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Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 2

Integers

Educators

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Problem 1

Write an integer for each situation. Then graph on a number line.
$$8^{\circ}$ below zero$$

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Problem 2

Write an integer for each situation. Then graph on a number line.
$$a 15 -yard gain$$

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Problem 3

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>$
$$-7^{\circ}$ is colder than $3^{\circ}$$

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Problem 4

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>$
$$-6$ is greater than $-10$.$

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Problem 5

Replace each with $<,>,$ or $=$ to make a true sentence.
$$-18 \cdot-8$$

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Problem 6

Replace each with $<,>,$ or $=$ to make a true sentence.$$0=-3$$

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Problem 7

Replace each with $<,>,$ or $=$ to make a true sentence. $$9 \cdot-9$$

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Problem 8

Order the integers $\{28,-6,0,-2,5,-52,115\}$ from least to greatest.

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Problem 9

The table shows the recorded acceleration for a new car at regular intervals. Order the accelerations from least to greatest.
$$\begin{aligned}&\left(\frac{5}{5}\right)\\&\begin{array}{|r|r|r|r|r|r|r|r|r|}\hline \text { Time (s) } & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 \\\hline \text { Acceleration }\left(\mathrm{m} /\mathrm{s}^{2}\right) & 16 & -31 & -10 & -6 & 9 & 34 & -23 & -19 & -2 \\\hline\end{array}\end{aligned}$$

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Problem 10

Evaluate each expression.
$$|-10|$$

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Problem 11

Evaluate each expression.
$$|10|-|-4|$S

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Problem 12

Evaluate each expression.
$$|16|+|-5|$$

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Problem 13

ALGEBRA Evaluate each expression if $a=-8$ and $b=5$
$$9+|a|$$4

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Problem 14

ALGEBRA Evaluate each expression if $a=-8$ and $b=5$
$$$|a|-b$$

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Problem 15

ALGEBRA Evaluate each expression if $a=-8$ and $b=5$
$$$2|a|$$

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Problem 16

Write an integer for each situation. Then graph on a number line.
$$a bank withdrawal of $\$ 100$$

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Problem 17

Write an integer for each situation. Then graph on a number line.
$$a loss of 6 pounds$$

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Problem 18

Write an integer for each situation. Then graph on a number line.
$$a salary increase of $\$ 250$$

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Problem 19

Write an integer for each situation. Then graph on a number line.
$$a gain of 9 yards$$

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Problem 20

Write an integer for each situation. Then graph on a number line.
$$12^{\circ}$ above zero$$

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Problem 21

Write an integer for each situation. Then graph on a number line.
$$5 seconds before liftoff$$

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Problem 22

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>$
$$3 meters is taller than 2 meters.

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Problem 23

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>
$$A temperature of $-5^{\circ} \mathrm{F}$ is warmer than a temperature of $-10^{\circ} \mathrm{F}$$

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Problem 24

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>
$$55 miles per hour is slower than 65 miles per hour.$$

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Problem 25

Write two inequalities using the numbers in each sentence. Use the symbols $<$ or $>
$$ A 4-yard loss is less than no gain.$$

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Problem 26

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$-6 \circ-2$

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Problem 27

$Replace each with $<,>,$ or $=$ to make a true sentence.
.4 $-10^{\circ}-13$

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Problem 28

$Replace each with $<,>,$ or $=$ to make a true sentence.
.4 $-10^{\circ}-13$

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Problem 29

Replace each with $\langle,>,$ or $=$ to make a true sentence.
$$
-6 __-2
$$

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Problem 30

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$14.0$$

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Problem 31

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$5 \cdot-23$$

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Problem 31

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$|9| \circ|-9|$$

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Problem 32

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$|-20| \cdot|-4|$$

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Problem 33

$Replace each with $<,>,$ or $=$ to make a true sentence.
$$|-20| \cdot|-4|$$

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Problem 34

Order the integers in each set from least to greatest.
$$\{5,0,-8\}$)$$

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Problem 35

Order the integers in each set from least to greatest.
$\{-15,-1,-2,-4\}$

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Problem 36

Order the integers in each set from least to greatest.
$(19,-16,4,62,-80)$

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Problem 37

Order the integers in each set from least to greatest.
$$$(41,-14,50,-23,-20)$

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Problem 38

Order the integers in each set from least to greatest.
$$\{24,5,-46,9,0,-3\}$

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Problem 39

Order the integers in each set from least to greatest.
$(98,-57,-60,38,188)$

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Problem 40

Evaluate each expression.
$$|-15|$$

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Problem 41

Evaluate each expression.
$$ |46| \quad$$

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Problem 42

Evaluate each expression
$$-|20|$$

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Problem 43

Evaluate each expression
$$-|5|$$

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Problem 44

Evaluate each expression
$|0| \quad$

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Problem 45

Evaluate each expression
$|7|$

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Problem 46

Evaluate each expression
$$|-5|+|4| \quad$ $

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Problem 47

Evaluate each expression
$$|0|+|-2|$$

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Problem 48

Evaluate each expression
\text { 48. }|15|-|-1|

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Problem 49

Evaluate each expression
a9. }|0+9| \quad \text

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Problem 50

Evaluate each expression
$$|9-5|-|6-8|$$

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Problem 51

Evaluate each expression
$$-|-6+1|-|5-6|$$

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Problem 52

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$14+|b|$$

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Problem 53

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$|c|-a$$

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Problem 54

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$a+b+|c|$$

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Problem 55

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$a b+|-40|$$

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Problem 56

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$|c|-b$$

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Problem 57

Evaluate each expression if $a=0, b=3,$ and $c=-4$
$$|a b|+b$$

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Problem 58

The Caribbean Sea has an average depth of 8448 feet below sea level. Use an integer to express this depth.to express this depth.\begin{array}{|l|l|c|c|}
\hline \multicolumn{1}{|c|} & \multicolumn{1}{c |}\text { Stur } \\
\hline \text { All } & \multicolumn{1}{|c|}\text { (t) } \\
\hline \text { Alaska } & \text { Prospect Creek Camp } & \text { Jan. 23, 1971 } & -80 \\
\hline \text { Montana } & \text { Rogers Pass } & \text { Jan. 20, 1954 } & -70 \\
\hline \text { Wisconsin } & \text { Danbury } & \text { Jan. 24, 1922 } & -54 \\
\hline\end{array}

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Problem 59

Graph the temperatures on a number line.

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Problem 60

Compare the lowest temperature in Alaska and the lowest temperature in Wisconsin using the $<$ symbol.

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Problem 61

Compare the lowest temperature in Montana and the lowest temperature in Wisconsin using the $>$ symbol.

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Problem 62

Write the temperatures in order from greatest to least.

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Problem 63

Compare the lowest temperature in Montana and the lowest temperature in Wisconsin using the $>$ symbol.

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Problem 64

Compare the lowest temperature in Alaska and the lowest temperature in Wisconsin using the $<$ symbol.Graph each set of integers on a number line.
\{-3,1,2,5\}

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Problem 65

Graph each set of integers on a number line.
$$\{-2,-4,-5,-8\}$$

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Problem 66

Graph each set of integers on a number line.
$$\{-4,0,6,-7,-1\}$$

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Problem 67

Vame the \begin{array}{ccccccc}
B & D & A & C & & \\
+ & + & + & + & + & + & + \\
-6 & -4 & -2 & 0 & 2 & 4 & 6
\end{array}coordinates of each point graphed on the number line.

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Problem 68

The average temperature of Saturn is $-218^{\circ} \mathrm{F}$ while the average temperature of Jupiter is $-162^{\circ} \mathrm{F}$. Which planet has the lower average temperature? Explain.

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Problem 69

FIND THE DAIA Refer to the United States Data File on pages $18-21$. Choose some data and write a real-world problem in which you would compare anc order integers.

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Problem 70

OPEN ENDED Write two inequalities using integers

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Problem 71

NUMBER SENSE Explain how to find the number of units apart $-4$ and 5 are on a number line.

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Problem 72

Which One Doesn't Belong? Identify the expression that does not belong with the other three. Explain your reasoning.
(graph can;t copy

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Problem 73

Is it altways, sometimes, or never true that the distance between $A$ and $B$ equals the distance between $|A|$ and $|B|$ ? Explain.

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Problem 74

Assume $A>B .$ Is it always, sometimes, or never true that $A-|B| \leq A+B ?$ Explain,

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Problem 75

Writing in Math Use the information about integers on page 78 to explain how they can be used to model real-world situations. Include arexplanation of how integers are used to describe rainfall.

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Problem 76

What is the temperature shown on the thermometer at the right?
$\mathbf{A} \&^{\circ} \mathrm{F}$
$\mathbf{B} \quad 7^{\circ} \mathrm{F}$
$\mathbf{C}-7^{\circ} \mathrm{F}$
$\mathbf{D}-8^{\circ} \mathrm{F}$

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Problem 77

How many units apart are $-4$ and 3 on a number line?

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Problem 79

Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. (lesson $1-7)$
height and arm length?

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Problem 80

relationship. Explain your answer.
birth month and weight

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Problem 81

Express each relation as a table and as a list of ordered pairs.
(graph can't copy)

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Problem 82

Express each relation as a table and as a list of ordered pairs -
(graph can't copy)

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Problem 83

Name the property shown by each statement.
$$20(18)=18(20)$$

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Problem 84

Name the property shown by each statement.
$$9(8)(0)=0$$

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Problem 85

Name the property shown by each statement.
$$3 a b=3 b a$$

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Problem 86

Find each sum or difference.
$$18+29+46$$

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Problem 87

Find each sum or difference.
$$232+156$$

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Problem 88

Find each sum or difference.
$451+629+1027$

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Problem 89

Find each sum or difference.
$$36-19$$

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Problem 90

Find each sum or difference.
$$479-281$$

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Problem 91

Find each sum or difference.
$$2011-962$$

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