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10.8: Exercise Supplement

  • Page ID
    53071
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    Variables, Constants, and Real Numbers

    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 \(\PageIndex{1}\)

    61

    Answer

    N, W, Z

    Exercise \(\PageIndex{2}\)

    -14

    Exercise \(\PageIndex{3}\)

    0

    Answer

    W, Z

    Exercise \(\PageIndex{4}\)

    1

    Exercise \(\PageIndex{5}\)

    Write all the integers that are strictly between −4 and 3

    Answer

    {-3, -2, -1, 0, 1, 2}

    Exercise \(\PageIndex{6}\)

    Write all the integers that are between and including -6 and -1

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

    Exercise \(\PageIndex{7}\)

    -5 □ -1

    Answer

    <

    Exercise \(\PageIndex{8}\)

    0 □ 2

    Exercise \(\PageIndex{9}\)

    -7 □ 0

    Answer

    <

    Exercise \(\PageIndex{10}\)

    -1 □ 0

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

    Exercise \(\PageIndex{11}\)

    \(-5 \le x \le -1\), \(x\) is an integer

    Answer

    {-5, -4, -3, -2, -1}

    Exercise \(\PageIndex{12}\)

    \(-10 < x \le 0\), \(x\) is a whole number.

    Exercise \(\PageIndex{13}\)

    \(0 \le x < 5\), \(x\) is a natural number.

    Answer

    {1, 2, 3, 4}

    Exercise \(\PageIndex{14}\)

    \(-3 < x < 3\), \(x\) is a natural number

    Exercise \(\PageIndex{15}\)

    \(-8 < x \le -2\), \(x\) is a whole number

    Answer

    none

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

    Exercise \(\PageIndex{16}\)

    0 and 4

    Exercise \(\PageIndex{17}\)

    -1 and 3

    Answer

    4

    Exercise \(\PageIndex{18}\)

    -7 and -4

    Exercise \(\PageIndex{19}\)

    -6 and 0

    Answer

    6

    Exercise \(\PageIndex{20}\)

    -1 and 1

    Exercise \(\PageIndex{21}\)

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

    Answer

    + (plus)

    Exercise \(\PageIndex{22}\)

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

    Signed Numbers

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

    Exercise \(\PageIndex{23}\)

    -8

    Answer

    negative eight

    Exercise \(\PageIndex{24}\)

    -(-4)

    Exercise \(\PageIndex{25}\)

    -(-1)

    Answer

    negative negative one or opposite negative one

    Exercise \(\PageIndex{26}\)

    -2

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

    Exercise \(\PageIndex{27}\)

    1 + (-7)

    Answer

    one plus negative seven

    Exercise \(\PageIndex{28}\)

    -2 - (-6)

    Exercise \(\PageIndex{29}\)

    -1 - (+4)

    Answer

    negative one minus four

    Exercise \(\PageIndex{30}\)

    -(-(-3))

    Exercise \(\PageIndex{31}\)

    0 - (-11)

    Answer

    zero minus negative eleven

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

    Exercise \(\PageIndex{32}\)

    -(-4)

    Exercise \(\PageIndex{33}\)

    -(-15)

    Answer

    15

    Exercise \(\PageIndex{34}\)

    -[-(-7)]

    Exercise \(\PageIndex{35}\)

    1 - (-18)

    Answer

    19 or 1 + 18

    Exercise \(\PageIndex{36}\)

    0 - (-1)

    Absolute Value

    For problems 37-52, determine each value.

    Exercise \(\PageIndex{37}\)

    |9|

    Answer

    9

    Exercise \(\PageIndex{38}\)

    |16|

    Exercise \(\PageIndex{39}\)

    |-5|

    Answer

    5

    Exercise \(\PageIndex{40}\)

    |-8|

    Exercise \(\PageIndex{41}\)

    -|-2|

    Answer

    -2

    Exercise \(\PageIndex{42}\)

    -|-1|

    Exercise \(\PageIndex{43}\)

    -(-|12|)

    Answer

    12

    Exercise \(\PageIndex{44}\)

    -(-|90|)

    Exercise \(\PageIndex{45}\)

    -(-|-16|)

    Answer

    16

    Exercise \(\PageIndex{46}\)

    -(-|0|)

    Exercise \(\PageIndex{47}\)

    \(|-4|^2\)

    Answer

    16

    Exercise \(\PageIndex{48}\)

    \(|-5|^2\)

    Exercise \(\PageIndex{49}\)

    \(|-2|^3\)

    Answer

    8

    Exercise \(\PageIndex{50}\)

    \(|-(3 \cdot 4)|\)

    Exercise \(\PageIndex{51}\)

    |-5| + |-2|

    Answer

    7

    Exercise \(\PageIndex{52}\)

    |-7| - |-10|

    Addition, Subtraction, Multiplication and Division of Signed Numbers ([link],[link],[link])

    For problems 53-71, perform each operation.

    Exercise \(\PageIndex{53}\)

    -6 + 4

    Answer

    -2

    Exercise \(\PageIndex{54}\)

    -10 + 8

    Exercise \(\PageIndex{55}\)

    -1 - 6

    Answer

    -7

    Exercise \(\PageIndex{56}\)

    8 - 12

    Exercise \(\PageIndex{57}\)

    0 - 14

    Answer

    -14

    Exercise \(\PageIndex{58}\)

    \(5 \cdot (-2)\)

    Exercise \(\PageIndex{59}\)

    \(-8 \cdot (-6)\)

    Answer

    48

    Exercise \(\PageIndex{60}\)

    \((-3) \cdot (-9)\)

    Exercise \(\PageIndex{61}\)

    \(14 \cdot (-3)\)

    Answer

    -42

    Exercise \(\PageIndex{62}\)

    \(5 \cdot (-70)\)

    Exercise \(\PageIndex{63}\)

    \(-18 \div -6\)

    Answer

    3

    Exercise \(\PageIndex{64}\)

    \(72 \div - 12\)

    Exercise \(\PageIndex{65}\)

    \(-16 \div -16\)

    Answer

    1

    Exercise \(\PageIndex{66}\)

    \(0 \div -8\)

    Exercise \(\PageIndex{67}\)

    \(-5 \div 0\)

    Answer

    not defined

    Exercise \(\PageIndex{68}\)

    \(\dfrac{-15}{-3}\)

    Exercise \(\PageIndex{69}\)

    \(\dfrac{-28}{7}\)

    Answer

    -4

    Exercise \(\PageIndex{70}\)

    \(\dfrac{-120}{-|2|}\)

    Exercise \(\PageIndex{71}\)

    \(\dfrac{|-66|}{-|-3|}\)

    Answer

    -22


    10.8: Exercise Supplement is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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