10.8: Exercise Supplement

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