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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

61

Solution

N, W, Z

Exercise 2

−14−14 size 12{-"14"} {}

Exercise 3

0

Solution

W, Z

Exercise 4

1

Exercise 5

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

Solution

−3,−2,−1, 0, 1, 2−3,−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 −6−6 size 12{-6} {} and −1−1 size 12{-1} {}

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

Exercise 7

-5 □ -1

Solution

<

Exercise 8

0 □ 2

Exercise 9

-7 □ 0

Solution

<

Exercise 10

-1 □ 0

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

Exercise 11

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

Solution

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

Exercise 12

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

Exercise 13

0≤x<50≤x<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<3−3<x<3 size 12{-3<x<3} {}, x is a natural number

Exercise 15

−8<x≤−2−8<x≤−2 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

−1−1 size 12{-1} {} and 3

Solution

4

Exercise 18

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

Exercise 19

−6−6 size 12{-6} {} and 0

Solution

6

Exercise 20

−1 and 1−1 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

−8−8 size 12{-8} {}

Solution

negative eight

Exercise 24

−−4−−4 size 12{- left (-4 right )} {}

Exercise 25

−−1−−1 size 12{- left (-1 right )} {}

Solution

negative negative one or opposite negative one

Exercise 26

−2−2 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

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

Exercise 29

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

Solution

negative one minus four

Exercise 30

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

Exercise 31

0−−110−−11 size 12{0- left (-"11" right )} {}

Solution

zero minus negative eleven

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

Exercise 32

−−4−−4 size 12{- left (-4 right )} {}

Exercise 33

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

Solution

15

Exercise 34

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

Exercise 35

1−−181−−18 size 12{1- left (-"18" right )} {}

Solution

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

Exercise 36

0−−10−−1 size 12{0- left (-1 right )} {}

Absolute Value ((Reference))

For problems 37-52, determine each value.

Exercise 37

∣9∣∣9∣ size 12{ lline 9 rline } {}

Solution

9

Exercise 38

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

Exercise 39

∣−5∣∣−5∣ size 12{ lline -5 rline } {}

Solution

5

Exercise 40

∣−8∣∣−8∣ size 12{ lline -8 rline } {}

Exercise 41

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

Solution

−2−2 size 12{-2} {}

Exercise 42

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

Exercise 43

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

Solution

12

Exercise 44

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

Exercise 45

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

Solution

16

Exercise 46

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

Exercise 47

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

Solution

16

Exercise 48

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

Exercise 49

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

Solution

8

Exercise 50

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

Exercise 51

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

Solution

7

Exercise 52

∣−7∣−∣−10∣∣−7∣−∣−10∣ 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+4−6+4 size 12{-6+4} {}

Solution

−2−2 size 12{-2} {}

Exercise 54

−10+8−10+8 size 12{-"10"+8} {}

Exercise 55

−1−6−1−6 size 12{-1-6} {}

Solution

−7−7 size 12{-7} {}

Exercise 56

8−128−12 size 12{8-"12"} {}

Exercise 57

0−140−14 size 12{0-"14"} {}

Solution

−14−14 size 12{-"14"} {}

Exercise 58

5⋅−25⋅−2 size 12{5 cdot left (-2 right )} {}

Exercise 59

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

Solution

48

Exercise 60

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

Exercise 61

14⋅−314⋅−3 size 12{"14" cdot left (-3 right )} {}

Solution

−42−42 size 12{-"42"} {}

Exercise 62

5⋅−705⋅−70 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÷ -16−16÷ -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

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

Exercise 69

−287−287 size 12{ { {-"28"} over {7} } } {}

Solution

−4−4 size 12{-4} {}

Exercise 70

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

Exercise 71

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

Solution

−22−22 size 12{-"22"} {}

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