Prealgebra

Julie Miller, Molly O’Neill, Nancy Hyde

Chapter 2

Integers and Algebraic Expressions - all with Video Answers

Educators

Section 1

Integers, Absolute Value, and Opposite

Problem 1

When working with signed numbers, keep a simple example in your mind, such as temperature. We understand that 10 degrees below zero is colder than 2 degrees below zero, so the inequality $-10<-2$ makes sense. Write down another example involving signed numbers that you can easily remember.

Brandon Fox

Brandon Fox

Numerade Educator

Problem 2

Define the key terms.
a. Absolute value
b. Integers
c. Negative numbers
d. Opposite
e. Positive numbers

Whitney Dillinger

Whitney Dillinger

Numerade Educator

Problem 3

Write an integer that represents each numerical value.
Death Valley, California, is $86 \mathrm{m}$ below sea level.

Brandon Fox

Numerade Educator

Problem 4

Write an integer that represents each numerical value.
In a card game, Jack lost 45 dollar.

Brandon Fox

Numerade Educator

Problem 5

Write an integer that represents each numerical value.
Playing Wheel of Fortune, Sally won 3800 dollar.

Brandon Fox

Numerade Educator

Problem 6

Write an integer that represents each numerical value.
Jim's golf score is 5 over par.

Brandon Fox

Numerade Educator

Problem 7

Write an integer that represents each numerical value.
Rena lost 500 dollar in the stock market in 1 month.

Brandon Fox

Numerade Educator

Problem 8

Write an integer that represents each numerical value.
LaTonya earned 23 dollar in interest on her saving account.

Brandon Fox

Numerade Educator

Problem 9

Write an integer that represents each numerical value.
Patrick lost 14 lb on a diet.

Brandon Fox

Numerade Educator

Problem 10

Write an integer that represents each numerical value.
A plane descended 2000 ft.

Brandon Fox

Numerade Educator

Problem 11

Write an integer that represents each numerical value.
The number of Internet users rose by about $1,400,000$.

Brandon Fox

Numerade Educator

Problem 12

Write an integer that represents each numerical value.
A small business experienced a loss of20,000 dollar last year.

Brandon Fox

Numerade Educator

Problem 13

Graph the numbers on the number line.
$$-6,0,-1,2$$
(GRAPH CAN NOT COPY)

Brandon Fox

Numerade Educator

Problem 14

Write an integer that represents each numerical value.
$$2,4,-5,1$$
(GRAPH CAN NOT COPY)

Brandon Fox

Numerade Educator

Problem 15

Which number is closer to $-4$ on the number line? $-2$ or $-7$

Brandon Fox

Numerade Educator

Problem 16

Which number is closer to 2 on the number line? $-5$ or 8

Brandon Fox

Numerade Educator

Problem 17

Fill in the blank with $<$ or $>$ to make a true statement.
$$0 \square-3$$

Brandon Fox

Numerade Educator

Problem 18

Fill in the blank with $<$ or $>$ to make a true statement.
$$-1 \square 0$$

Brandon Fox

Numerade Educator

Problem 19

Fill in the blank with $<$ or $>$ to make a true statement.
$$-8 \square-9$$

Brandon Fox

Numerade Educator

Problem 20

Fill in the blank with $<$ or $>$ to make a true statement.
$$-5 \square-2$$

Brandon Fox

Numerade Educator

Problem 21

Fill in the blank with $<$ or $>$ to make a true statement.
$$8 \square 9$$

Brandon Fox

Numerade Educator

Problem 22

Fill in the blank with $<$ or $>$ to make a true statement.
$$5 \square 2$$

Brandon Fox

Numerade Educator

Problem 23

Fill in the blank with $<$ or $>$ to make a true statement.
$$-226 \square 198$$

Brandon Fox

Numerade Educator

Problem 24

Fill in the blank with $<$ or $>$ to make a true statement.
$$408 \square-416$$

Brandon Fox

Numerade Educator

Problem 25

Determine the absolute value.
$$|-2|$$

Brandon Fox

Numerade Educator

Problem 26

Determine the absolute value.
$$|-9|$$

Brandon Fox

Numerade Educator

Problem 27

Determine the absolute value.
$$|2|$$

Brandon Fox

Numerade Educator

Problem 28

Determine the absolute value.
$$|9|$$

Brandon Fox

Numerade Educator

Problem 29

Determine the absolute value.
$$|-427|$$

Brandon Fox

Numerade Educator

Problem 30

Determine the absolute value.
$$|-615|$$

Brandon Fox

Numerade Educator

Problem 31

Determine the absolute value.
$$|100,000|$$

Brandon Fox

Numerade Educator

Problem 32

Determine the absolute value.
$$| 64,000$$

Brandon Fox

Numerade Educator

Problem 33

a. Which is greater, $-12$ or $-8 ?$
b. Which is greater, $|-12|$ or $|-8| ?$

Brandon Fox

Numerade Educator

Problem 34

a. Which is greater, $-14$ or $-20 ?$
b. Which is greater, $|-14|$ or $|-20| ?$

Brandon Fox

Numerade Educator

Problem 35

a. Which is greater, 5 or $7 ?$
b. Which is greater, $|5|$ or $|7| ?$

Brandon Fox

Numerade Educator

Problem 36

a. Which is greater, 3 or $4 ?$
b. Which is greater, $|3|$ or $|4| ?$

Brandon Fox

Numerade Educator

Problem 37

Which is greater, $-5$ or $|-5| ?$

Brandon Fox

Numerade Educator

Problem 38

Which is greater, $-5$ or $|-5| ?$

Brandon Fox

Numerade Educator

Problem 39

Which is greater 10 or $|10| ?$

Brandon Fox

Numerade Educator

Problem 40

Which is greater 256 or $|256| ?$

Brandon Fox

Numerade Educator

Problem 41

Find the opposite.
$$5$$

Brandon Fox

Numerade Educator

Problem 42

Find the opposite.
$$31$$

Brandon Fox

Numerade Educator

Problem 43

Find the opposite.
$$-12$$

Brandon Fox

Numerade Educator

Problem 44

Find the opposite.
$$-25$$

Brandon Fox

Numerade Educator

Problem 45

Find the opposite.
$$0$$

Brandon Fox

Numerade Educator

Problem 46

Find the opposite.
$$1$$

Brandon Fox

Numerade Educator

Problem 47

Find the opposite.
$$1$$

Brandon Fox

Numerade Educator

Problem 48

Find the opposite.
$$-612$$

Brandon Fox

Numerade Educator

Problem 49

Simplify the expression.
$$-(-15)$$

Brandon Fox

Numerade Educator

Problem 50

Simplify the expression.
$$-(-4)$$

Brandon Fox

Numerade Educator

Problem 51

Simplify the expression.
$$-|-15|$$

Breanna Ollech

Numerade Educator

Problem 52

Simplify the expression.
$$-|-4|$$

Brandon Fox

Numerade Educator

Problem 53

Simplify the expression.
$$-|15|$$

Julie Silva

Numerade Educator

Problem 54

Simplify the expression.
$$-|4|$$

Brandon Fox

Numerade Educator

Problem 55

Simplify the expression.
$$|-15|$$

Brandon Fox

Numerade Educator

Problem 56

Simplify the expression.
$$|-4|$$

Brandon Fox

Numerade Educator

Problem 57

Simplify the expression.
$$-(-36)$$

Brandon Fox

Numerade Educator

Problem 58

Simplify the expression.
$$-(-19)$$

Brandon Fox

Numerade Educator

Problem 59

Simplify the expression.
$$-|-107|$$

Brandon Fox

Numerade Educator

Problem 60

Simplify the expression.
$$-|-26$$

Brandon Fox

Numerade Educator

Problem 61

Simplify the expression.
a. $|-6|$
b. $-(-6)$
c. $-|6|$
d. $|6|$
e. $-|-6|$

Brandon Fox

Numerade Educator

Problem 62

Simplify the expression.
a. $-(-12)$
b. $|12|$
c. $|-12|$
d. $-|-12|$
e. $-|12|$

Brandon Fox

Numerade Educator

Problem 63

Simplify the expression.
a. $-|8|$
b. $|8|$
c. $-|-8|$
d. $-(-8)$
e. $|-8|$

Brandon Fox

Numerade Educator

Problem 64

a. $-|-1|$
b. $-(-1)$
c. $|1|$
d. $|-1|$
e. $-|1|$

Brandon Fox

Numerade Educator

Problem 65

Write in symbols, do not simplify.
The opposite of 6

Brandon Fox

Numerade Educator

Problem 66

Write in symbols, do not simplify.
The opposite of 23

Brandon Fox

Numerade Educator

Problem 67

Write in symbols, do not simplify.
The opposite of negative 2

Brandon Fox

Numerade Educator

Problem 68

Write in symbols, do not simplify.
The opposite of negative 9

Brandon Fox

Numerade Educator

Problem 69

Write in symbols, do not simplify.
The absolute value of 7

Brandon Fox

Numerade Educator

Problem 70

Write in symbols, do not simplify.
The absolute value of 11

Brandon Fox

Numerade Educator

Problem 71

Write in symbols, do not simplify.
The absolute value of negative 3

Brandon Fox

Numerade Educator

Problem 72

Write in symbols, do not simplify.
The absolute value of negative 10

Brandon Fox

Numerade Educator

Problem 73

Write in symbols, do not simplify.
The opposite of the absolute value of 14

Brandon Fox

Numerade Educator

Problem 74

Write in symbols, do not simplify.
The opposite of the absolute value of 42

Brandon Fox

Numerade Educator

Problem 75

Fill in the blank with $<,>,$ or $=$
$$|-12| \square|12|$$

Brandon Fox

Numerade Educator

Problem 76

Fill in the blank with $<,>,$ or $=$
$$-(-4) \square-|-4|$$

Brandon Fox

Numerade Educator

Problem 77

Fill in the blank with $<,>,$ or $=$
$$|-22| \square-(22)$$

Brandon Fox

Numerade Educator

Problem 78

Fill in the blank with $<,>,$ or $=$
$$-8 \square-10$$

Brandon Fox

Numerade Educator

Problem 79

Fill in the blank with $<,>,$ or $=$
$$-44 \square-54$$

Brandon Fox

Numerade Educator

Problem 80

Fill in the blank with $<,>,$ or $=$
$$-|0| \square-|1|$$

Brandon Fox

Numerade Educator

Problem 81

Fill in the blank with $<,>,$ or $=$
$$|-55| \square-(-65)$$

Brandon Fox

Numerade Educator

Problem 82

Fill in the blank with $<,>,$ or $=$
$$-(82) \square|46|$$

Brandon Fox

Numerade Educator

Problem 83

Fill in the blank with $<,>,$ or $=$
$$-|32| \square|0|$$

Brandon Fox

Numerade Educator

Problem 84

Fill in the blank with $<,>,$ or $=$
$$-|22| \square 0$$

Brandon Fox

Numerade Educator

Problem 85

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Portland

Brandon Fox

Numerade Educator

Problem 86

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Atlanta

Brandon Fox

Numerade Educator

Problem 87

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Denver

Brandon Fox

Numerade Educator

Problem 88

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Bismarck

Brandon Fox

Numerade Educator

Problem 89

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Eugene

Brandon Fox

Numerade Educator

Problem 90

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Orlando

Brandon Fox

Numerade Educator

Problem 91

Refer to the contour map for wind chill temperatures for a day in January. Give an estimate of the wind chill for the given city. For example, the wind chill in Phoenix is between $30^{\circ} \mathrm{F}$ and $40^{\circ} \mathrm{F}$ but closer to $30^{\circ} \mathrm{F}$. We might estimate the wind chill in Phoenix to be $33^{\circ} \mathrm{F}$.
(IMAGE CAN NOT COPY)
Dallas

Brandon Fox

Numerade Educator

Problem 92

Late spring and summer rainfall in the Lake Okeechobee region in Florida is important to replenish the water supply for large areas of south Florida. Each bar in the graph indicates the number of inches of rainfall above or below average for the given month. Use the graph
(GRAPH CAN NOT COPY)
Which month had the greatest amount of rainfall below average? What was the departure from average?

Brandon Fox

Numerade Educator

Problem 93

Late spring and summer rainfall in the Lake Okeechobee region in Florida is important to replenish the water supply for large areas of south Florida. Each bar in the graph indicates the number of inches of rainfall above or below average for the given month. Use the graph
(GRAPH CAN NOT COPY)
Which month had the greatest amount of rainfall above average?

Brandon Fox

Numerade Educator

Problem 94

Late spring and summer rainfall in the Lake Okeechobee region in Florida is important to replenish the water supply for large areas of south Florida. Each bar in the graph indicates the number of inches of rainfall above or below average for the given month. Use the graph
(GRAPH CAN NOT COPY)
Which month had the average amount of rainfall?

Brandon Fox

Numerade Educator

Problem 95

Rank the numbers from least to greatest.
$$-|-46|,-(-24),-60,5^{2},|-12|$$

Brandon Fox

Numerade Educator

Problem 96

Rank the numbers from least to greatest.
$$-15,-(-18),-|20|, 4^{2},|-3|^{2}$$

Brandon Fox

Numerade Educator

Problem 97

Rank the numbers from least to greatest.
If $a$ represents a negative number, then what is the sign of $-a ?$

Brandon Fox

Numerade Educator

Problem 98

Rank the numbers from least to greatest.
If $b$ represents a negative number, then what is the sign of $|b| ?$

Brandon Fox

Numerade Educator

Problem 99

Rank the numbers from least to greatest.
If $c$ represents a negative number, then what is the sign of $-|c| ?$

Brandon Fox

Numerade Educator

Problem 100

Rank the numbers from least to greatest.
If $d$ represents a negative number, then what is the sign of $-(-d) ?$

Brandon Fox

Numerade Educator