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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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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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