10.8: Exercise Supplement

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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 \(\PageIndex{1}\)

Answer: N, W, Z

Exercise \(\PageIndex{2}\)

-14

Exercise \(\PageIndex{3}\)

Answer: W, Z

Exercise \(\PageIndex{4}\)

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