Prealgebra

Charles P. McKeague

Chapter 2

Introduction to Algebra - all with Video Answers

Educators

Section 1

Positive and Negative Numbers

Problem 1

Write each of the following in words.
$$4<7$$

Amy Jiang

Amy Jiang

Numerade Educator

Problem 2

Write each of the following in words.
$$0<10$$

TH

Tristan Hutcheson

Numerade Educator

Problem 3

Write each of the following in words.
$$5>-2$$

BH

Bridget Hintz

Numerade Educator

Problem 4

Write each of the following in words.
$$8>-8$$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 5

Write each of the following in words.
$$-10<-3$$

TH

Tristan Hutcheson

Numerade Educator

Problem 6

Write each of the following in words.
$$-20<-5$$

Victor Salazar

Numerade Educator

Problem 7

Write each of the following in words.
$$0>-4$$

BH

Bridget Hintz

Numerade Educator

Problem 8

Write each of the following in words.
$$0>-100$$

Joshua Washington

Joshua Washington

Numerade Educator

Problem 9

Write each of the following in symbols.
30 is greater than $-30$

Rick Faulk

Numerade Educator

Problem 10

Write each of the following in symbols.
$-30$ is less than 30

Rick Faulk

Numerade Educator

Problem 11

Write each of the following in symbols.
10 is less than $0 .$

Pammi Eswari

Numerade Educator

Problem 12

Write each of the following in symbols.
0 is greater than $-10$

Rick Faulk

Numerade Educator

Problem 13

Write each of the following in symbols.
$-3$ is greater than $-15$

Ian Maurer

Numerade Educator

Problem 14

Write each of the following in symbols.
$-15$ is less than $-3$

Kelsey Van Horn

Kelsey Van Horn

Numerade Educator

Problem 15

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. 3 $\quad$ 7

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 16

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$17 \quad 0$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 17

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$7 \quad -5$$

Amy Jiang

Numerade Educator

Problem 18

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$2 \quad -13$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 19

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-6 \quad 0$$

Amy Jiang

Numerade Educator

Problem 20

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-14 \quad 0$$

Amy Jiang

Numerade Educator

Problem 21

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-12 \quad -2$$

Prahith Chakka

Numerade Educator

Problem 22

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-20 \quad -1$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 23

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-\frac{1}{2}\quad-\frac{3}{4}$$

Prahith Chakka

Numerade Educator

Problem 24

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-\frac{6}{7} \quad \frac{5}{6}$$

Prahith Chakka

Numerade Educator

Problem 25

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.75 \quad 0.25$$

Amy Jiang

Numerade Educator

Problem 26

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-1 \quad-3.5$$

Amy Jiang

Numerade Educator

Problem 27

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.1 \quad-0.01$$

Amy Jiang

Numerade Educator

Problem 28

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.04\quad-0.4$$

Vysakh M

Numerade Educator

Problem 29

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-3 \quad|6|$$

JL

Jacob Lombardo

Numerade Educator

Problem 30

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|8| \quad -2$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 31

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$15 \quad|-4|$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 32

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$20 \quad|-6|$$

JL

Jacob Lombardo

Numerade Educator

Problem 33

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|-2| \quad|-7|$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 34

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|-3| \quad|-1|$$

Edward Downes

Numerade Educator

Problem 35

Find each of the following absolute values.
$$|2|$$

Ramzi Deek

Numerade Educator

Problem 36

Find each of the following absolute values.
$$|7|$$

John Irizar

Numerade Educator

Problem 37

Find each of the following absolute values.
$$|100|$$

Julie Silva

Numerade Educator

Problem 38

Find each of the following absolute values.
$$|10,000|$$

AG

Ankit Gupta

Numerade Educator

Problem 39

Find each of the following absolute values.
$$|-8|$$

Supratim Roy

Numerade Educator

Problem 40

Find each of the following absolute values.
$$|-9|$$

Arya Patel

Numerade Educator

Problem 41

Find each of the following absolute values.
$$|-231|$$

AG

Ankit Gupta

Numerade Educator

Problem 42

Find each of the following absolute values.
$$|-457|$$

AG

Ankit Gupta

Numerade Educator

Problem 43

Find each of the following absolute values.
$$\left|-\frac{3}{4}\right|$$

Rebecca Dias

Numerade Educator

Problem 44

Find each of the following absolute values.
$$\left|-\frac{1}{10}\right|$$

AG

Ankit Gupta

Numerade Educator

Problem 45

Find each of the following absolute values.
$$|-200|$$

Stephanie Carter

Stephanie Carter

Numerade Educator

Problem 46

Find each of the following absolute values.
$$|-350|$$

AG

Ankit Gupta

Numerade Educator

Problem 47

Find each of the following absolute values.
$$|8|$$

Supratim Roy

Numerade Educator

Problem 48

Find each of the following absolute values.
$$|9|$$

Arya Patel

Numerade Educator

Problem 49

Find each of the following absolute values.
$$|231|$$

AG

Ankit Gupta

Numerade Educator

Problem 50

Find each of the following absolute values.
$$|457|$$

AG

Ankit Gupta

Numerade Educator

Problem 51

Give the opposite of each of the following numbers.
$$3$$

K Joseph

Numerade Educator

Problem 52

Give the opposite of each of the following numbers.
$$-5$$

K Joseph

Numerade Educator

Problem 53

Give the opposite of each of the following numbers.
$$-2$$

K Joseph

Numerade Educator

Problem 54

Give the opposite of each of the following numbers.
$$15$$

K Joseph

Numerade Educator

Problem 55

Give the opposite of each of the following numbers.
$$75$$

Cory Kuzinski

Numerade Educator

Problem 56

Give the opposite of each of the following numbers.
$$-32$$

K Joseph

Numerade Educator

Problem 57

Give the opposite of each of the following numbers.
$$0$$

James Kiss

Numerade Educator

Problem 58

Give the opposite of each of the following numbers.
$$1$$

K Joseph

Numerade Educator

Problem 59

Give the opposite of each of the following numbers.
$$-121$$

K Joseph

Numerade Educator

Problem 60

Give the opposite of each of the following numbers.
$$-200$$

Brittany Scott

Numerade Educator

Problem 61

Give the opposite of each of the following numbers.
$$555$$

K Joseph

Numerade Educator

Problem 62

Give the opposite of each of the following numbers.
$$125$$

K Joseph

Numerade Educator

Problem 63

Simplify each of the following.
$$-(-2)$$

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 64

Simplify each of the following.
$$-(-5)$$

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 65

Simplify each of the following.
$$-(-8)$$

Emma Chickles

Numerade Educator

Problem 66

Simplify each of the following.
$$-(-3)$$

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 67

Simplify each of the following.
$$-|-2|$$

K Joseph

Numerade Educator

Problem 68

Simplify each of the following.
$$-|-5|$$

Palitha Reddy

Numerade Educator

Problem 69

Simplify each of the following.
$$-|-8|$$

Karuna Ramroop

Numerade Educator

Problem 70

Simplify each of the following.
$$-|-3|$$

Pranav Sukumar

Numerade Educator

Problem 71

What number is its own opposite?

Karly Williams

Numerade Educator

Problem 72

Is $|a|=a$ always a true statement?

Margaret Farmer

Margaret Farmer

Numerade Educator

Problem 73

If $n$ is a negative number, is $-n$ positive or negative?

AG

Ankit Gupta

Numerade Educator

Problem 74

If $n$ is a positive number, is $-n$ positive or negative?

AG

Ankit Gupta

Numerade Educator

Problem 75

Without pencil and paper or a calculator.
Is $-60$ closer to 0 or $-100 ?$

Nick Johnson

Numerade Educator

Problem 76

Without pencil and paper or a calculator.
Is $-20$ closer to 0 or $-30 ?$

Nick Johnson

Numerade Educator

Problem 77

Without pencil and paper or a calculator.
Is $-10$ closer to $-20$ or $20 ?$

Dwijendra Rao

Numerade Educator

Problem 78

Without pencil and paper or a calculator.
Is $-20$ closer to $-40$ or $10 ?$

Ernest Castorena

Ernest Castorena

Numerade Educator

Problem 79

Without pencil and paper or a calculator.
Is $-362$ closer to $-360$ or $-370 ?$

Alicia Amason

Numerade Educator

Problem 80

Without pencil and paper or a calculator.
Is $-368$ closer to $-360$ or $-370 ?$

Ernest Castorena

Ernest Castorena

Numerade Educator

Problem 81

The London Eye has a height of 450 feet. Describe the location of someone standing on the ground in relation to someone at the top of the London Eye.

Prabhu Ramji

Numerade Educator

Problem 82

The Eiffel Tower has several levels visitors can walk around on. The first is 57 meters above the ground, the second is 115 meters high, and the third level is 276 meters high. What is the location of someone standing on the first level in relation to someone standing on the third level?

Julian Wong

Numerade Educator

Problem 83

The Bright Angel trail at Grand Canyon National Park ends at Indian Garden, $3,060$ feet below the trailhead. Write this as a negative number with respect to the trailhead.

Dani Dutmer

Numerade Educator

Problem 84

The South Kaibab Trail at Grand Canyon National Park ends at Cedar Ridge, $1,140$ feet below the trailhead. Write this as a negative number with respect to the trailhead.

Dani Dutmer

Numerade Educator

Problem 85

Depreciation refers to the decline in a car's market value during the time you own the car. According to sources such as Kelley Blue Book and Edmunds.com, not all cars depreciate at the same rate. Suppose you pay 25,000 dollars for a new car which has a high rate of depreciation. Your car loses about 5,000 dollars in value per year. Represent this loss in value as a negative number. A car with a low rate of depreciation loses about 2,750 dollars in value each year. Represent this loss as a negative number.

Harmender Singh Yadav

Harmender Singh Yadav

Numerade Educator

Problem 86

In June, 2007 the U.S. Census Bureau released population estimates for the twenty-five cities with the largest population loss between July $1,2005$ and July $1,2006 .$ New Orleans had the largest population loss. The city's population fell by $228,782$ people. Detroit, Michigan experienced a population loss of $12,344$ people during the same time period. Represent the loss of population for New Orleans and for Detroit as a negative number.

Vysakh M

Numerade Educator

Problem 87

Yamina is flying from Phoenix to San Francisco on a Boeing 737 jet. When the plane reaches an altitude of $33,000$ feet, the temperature outside the plane is 61 degrees below zero Fahrenheit. Represent this temperature with a negative number. If the temperature outside the plane gets warmer by 10 degrees, what will the new temperature be?

Amrita Bhasin

Numerade Educator

Problem 88

At 11: 00 in the morning in Superior, Wisconsin, Jim notices the temperature is 15 degrees below zero Fahrenheit. Write this temperature as a negative number. At noon it has warmed up by 8 degrees. What is the temperature at noon?

Erika Bustos

Numerade Educator

Problem 89

At 10: 00 in the morning in White Bear Lake, Minnesota, Zach notices the temperature is 5 degrees below zero Fahrenheit. Write this temperature as a negative number. By noon the temperature has dropped another 10 degrees. What is the temperature at noon?

Breanna Ollech

Numerade Educator

Problem 90

Steve is snorkeling in the ocean near his home in Maui. At one point he is 6 feet below the surface. Represent this situation with a negative number. If he descends another 6 feet, what negative number will represent his new position?

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 91

New Orleans, Louisiana, is 1 time zone west of New York City. Represent this time zone as a negative number, as discussed in the introduction to this chapter.

Yiming Zhang

Numerade Educator

Problem 92

Seattle, Washington, is 2 time zones west of New Orleans, Louisiana. Represent this time zone as a negative number, as discussed in the introduction to this chapter.

Jonathan Zhang

Numerade Educator

Problem 93

Find the wind chill temperature if the thermometer reads $25^{\circ} \mathrm{F}$ and the wind is blowing at 25 miles per hour.

Carson Merrill

Numerade Educator

Problem 94

Find the wind chill temperature if the thermometer reads $10^{\circ} \mathrm{F}$ and the wind is blowing at 25 miles per hour.

Amy Jiang

Numerade Educator

Problem 95

Which will feel colder: a day with an air temperature of $10^{\circ} \mathrm{F}$ and a 25 -mph wind, or a day with an air temperature of $-5^{\circ} \mathrm{F}$ and a $10-\mathrm{mph}$ wind?

Amy Jiang

Numerade Educator

Problem 96

Which will feel colder: a day with an air temperature of $15^{\circ} \mathrm{F}$ and a 20 -mph wind, or a day with an air temperature of $5^{\circ} \mathrm{F}$ and a $10-\mathrm{mph}$ wind?

Amy Jiang

Numerade Educator

Problem 97

Figure 5 is a bar chart of the information in Table $3 .$ Use the template in Figure 6 to construct a scatter diagram of the same information. Then connect the dots in the scatter diagram to obtain a line graph of that same information. (Notice that we have used the numbers 1 through 12 to represent the months January through December.) (GRAPH CANNOT COPY).

Norman Atentar

Numerade Educator

Problem 98

Figure 7 is a bar chart of the information in Table $4 .$ Use the template in Figure 8 to construct a scatter diagram of the same information. Then connect the dots in the scatter diagram to obtain a line graph of that same information. (Again, we have used the numbers 1 through 12 to represent the months January through December.) (GRAPH CANNOT COPY).

Kaitlin Yaeger

Numerade Educator

Problem 99

Add or subtract.
$$10+15$$

Jake Zanazzi

Numerade Educator

Problem 100

Add or subtract.
$$12+15$$

James Kiss

Numerade Educator

Problem 101

Add or subtract.
$$15-10$$

Debasish Das

Numerade Educator

Problem 102

Add or subtract.
$$15-12$$

James Kiss

Numerade Educator

Problem 103

Add or subtract.
$$10-5-3+4$$

SM

Sara Mendoza

Numerade Educator

Problem 104

Add or subtract.
$$12-3-7+5$$

Luke P

Numerade Educator

Problem 105

Add or subtract.
$$[3+10]+[8-2]$$

Narayan Hari

Numerade Educator

Problem 106

Add or subtract.
$$[2+12]+[7-5]$$

Luke P

Numerade Educator

Problem 107

Add or subtract.
$$276+32+4,005$$

Ashley Jordon

Numerade Educator

Problem 108

Add or subtract.
$$17+3+152+1,200$$

Jake Zanazzi

Numerade Educator

Problem 109

Add or subtract.
$$635-579$$

Michelle Nguyen

Michelle Nguyen

Numerade Educator

Problem 110

Add or subtract.
$$2,987-1,130$$

Luke P

Numerade Educator