Developmental Mathematics with Applications
ST
and Visualization: Prealgebra, Beginning
Algebra, and Intermediate Algebra – 2nd Edition
UV
SOLUTIONS
IA
_A
MANUAL
PP
Gary K. Rockswold
RO
Comprehensive Solutions Manual for Instructors
VE
and Students
D?
© Gary K. Rockswold
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Contents
Mini-Lectures (ML)
ST
Chapter 1 .......................................................................................................................................... 1
Chapter 2 .......................................................................................................................................... 8
Chapter 3 ........................................................................................................................................ 14
Chapter 4 ........................................................................................................................................ 19
Chapter 5 ........................................................................................................................................ 29
Chapter 6 ........................................................................................................................................ 38
UV
Chapter 7 ........................................................................................................................................ 45
Chapter 8 ........................................................................................................................................ 52
Chapter 9 ........................................................................................................................................ 57
Chapter 10 ...................................................................................................................................... 63
Chapter 11 ...................................................................................................................................... 71
Chapter 12 ...................................................................................................................................... 77
IA
Chapter 13 ...................................................................................................................................... 84
Chapter 14 ...................................................................................................................................... 94
Chapter 15 .................................................................................................................................... 103
Chapter 16 .................................................................................................................................... 114
Chapter 17 .................................................................................................................................... 117
_A
Chapter 18 .................................................................................................................................... 128
Chapter 19 .................................................................................................................................... 135
Chapter 20 .................................................................................................................................... 145
Chapter 21 .................................................................................................................................... 151
Printable Test Forms (T)
PP
Chapter 1 .......................................................................................................................................... 1
Chapter 2 ........................................................................................................................................ 11
Chapter 3 ........................................................................................................................................ 21
Chapter 4 ........................................................................................................................................ 31
Chapter 5 ........................................................................................................................................ 47
Chapter 6 ........................................................................................................................................ 57
RO
Chapter 7 ........................................................................................................................................ 67
Chapter 8 ........................................................................................................................................ 83
Chapter 9 ...................................................................................................................................... 101
Chapter 10 .................................................................................................................................... 111
Chapter 11 .................................................................................................................................... 129
Chapter 12 .................................................................................................................................... 147
Chapter 13 .................................................................................................................................... 157
VE
Chapter 14 .................................................................................................................................... 167
Chapter 15 .................................................................................................................................... 179
Chapter 16 .................................................................................................................................... 197
Chapter 17 .................................................................................................................................... 213
Chapter 18 .................................................................................................................................... 223
D?
Chapter 19 .................................................................................................................................... 241
Chapter 20 .................................................................................................................................... 259
Chapter 21 .................................................................................................................................... 287
Answers to Chapter Tests ............................................................................................................. 303
Cumulative Review Exercises and Answers ................................................................................ 371
Final Exams and Answers ............................................................................................................ 447
??
Additional Instructor Resources (R)
Resources for Success ...................................................................................................................... 1
Group Activities and Answers.......................................................................................................... 5
Teaching Tips Correlated to Textbook Sections ............................................................................ 55
Graphing Calculator Resources .................................................................................................... 129
, Mini-Lecture 1.1 DEVELOPMENTAL MATHEMATICS
Introduction to Whole Numbers
Objectives:
ST
• Reviewing Natural Numbers and Whole Numbers
• Understanding Place Value
• Writing Whole Numbers in Word Form
•
UV
Writing Whole Numbers in Expanded Form
• Graphing Whole Numbers on the Number Line
o Graphing Whole Numbers
o Comparing Whole Numbers
• Reading Graphs and Tables
o Bar Graphs
o Line Graphs
IA
o Spider Charts
o Tables
Examples:
_A
1. Identify the whole number(s).
2
a) 9 b) 7 c) 0 d) 5.631
3
9
e) –3 f) 2.1 g) 4 h)
5
PP
2. Identify the place value of the digit 2 in each number.
a) 72,365 b) 126,301,840 c) 296,431,860,806
3. Write each number in word form.
RO
a) 5302 b) 3,643,112 c) 502,000,076,000
4. Write each number in standard form.
a) two million, three hundred thousand, three
b) thirty-eight billion, five hundred forty-one million, seventy four thousand, eight hundred two
VE
c) one hundred six trillion, four hundred two million
Teaching Notes:
D?
• Some ESL students may need extra help learning the number period vocabulary such as ones, thousands,
millions, billions, trillions, etc. They may be accustomed to using periods instead of commas in place value.
• Many examples of tables are available on the Internet. Assign students to find examples and ask them to
explain how to read the tables and write the numbers in words.
??
Answers: 1) choices a, c, and g are whole numbers; 2a) thousands, b) ten-millions, c) hundred-billions; 3a) five
thousand, three hundred two, b) three million, six hundred forty-three thousand, one hundred twelve, c) five hundred
two billion, seventy-six thousand; 4a) 2,300,003, b) 38,541,074,802, c) 106,000,402,000,000
ML-1
Copyright © 2018 Pearson Education, Inc.
, DEVELOPMENTAL MATHEMATICS Mini-Lecture 1.2
Adding and Subtracting Whole Numbers; Perimeter
Objectives:
ST
• Adding Whole Numbers
o Adding Whole Numbers without Regrouping
o Adding Whole Numbers with Regrouping
• Using Properties of Addition
UV
o Commutative Property
o Associative Property
o Identity Property
• Recognizing Words Associated with Addition
• Subtracting Whole Numbers
o Subtracting Whole Numbers without Regrouping
IA
o Subtracting Whole Numbers with Regrouping
• Using Properties of Subtraction
• Recognizing Words Associated with Subtraction
• Solving Equations Involving Addition and Subtraction
• Solving Perimeter and Other Applications Involving Addition and Subtraction
_A
Examples:
1. Add.
a) 5+ 3 b) 4+7 c) 8+9 d) 6+2
PP
e) 3+ 3 f) 6 + 4 + 3+ 7 g) 8+8+0+5
2. Add.
40,001 6505
53 1123 96 5678
32, 442 173
RO
a) + 12 b) + 345 c) d) + 47 e) + 3574 f)
+ 15,333 7044
+ 168
3. Solve each equation by finding the unknown value.
a) 13 − =8 b) − 14 = 3 c) 26 + = 54
VE
4. Subtract.
664 51 1123 40,001
a) 98 − 51 b) 54 − 22 c) d) e) f)
− 51 − 12 − 345 − 15, 333
5. Find the perimeter of a triangle with sides of length 12 ft, 22 ft, and 25 ft.
D?
Teaching Notes:
• Point out that the commutative property deals with the order of addends, whereas the associative property
deals with the grouping (order does not change) of addends.
??
• Have students practice basic subtraction facts. Some have trouble borrowing when zeros are involved.
Answers: 1a) 8, b) 11, c) 17, d) 8, e) 6, f) 20, g) 21; 2a) 65, b) 1468, c) 87,776, d) 143, e) 9252, f) 13,890; 3a) 4, b)
17, c) 28; 4a) 47, b) 32, c) 613, d) 39, e) 778, f) 24,668; 5) 59 ft
ML-2
Copyright © 2018 Pearson Education, Inc.
ST
and Visualization: Prealgebra, Beginning
Algebra, and Intermediate Algebra – 2nd Edition
UV
SOLUTIONS
IA
_A
MANUAL
PP
Gary K. Rockswold
RO
Comprehensive Solutions Manual for Instructors
VE
and Students
D?
© Gary K. Rockswold
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Contents
Mini-Lectures (ML)
ST
Chapter 1 .......................................................................................................................................... 1
Chapter 2 .......................................................................................................................................... 8
Chapter 3 ........................................................................................................................................ 14
Chapter 4 ........................................................................................................................................ 19
Chapter 5 ........................................................................................................................................ 29
Chapter 6 ........................................................................................................................................ 38
UV
Chapter 7 ........................................................................................................................................ 45
Chapter 8 ........................................................................................................................................ 52
Chapter 9 ........................................................................................................................................ 57
Chapter 10 ...................................................................................................................................... 63
Chapter 11 ...................................................................................................................................... 71
Chapter 12 ...................................................................................................................................... 77
IA
Chapter 13 ...................................................................................................................................... 84
Chapter 14 ...................................................................................................................................... 94
Chapter 15 .................................................................................................................................... 103
Chapter 16 .................................................................................................................................... 114
Chapter 17 .................................................................................................................................... 117
_A
Chapter 18 .................................................................................................................................... 128
Chapter 19 .................................................................................................................................... 135
Chapter 20 .................................................................................................................................... 145
Chapter 21 .................................................................................................................................... 151
Printable Test Forms (T)
PP
Chapter 1 .......................................................................................................................................... 1
Chapter 2 ........................................................................................................................................ 11
Chapter 3 ........................................................................................................................................ 21
Chapter 4 ........................................................................................................................................ 31
Chapter 5 ........................................................................................................................................ 47
Chapter 6 ........................................................................................................................................ 57
RO
Chapter 7 ........................................................................................................................................ 67
Chapter 8 ........................................................................................................................................ 83
Chapter 9 ...................................................................................................................................... 101
Chapter 10 .................................................................................................................................... 111
Chapter 11 .................................................................................................................................... 129
Chapter 12 .................................................................................................................................... 147
Chapter 13 .................................................................................................................................... 157
VE
Chapter 14 .................................................................................................................................... 167
Chapter 15 .................................................................................................................................... 179
Chapter 16 .................................................................................................................................... 197
Chapter 17 .................................................................................................................................... 213
Chapter 18 .................................................................................................................................... 223
D?
Chapter 19 .................................................................................................................................... 241
Chapter 20 .................................................................................................................................... 259
Chapter 21 .................................................................................................................................... 287
Answers to Chapter Tests ............................................................................................................. 303
Cumulative Review Exercises and Answers ................................................................................ 371
Final Exams and Answers ............................................................................................................ 447
??
Additional Instructor Resources (R)
Resources for Success ...................................................................................................................... 1
Group Activities and Answers.......................................................................................................... 5
Teaching Tips Correlated to Textbook Sections ............................................................................ 55
Graphing Calculator Resources .................................................................................................... 129
, Mini-Lecture 1.1 DEVELOPMENTAL MATHEMATICS
Introduction to Whole Numbers
Objectives:
ST
• Reviewing Natural Numbers and Whole Numbers
• Understanding Place Value
• Writing Whole Numbers in Word Form
•
UV
Writing Whole Numbers in Expanded Form
• Graphing Whole Numbers on the Number Line
o Graphing Whole Numbers
o Comparing Whole Numbers
• Reading Graphs and Tables
o Bar Graphs
o Line Graphs
IA
o Spider Charts
o Tables
Examples:
_A
1. Identify the whole number(s).
2
a) 9 b) 7 c) 0 d) 5.631
3
9
e) –3 f) 2.1 g) 4 h)
5
PP
2. Identify the place value of the digit 2 in each number.
a) 72,365 b) 126,301,840 c) 296,431,860,806
3. Write each number in word form.
RO
a) 5302 b) 3,643,112 c) 502,000,076,000
4. Write each number in standard form.
a) two million, three hundred thousand, three
b) thirty-eight billion, five hundred forty-one million, seventy four thousand, eight hundred two
VE
c) one hundred six trillion, four hundred two million
Teaching Notes:
D?
• Some ESL students may need extra help learning the number period vocabulary such as ones, thousands,
millions, billions, trillions, etc. They may be accustomed to using periods instead of commas in place value.
• Many examples of tables are available on the Internet. Assign students to find examples and ask them to
explain how to read the tables and write the numbers in words.
??
Answers: 1) choices a, c, and g are whole numbers; 2a) thousands, b) ten-millions, c) hundred-billions; 3a) five
thousand, three hundred two, b) three million, six hundred forty-three thousand, one hundred twelve, c) five hundred
two billion, seventy-six thousand; 4a) 2,300,003, b) 38,541,074,802, c) 106,000,402,000,000
ML-1
Copyright © 2018 Pearson Education, Inc.
, DEVELOPMENTAL MATHEMATICS Mini-Lecture 1.2
Adding and Subtracting Whole Numbers; Perimeter
Objectives:
ST
• Adding Whole Numbers
o Adding Whole Numbers without Regrouping
o Adding Whole Numbers with Regrouping
• Using Properties of Addition
UV
o Commutative Property
o Associative Property
o Identity Property
• Recognizing Words Associated with Addition
• Subtracting Whole Numbers
o Subtracting Whole Numbers without Regrouping
IA
o Subtracting Whole Numbers with Regrouping
• Using Properties of Subtraction
• Recognizing Words Associated with Subtraction
• Solving Equations Involving Addition and Subtraction
• Solving Perimeter and Other Applications Involving Addition and Subtraction
_A
Examples:
1. Add.
a) 5+ 3 b) 4+7 c) 8+9 d) 6+2
PP
e) 3+ 3 f) 6 + 4 + 3+ 7 g) 8+8+0+5
2. Add.
40,001 6505
53 1123 96 5678
32, 442 173
RO
a) + 12 b) + 345 c) d) + 47 e) + 3574 f)
+ 15,333 7044
+ 168
3. Solve each equation by finding the unknown value.
a) 13 − =8 b) − 14 = 3 c) 26 + = 54
VE
4. Subtract.
664 51 1123 40,001
a) 98 − 51 b) 54 − 22 c) d) e) f)
− 51 − 12 − 345 − 15, 333
5. Find the perimeter of a triangle with sides of length 12 ft, 22 ft, and 25 ft.
D?
Teaching Notes:
• Point out that the commutative property deals with the order of addends, whereas the associative property
deals with the grouping (order does not change) of addends.
??
• Have students practice basic subtraction facts. Some have trouble borrowing when zeros are involved.
Answers: 1a) 8, b) 11, c) 17, d) 8, e) 6, f) 20, g) 21; 2a) 65, b) 1468, c) 87,776, d) 143, e) 9252, f) 13,890; 3a) 4, b)
17, c) 28; 4a) 47, b) 32, c) 613, d) 39, e) 778, f) 24,668; 5) 59 ft
ML-2
Copyright © 2018 Pearson Education, Inc.
