INSTRUCTOR’S
SOLUTIONS MANUAL
BEVERLY FUSFIELD
M
E
D EVELOPMENTAL M ATHEMATICS
D
C
B ASIC M ATHEMATICS AND A LGEBRA
FOURTH EDITION
O
N
N
Margaret L. Lial
O
American River College
S I
John Hornsby
S
University of New Orleans
E
Terry McGinnis
U
R
Stanley A. Salzman
American River College
Diana L. Hestwood
Minneapolis Community and Technical College
, Table of Contents
1 Whole Numbers.............................................................................................................................1
1.1 Reading and Writing Whole Numbers • ......................................................... 1
1.2 Adding Whole Numbers • .............................................................................. 2
1.3 Subtracting Whole Numbers • ........................................................................ 9
1.4 Multiplying Whole Numbers • ....................................................................... 16
M
1.5 Dividing Whole Numbers • ............................................................................ 24
1.6 Long Division • .............................................................................................. 30
E
1.7 Rounding Whole Numbers • ........................................................................... 36
1.8 Exponents, Roots, and Order of Operations • ................................................. 43
D
1.9 Reading Pictographs, Bar Graphs, and Line Graphs • .................................... 47
1.10 Solving Application Problems • ..................................................................... 49
C
Chapter 1 Review Exercises • ......................................................................... 60
Chapter 1 Mixed Review Exercises • ............................................................. 68
O
Chapter 1 Test • .............................................................................................. 70
2 Multiplying and Dividing Fractions.......................................................................................... 73
1.1
N
Basics of Fractions • ....................................................................................... 73
1.2 Mixed Numbers • ............................................................................................ 74
N
1.3 Factors • .......................................................................................................... 81
O
1.4 Writing a Fraction in Lowest Terms • ............................................................ 88
1.5 Multiplying Fractions • ................................................................................... 92
I
1.6 Applications of Multiplication • ..................................................................... 96
S
1.7 Dividing Fractions • ........................................................................................ 100
1.8 Multiplying and Dividing Mixed Numbers • .................................................. 104
S
Chapter 1 Review Exercises • ......................................................................... 110
Chapter 2 Mixed Review Exercises • ............................................................. 113
E
Chapter 1 Test • .............................................................................................. 114
U
3 Adding and Subtracting Fractions.......................................................................................... 117
3.1 Adding and Subtracting Like Fractions • ....................................................... 117
R
3.2 Least Common Multiples • ............................................................................. 119
3.3 Adding and Subtracting Unlike Fractions • .................................................... 125
3.4 Adding and Subtracting Mixed Numbers • ..................................................... 130
3.5 Order Relations and the Order of Operations • ............................................... 140
Chapter 3 Review Exercises • ......................................................................... 146
Chapter 3 Mixed Review Exercises • .............................................................. 150
Chapter 3 Test • .............................................................................................. 152
Copyright © 2018 Pearson Education, Inc.
,4 Decimals.....................................................................................................................................154
4.1 Reading and Writing Decimal Numbers • ...................................................... 154
4.2 Rounding Decimal Numbers • ........................................................................ 157
4.3 Adding and Subtracting Decimal Numbers • ................................................. 162
4.4 Multiplying Decimal Numbers • ..................................................................... 168
4.5 Dividing Decimal Numbers • ......................................................................... 174
4.6 Fractions and Decimals • ................................................................................ 183
Chapter 4 Review Exercises • ......................................................................... 190
Chapter 4 Mixed Review Exercises • .............................................................. 194
M
Chapter 4 Test • .............................................................................................. 195
5 Ratio and Proportion................................................................................................................198
E
5.1 Ratios • ........................................................................................................... 198
5.2 Rates • ............................................................................................................. 202
D
5.3 Proportions • ................................................................................................... 206
5.4 Solving Proportions • ...................................................................................... 210
C
5.5 Solving Application Problems with Proportions • .......................................... 216
Chapter 5 Review Exercises • ......................................................................... 222
O
Chapter 5 Mixed Review Exercises • ............................................................. 226
Chapter 5 Test • .............................................................................................. 228
N
6 Percent....................................................................................................................................... 230
N
6.1 Basics of Percent • .......................................................................................... 230
6.2 Percents and Fractions • .................................................................................. 234
O
6.3 Using the Percent Proportion and Identifying the Components
in a Percent Problem • .................................................................................... 241
I
6.4 Using Proportions to Solve Percent Problems • ............................................. 247
S
6.5 Using the Percent Equation • .......................................................................... 255
6.6 Solving Application Problems with Percent • ................................................ 260
S
6.7 Simple Interest • ............................................................................................. 267
6.8 Compound Interest • ....................................................................................... 272
E
Chapter 6 Review Exercises • ......................................................................... 276
Chapter 6 Mixed Review Exercises • ............................................................. 280
U
Chapter 6 Test • .............................................................................................. 282
R
7 Geometry................................................................................................................................... 285
7.1 Geometry: Lines and Angles • ........................................................................ 285
7.2 Rectangles and Squares • ................................................................................ 288
7.3 Parallelograms and Trapezoids • .................................................................... 294
7.4 Triangles • ....................................................................................................... 296
7.5 Circles • .......................................................................................................... 299
7.6 Volume and Surface Area • ............................................................................ 304
7.7 Pythagorean Theorem • .................................................................................. 308
7.8 Congruent and Similar Triangles • ................................................................. 312
Chapter 7 Review Exercises • ......................................................................... 316
Chapter 7 Mixed Review Exercises • ............................................................. 321
Chapter 7 Test • .............................................................................................. 323
Copyright © 2018 Pearson Education, Inc.
, 8 Statistics..................................................................................................................................... 325
8.1 Circle Graphs • ............................................................................................... 325
8.2 Bar Graphs and Line Graphs • ........................................................................ 329
8.3 Frequency Distributions and Histograms • ..................................................... 332
8.4 Mean, Median, and Mode • ............................................................................ 333
Chapter 8 Review Exercises • ......................................................................... 337
Chapter 8 Mixed Review Exercises • ............................................................. 339
Chapter 8 Test • .............................................................................................. 340
Cumulative Review Exercises (Chapters 1–8) • ............................................. 342
M
9 The Real Number System.........................................................................................................349
9.1 Exponents, Order of Operations, and Inequality • .......................................... 349
E
9.2 Variables, Expressions, and Equations • ........................................................ 354
D
9.3 Real Numbers and the Number Line • ............................................................ 361
9.4 Adding Real Numbers • .................................................................................. 365
C
9.5 Subtracting Real Numbers • ........................................................................... 370
9.6 Multiplying and Dividing Real Numbers • ..................................................... 376
O
9.7 Properties of Real Numbers • ......................................................................... 383
9.8 Simplifying Expressions • .............................................................................. 388
N
Chapter 9 Review Exercises • ......................................................................... 393
Chapter 9 Mixed Review Exercises • ............................................................. 398
N
Chapter 9 Test • .............................................................................................. 399
10 Equations, Inequalities, and Applications.............................................................................. 401
O
10.1 The Addition Property of Equality • ............................................................... 401
10.2 The Multiplication Property of Equality • ...................................................... 410
S I
10.3 More on Solving Linear Equations • .............................................................. 419
10.4 An Introduction to Applications of Linear Equations • .................................. 432
S
10.5 Formulas and Additional Applications from Geometry • ............................... 446
10.6 Solving Linear Inequalities • .......................................................................... 457
E
Chapter 10 Review Exercises • ....................................................................... 468
Chapter 10 Mixed Review Exercises • ........................................................... 472
U
Chapter 10 Test • ............................................................................................ 474
R
11 Graphs of Linear Equations and Inequalities in Two Variables..........................................477
11.1 Linear Equations and Rectangular Coordinates • ........................................... 477
11.2 Graphing Linear Equations in Two Variables • .............................................. 487
11.3 The Slope of a Line • ...................................................................................... 500
11.4 Slope-Intercept Form of a Linear Equation • .................................................. 508
11.5 Point-Slope Form of a Linear Equation and Modeling • ................................ 518
11.6 Graphing Linear Inequalities in Two Variables • ........................................... 526
Chapter 11 Review Exercises • ....................................................................... 534
Chapter 11 Mixed Review Exercises • ........................................................... 539
Chapter 11 Test • ............................................................................................ 541
Copyright © 2018 Pearson Education, Inc.
SOLUTIONS MANUAL
BEVERLY FUSFIELD
M
E
D EVELOPMENTAL M ATHEMATICS
D
C
B ASIC M ATHEMATICS AND A LGEBRA
FOURTH EDITION
O
N
N
Margaret L. Lial
O
American River College
S I
John Hornsby
S
University of New Orleans
E
Terry McGinnis
U
R
Stanley A. Salzman
American River College
Diana L. Hestwood
Minneapolis Community and Technical College
, Table of Contents
1 Whole Numbers.............................................................................................................................1
1.1 Reading and Writing Whole Numbers • ......................................................... 1
1.2 Adding Whole Numbers • .............................................................................. 2
1.3 Subtracting Whole Numbers • ........................................................................ 9
1.4 Multiplying Whole Numbers • ....................................................................... 16
M
1.5 Dividing Whole Numbers • ............................................................................ 24
1.6 Long Division • .............................................................................................. 30
E
1.7 Rounding Whole Numbers • ........................................................................... 36
1.8 Exponents, Roots, and Order of Operations • ................................................. 43
D
1.9 Reading Pictographs, Bar Graphs, and Line Graphs • .................................... 47
1.10 Solving Application Problems • ..................................................................... 49
C
Chapter 1 Review Exercises • ......................................................................... 60
Chapter 1 Mixed Review Exercises • ............................................................. 68
O
Chapter 1 Test • .............................................................................................. 70
2 Multiplying and Dividing Fractions.......................................................................................... 73
1.1
N
Basics of Fractions • ....................................................................................... 73
1.2 Mixed Numbers • ............................................................................................ 74
N
1.3 Factors • .......................................................................................................... 81
O
1.4 Writing a Fraction in Lowest Terms • ............................................................ 88
1.5 Multiplying Fractions • ................................................................................... 92
I
1.6 Applications of Multiplication • ..................................................................... 96
S
1.7 Dividing Fractions • ........................................................................................ 100
1.8 Multiplying and Dividing Mixed Numbers • .................................................. 104
S
Chapter 1 Review Exercises • ......................................................................... 110
Chapter 2 Mixed Review Exercises • ............................................................. 113
E
Chapter 1 Test • .............................................................................................. 114
U
3 Adding and Subtracting Fractions.......................................................................................... 117
3.1 Adding and Subtracting Like Fractions • ....................................................... 117
R
3.2 Least Common Multiples • ............................................................................. 119
3.3 Adding and Subtracting Unlike Fractions • .................................................... 125
3.4 Adding and Subtracting Mixed Numbers • ..................................................... 130
3.5 Order Relations and the Order of Operations • ............................................... 140
Chapter 3 Review Exercises • ......................................................................... 146
Chapter 3 Mixed Review Exercises • .............................................................. 150
Chapter 3 Test • .............................................................................................. 152
Copyright © 2018 Pearson Education, Inc.
,4 Decimals.....................................................................................................................................154
4.1 Reading and Writing Decimal Numbers • ...................................................... 154
4.2 Rounding Decimal Numbers • ........................................................................ 157
4.3 Adding and Subtracting Decimal Numbers • ................................................. 162
4.4 Multiplying Decimal Numbers • ..................................................................... 168
4.5 Dividing Decimal Numbers • ......................................................................... 174
4.6 Fractions and Decimals • ................................................................................ 183
Chapter 4 Review Exercises • ......................................................................... 190
Chapter 4 Mixed Review Exercises • .............................................................. 194
M
Chapter 4 Test • .............................................................................................. 195
5 Ratio and Proportion................................................................................................................198
E
5.1 Ratios • ........................................................................................................... 198
5.2 Rates • ............................................................................................................. 202
D
5.3 Proportions • ................................................................................................... 206
5.4 Solving Proportions • ...................................................................................... 210
C
5.5 Solving Application Problems with Proportions • .......................................... 216
Chapter 5 Review Exercises • ......................................................................... 222
O
Chapter 5 Mixed Review Exercises • ............................................................. 226
Chapter 5 Test • .............................................................................................. 228
N
6 Percent....................................................................................................................................... 230
N
6.1 Basics of Percent • .......................................................................................... 230
6.2 Percents and Fractions • .................................................................................. 234
O
6.3 Using the Percent Proportion and Identifying the Components
in a Percent Problem • .................................................................................... 241
I
6.4 Using Proportions to Solve Percent Problems • ............................................. 247
S
6.5 Using the Percent Equation • .......................................................................... 255
6.6 Solving Application Problems with Percent • ................................................ 260
S
6.7 Simple Interest • ............................................................................................. 267
6.8 Compound Interest • ....................................................................................... 272
E
Chapter 6 Review Exercises • ......................................................................... 276
Chapter 6 Mixed Review Exercises • ............................................................. 280
U
Chapter 6 Test • .............................................................................................. 282
R
7 Geometry................................................................................................................................... 285
7.1 Geometry: Lines and Angles • ........................................................................ 285
7.2 Rectangles and Squares • ................................................................................ 288
7.3 Parallelograms and Trapezoids • .................................................................... 294
7.4 Triangles • ....................................................................................................... 296
7.5 Circles • .......................................................................................................... 299
7.6 Volume and Surface Area • ............................................................................ 304
7.7 Pythagorean Theorem • .................................................................................. 308
7.8 Congruent and Similar Triangles • ................................................................. 312
Chapter 7 Review Exercises • ......................................................................... 316
Chapter 7 Mixed Review Exercises • ............................................................. 321
Chapter 7 Test • .............................................................................................. 323
Copyright © 2018 Pearson Education, Inc.
, 8 Statistics..................................................................................................................................... 325
8.1 Circle Graphs • ............................................................................................... 325
8.2 Bar Graphs and Line Graphs • ........................................................................ 329
8.3 Frequency Distributions and Histograms • ..................................................... 332
8.4 Mean, Median, and Mode • ............................................................................ 333
Chapter 8 Review Exercises • ......................................................................... 337
Chapter 8 Mixed Review Exercises • ............................................................. 339
Chapter 8 Test • .............................................................................................. 340
Cumulative Review Exercises (Chapters 1–8) • ............................................. 342
M
9 The Real Number System.........................................................................................................349
9.1 Exponents, Order of Operations, and Inequality • .......................................... 349
E
9.2 Variables, Expressions, and Equations • ........................................................ 354
D
9.3 Real Numbers and the Number Line • ............................................................ 361
9.4 Adding Real Numbers • .................................................................................. 365
C
9.5 Subtracting Real Numbers • ........................................................................... 370
9.6 Multiplying and Dividing Real Numbers • ..................................................... 376
O
9.7 Properties of Real Numbers • ......................................................................... 383
9.8 Simplifying Expressions • .............................................................................. 388
N
Chapter 9 Review Exercises • ......................................................................... 393
Chapter 9 Mixed Review Exercises • ............................................................. 398
N
Chapter 9 Test • .............................................................................................. 399
10 Equations, Inequalities, and Applications.............................................................................. 401
O
10.1 The Addition Property of Equality • ............................................................... 401
10.2 The Multiplication Property of Equality • ...................................................... 410
S I
10.3 More on Solving Linear Equations • .............................................................. 419
10.4 An Introduction to Applications of Linear Equations • .................................. 432
S
10.5 Formulas and Additional Applications from Geometry • ............................... 446
10.6 Solving Linear Inequalities • .......................................................................... 457
E
Chapter 10 Review Exercises • ....................................................................... 468
Chapter 10 Mixed Review Exercises • ........................................................... 472
U
Chapter 10 Test • ............................................................................................ 474
R
11 Graphs of Linear Equations and Inequalities in Two Variables..........................................477
11.1 Linear Equations and Rectangular Coordinates • ........................................... 477
11.2 Graphing Linear Equations in Two Variables • .............................................. 487
11.3 The Slope of a Line • ...................................................................................... 500
11.4 Slope-Intercept Form of a Linear Equation • .................................................. 508
11.5 Point-Slope Form of a Linear Equation and Modeling • ................................ 518
11.6 Graphing Linear Inequalities in Two Variables • ........................................... 526
Chapter 11 Review Exercises • ....................................................................... 534
Chapter 11 Mixed Review Exercises • ........................................................... 539
Chapter 11 Test • ............................................................................................ 541
Copyright © 2018 Pearson Education, Inc.
