66 size 12{-6} {} and 11 size 12{-1} {}

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

Exercise 7

Exercise 8

0 □ 2

Exercise 9

Exercise 10

-1 □ 0

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

Exercise 11

5x15x1 size 12{-5 <= x <= -1} {}, x is an integer

Solution

5,4,3,2,15,4,3,2,1 size 12{ left lbrace -5,-4,-3,-2,-1 right rbrace } {}

Exercise 12

10<x010<x0 size 12{-"10"<x <= 0} {}, x is a whole number.

Exercise 13

0x<50x<5 size 12{0 <= x<5} {}, x is a natural number.

Solution

1, 2, 3, 41, 2, 3, 4 size 12{ left lbrace 1, 2, 3, 4 right rbrace } {}

Exercise 14

3<x<33<x<3 size 12{-3<x<3} {}, x is a natural number

Exercise 15

8<x28<x2 size 12{-8<x <= -2} {}, x is a whole number.

Solution

none

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

Exercise 16

0 and 4

Exercise 17

11 size 12{-1} {} and 3

Solution

4

Exercise 18

77 size 12{-7} {} and 44 size 12{-4} {}

Exercise 19

66 size 12{-6} {} and 0

Solution

6

Exercise 20

1 and 11 and 1 size 12{-"1 and 1"} {}

Exercise 21

A number is positive if it is directly preceded by a

               
sign or no sign at all.

Solution

+ (plus)

Exercise 22

A number is negative if it is directly preceded by a

               
sign.

Signed Numbers ((Reference))

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

Exercise 23

88 size 12{-8} {}

Solution

negative eight

Exercise 24

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

Exercise 25

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

Solution

negative negative one or opposite negative one

Exercise 26

22 size 12{-2} {}

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

Exercise 27

1+71+7 size 12{1+ left (-7 right )} {}

Solution

one plus negative seven

Exercise 28

2626 size 12{-2- left (-6 right )} {}

Exercise 29

1+41+4 size 12{-1- left (+4 right )} {}

Solution

negative one minus four

Exercise 30

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

Exercise 31

011011 size 12{0- left (-"11" right )} {}

Solution

zero minus negative eleven

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

Exercise 32

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

Exercise 33

1515 size 12{- left (-"15" right )} {}

Solution

15

Exercise 34

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

Exercise 35

118118 size 12{1- left (-"18" right )} {}

Solution

19 or 1+181+18 size 12{1+"18"} {}

Exercise 36

0101 size 12{0- left (-1 right )} {}

Absolute Value ((Reference))

For problems 37-52, determine each value.

Exercise 37

99 size 12{ lline 9 rline } {}

Solution

9

Exercise 38

1616 size 12{ lline "16" rline } {}

Exercise 39

55 size 12{ lline -5 rline } {}

Solution

5

Exercise 40

88 size 12{ lline -8 rline } {}

Exercise 41

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

Solution

22 size 12{-2} {}

Exercise 42

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

Exercise 43

1212 size 12{- left (- lline "12" rline right )} {}

Solution

12

Exercise 44

9090 size 12{- left (- lline "90" rline right )} {}

Exercise 45

1616 size 12{- left (- lline -"16" rline right )} {}

Solution

16

Exercise 46

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

Exercise 47

4242 size 12{ lline -4 rline rSup { size 8{2} } } {}

Solution

16

Exercise 48

5252 size 12{ lline -5 rline rSup { size 8{2} } } {}

Exercise 49

2323 size 12{ lline -2 rline rSup { size 8{3} } } {}

Solution

8

Exercise 50

3434 size 12{ lline - left (3 cdot 4 right ) rline } {}

Exercise 51

5+25+2 size 12{ lline -5 rline + lline -2 rline } {}

Solution

7

Exercise 52

710710 size 12{ lline -7 rline - lline -"10" rline } {}

Addition, Subtraction, Multiplication and Division of Signed Numbers ((Reference),(Reference),(Reference))

For problems 53-71, perform each operation.

Exercise 53

6+46+4 size 12{-6+4} {}

Solution

22 size 12{-2} {}

Exercise 54

10+810+8 size 12{-"10"+8} {}

Exercise 55

1616 size 12{-1-6} {}

Solution

77 size 12{-7} {}

Exercise 56

812812 size 12{8-"12"} {}

Exercise 57

014014 size 12{0-"14"} {}

Solution

1414 size 12{-"14"} {}

Exercise 58

5252 size 12{5 cdot left (-2 right )} {}

Exercise 59

8686 size 12{-8 cdot left (-6 right )} {}

Solution

48

Exercise 60

3939 size 12{ left (-3 right ) cdot left (-9 right )} {}

Exercise 61

143143 size 12{"14" cdot left (-3 right )} {}

Solution

4242 size 12{-"42"} {}

Exercise 62

570570 size 12{5 cdot left (-"70" right )} {}

Exercise 63

-18÷ -6-18÷ -6 size 12{–"18""÷–"6} {}

Solution

3

Exercise 64

72÷ -1272÷ -12 size 12{"72""÷–""12"} {}

Exercise 65

16÷ -1616÷ -16 size 12{–"16""÷–""16"} {}

Solution

1

Exercise 66

0÷- 80÷- 8 size 12{0"÷–"8} {}

Exercise 67

-5÷0-5÷0 size 12{–5÷0} {}

Solution

not defined

Exercise 68

153153 size 12{ { {-"15"} over {-3} } } {}

Exercise 69

287287 size 12{ { {-"28"} over {7} } } {}

Solution

44 size 12{-4} {}

Exercise 70

12021202 size 12{ { {-"120"} over {- lline 2 rline } } } {}

Exercise 71

663663 size 12{ { { lline -"66" rline } over {- lline -3 rline } } } {}

Solution

2222 size 12{-"22"} {}

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