Developmental Mathematics: Basic
Mathematics and Algebra – 4th Edition
ST
SOLUTIONS
UV
MANUAL
IA
_A
Margaret Lial
John Hornsby
PP
Terry McGinnis
Stanley Salzman
RO
Diana Hestwood
Comprehensive Solutions Manual for Instructors and
VE
Students
D?
© Margaret Lial, John Hornsby, Terry McGinnis, Stanley Salzman & Diana Hestwood
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Table of Contents
ST
1 Whole Numbers.............................................................................................................................1
1.1 Reading and Writing Whole Numbers • ......................................................... 1
1.2 Adding Whole Numbers • .............................................................................. 2
1.3 Subtracting Whole Numbers • ........................................................................ 9
UV
1.4 Multiplying Whole Numbers • ....................................................................... 16
1.5 Dividing Whole Numbers • ............................................................................ 24
1.6 Long Division • .............................................................................................. 30
1.7 Rounding Whole Numbers • ........................................................................... 36
1.8 Exponents, Roots, and Order of Operations • ................................................. 43
IA
1.9 Reading Pictographs, Bar Graphs, and Line Graphs • .................................... 47
1.10 Solving Application Problems • ..................................................................... 49
Chapter 1 Review Exercises • ......................................................................... 60
Chapter 1 Mixed Review Exercises • ............................................................. 68
_A
Chapter 1 Test • .............................................................................................. 70
2 Multiplying and Dividing Fractions.......................................................................................... 73
1.1 Basics of Fractions • ....................................................................................... 73
1.2 Mixed Numbers • ............................................................................................ 74
PP
1.3 Factors • .......................................................................................................... 81
1.4 Writing a Fraction in Lowest Terms • ............................................................ 88
1.5 Multiplying Fractions • ................................................................................... 92
1.6 Applications of Multiplication • ..................................................................... 96
1.7 Dividing Fractions • ........................................................................................ 100
RO
1.8 Multiplying and Dividing Mixed Numbers • .................................................. 104
Chapter 1 Review Exercises • ......................................................................... 110
Chapter 2 Mixed Review Exercises • ............................................................. 113
Chapter 1 Test • .............................................................................................. 114
3 Adding and Subtracting Fractions.......................................................................................... 117
VE
3.1 Adding and Subtracting Like Fractions • ....................................................... 117
3.2 Least Common Multiples • ............................................................................. 119
3.3 Adding and Subtracting Unlike Fractions • .................................................... 125
3.4 Adding and Subtracting Mixed Numbers • ..................................................... 130
D?
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
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Copyright © 2018 Pearson Education, Inc.
, 4 Decimals.....................................................................................................................................154
4.1 Reading and Writing Decimal Numbers • ...................................................... 154
4.2 Rounding Decimal Numbers • ........................................................................ 157
ST
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
UV
Chapter 4 Review Exercises • ......................................................................... 190
Chapter 4 Mixed Review Exercises • .............................................................. 194
Chapter 4 Test • .............................................................................................. 195
5 Ratio and Proportion................................................................................................................198
5.1 Ratios • ........................................................................................................... 198
5.2 Rates • ............................................................................................................. 202
IA
5.3 Proportions • ................................................................................................... 206
5.4 Solving Proportions • ...................................................................................... 210
5.5 Solving Application Problems with Proportions • .......................................... 216
_A
Chapter 5 Review Exercises • ......................................................................... 222
Chapter 5 Mixed Review Exercises • ............................................................. 226
Chapter 5 Test • .............................................................................................. 228
6 Percent....................................................................................................................................... 230
6.1 Basics of Percent • .......................................................................................... 230
PP
6.2 Percents and Fractions • .................................................................................. 234
6.3 Using the Percent Proportion and Identifying the Components
in a Percent Problem • .................................................................................... 241
6.4 Using Proportions to Solve Percent Problems • ............................................. 247
6.5 Using the Percent Equation • .......................................................................... 255
RO
6.6 Solving Application Problems with Percent • ................................................ 260
6.7 Simple Interest • ............................................................................................. 267
6.8 Compound Interest • ....................................................................................... 272
Chapter 6 Review Exercises • ......................................................................... 276
Chapter 6 Mixed Review Exercises • ............................................................. 280
VE
Chapter 6 Test • .............................................................................................. 282
7 Geometry................................................................................................................................... 285
7.1 Geometry: Lines and Angles • ........................................................................ 285
7.2 Rectangles and Squares • ................................................................................ 288
7.3 Parallelograms and Trapezoids • .................................................................... 294
D?
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
ST
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
UV
Chapter 8 Test • .............................................................................................. 340
Cumulative Review Exercises (Chapters 1–8) • ............................................. 342
9 The Real Number System.........................................................................................................349
9.1 Exponents, Order of Operations, and Inequality • .......................................... 349
9.2 Variables, Expressions, and Equations • ........................................................ 354
IA
9.3 Real Numbers and the Number Line • ............................................................ 361
9.4 Adding Real Numbers • .................................................................................. 365
9.5 Subtracting Real Numbers • ........................................................................... 370
9.6 Multiplying and Dividing Real Numbers • ..................................................... 376
_A
9.7 Properties of Real Numbers • ......................................................................... 383
9.8 Simplifying Expressions • .............................................................................. 388
Chapter 9 Review Exercises • ......................................................................... 393
Chapter 9 Mixed Review Exercises • ............................................................. 398
Chapter 9 Test • .............................................................................................. 399
PP
10 Equations, Inequalities, and Applications.............................................................................. 401
10.1 The Addition Property of Equality • ............................................................... 401
10.2 The Multiplication Property of Equality • ...................................................... 410
10.3 More on Solving Linear Equations • .............................................................. 419
RO
10.4 An Introduction to Applications of Linear Equations • .................................. 432
10.5 Formulas and Additional Applications from Geometry • ............................... 446
10.6 Solving Linear Inequalities • .......................................................................... 457
Chapter 10 Review Exercises • ....................................................................... 468
Chapter 10 Mixed Review Exercises • ........................................................... 472
VE
Chapter 10 Test • ............................................................................................ 474
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
D?
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.
Mathematics and Algebra – 4th Edition
ST
SOLUTIONS
UV
MANUAL
IA
_A
Margaret Lial
John Hornsby
PP
Terry McGinnis
Stanley Salzman
RO
Diana Hestwood
Comprehensive Solutions Manual for Instructors and
VE
Students
D?
© Margaret Lial, John Hornsby, Terry McGinnis, Stanley Salzman & Diana Hestwood
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©STUDYSTREAM
, Table of Contents
ST
1 Whole Numbers.............................................................................................................................1
1.1 Reading and Writing Whole Numbers • ......................................................... 1
1.2 Adding Whole Numbers • .............................................................................. 2
1.3 Subtracting Whole Numbers • ........................................................................ 9
UV
1.4 Multiplying Whole Numbers • ....................................................................... 16
1.5 Dividing Whole Numbers • ............................................................................ 24
1.6 Long Division • .............................................................................................. 30
1.7 Rounding Whole Numbers • ........................................................................... 36
1.8 Exponents, Roots, and Order of Operations • ................................................. 43
IA
1.9 Reading Pictographs, Bar Graphs, and Line Graphs • .................................... 47
1.10 Solving Application Problems • ..................................................................... 49
Chapter 1 Review Exercises • ......................................................................... 60
Chapter 1 Mixed Review Exercises • ............................................................. 68
_A
Chapter 1 Test • .............................................................................................. 70
2 Multiplying and Dividing Fractions.......................................................................................... 73
1.1 Basics of Fractions • ....................................................................................... 73
1.2 Mixed Numbers • ............................................................................................ 74
PP
1.3 Factors • .......................................................................................................... 81
1.4 Writing a Fraction in Lowest Terms • ............................................................ 88
1.5 Multiplying Fractions • ................................................................................... 92
1.6 Applications of Multiplication • ..................................................................... 96
1.7 Dividing Fractions • ........................................................................................ 100
RO
1.8 Multiplying and Dividing Mixed Numbers • .................................................. 104
Chapter 1 Review Exercises • ......................................................................... 110
Chapter 2 Mixed Review Exercises • ............................................................. 113
Chapter 1 Test • .............................................................................................. 114
3 Adding and Subtracting Fractions.......................................................................................... 117
VE
3.1 Adding and Subtracting Like Fractions • ....................................................... 117
3.2 Least Common Multiples • ............................................................................. 119
3.3 Adding and Subtracting Unlike Fractions • .................................................... 125
3.4 Adding and Subtracting Mixed Numbers • ..................................................... 130
D?
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
ST
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
UV
Chapter 4 Review Exercises • ......................................................................... 190
Chapter 4 Mixed Review Exercises • .............................................................. 194
Chapter 4 Test • .............................................................................................. 195
5 Ratio and Proportion................................................................................................................198
5.1 Ratios • ........................................................................................................... 198
5.2 Rates • ............................................................................................................. 202
IA
5.3 Proportions • ................................................................................................... 206
5.4 Solving Proportions • ...................................................................................... 210
5.5 Solving Application Problems with Proportions • .......................................... 216
_A
Chapter 5 Review Exercises • ......................................................................... 222
Chapter 5 Mixed Review Exercises • ............................................................. 226
Chapter 5 Test • .............................................................................................. 228
6 Percent....................................................................................................................................... 230
6.1 Basics of Percent • .......................................................................................... 230
PP
6.2 Percents and Fractions • .................................................................................. 234
6.3 Using the Percent Proportion and Identifying the Components
in a Percent Problem • .................................................................................... 241
6.4 Using Proportions to Solve Percent Problems • ............................................. 247
6.5 Using the Percent Equation • .......................................................................... 255
RO
6.6 Solving Application Problems with Percent • ................................................ 260
6.7 Simple Interest • ............................................................................................. 267
6.8 Compound Interest • ....................................................................................... 272
Chapter 6 Review Exercises • ......................................................................... 276
Chapter 6 Mixed Review Exercises • ............................................................. 280
VE
Chapter 6 Test • .............................................................................................. 282
7 Geometry................................................................................................................................... 285
7.1 Geometry: Lines and Angles • ........................................................................ 285
7.2 Rectangles and Squares • ................................................................................ 288
7.3 Parallelograms and Trapezoids • .................................................................... 294
D?
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
ST
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
UV
Chapter 8 Test • .............................................................................................. 340
Cumulative Review Exercises (Chapters 1–8) • ............................................. 342
9 The Real Number System.........................................................................................................349
9.1 Exponents, Order of Operations, and Inequality • .......................................... 349
9.2 Variables, Expressions, and Equations • ........................................................ 354
IA
9.3 Real Numbers and the Number Line • ............................................................ 361
9.4 Adding Real Numbers • .................................................................................. 365
9.5 Subtracting Real Numbers • ........................................................................... 370
9.6 Multiplying and Dividing Real Numbers • ..................................................... 376
_A
9.7 Properties of Real Numbers • ......................................................................... 383
9.8 Simplifying Expressions • .............................................................................. 388
Chapter 9 Review Exercises • ......................................................................... 393
Chapter 9 Mixed Review Exercises • ............................................................. 398
Chapter 9 Test • .............................................................................................. 399
PP
10 Equations, Inequalities, and Applications.............................................................................. 401
10.1 The Addition Property of Equality • ............................................................... 401
10.2 The Multiplication Property of Equality • ...................................................... 410
10.3 More on Solving Linear Equations • .............................................................. 419
RO
10.4 An Introduction to Applications of Linear Equations • .................................. 432
10.5 Formulas and Additional Applications from Geometry • ............................... 446
10.6 Solving Linear Inequalities • .......................................................................... 457
Chapter 10 Review Exercises • ....................................................................... 468
Chapter 10 Mixed Review Exercises • ........................................................... 472
VE
Chapter 10 Test • ............................................................................................ 474
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
D?
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.
