# Solution Manual For Developmental Math 3rd Edition By Lial

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Edition: 3rd Edition

Resource Type: Solution Manual

## Solution Manual For Developmental Math 3rd Edition By Lial

ISBN-10: 0321900375, ISBN-13: 978-0321900371

1 Whole Numbers………………………………………………………………………………………………………… 1
1.1 Reading and Writing Whole Numbers • ………………………………………………… 1
1.2 Adding Whole Numbers • ……………………………………………………………………. 2
1.3 Subtracting Whole Numbers • ……………………………………………………………… 8
1.4 Multiplying Whole Numbers • ……………………………………………………………… 14
1.5 Dividing Whole Numbers • ………………………………………………………………….. 22
1.6 Long Division • ………………………………………………………………………………….. 28
1.7 Rounding Whole Numbers • ………………………………………………………………… 33
1.8 Exponents, Roots, and Order of Operations • …………………………………………. 40
1.9 Reading Pictographs, Bar Graphs, and Line Graphs • ……………………………… 44
1.10 Solving Application Problems • ……………………………………………………………. 46
Chapter 1 Review Exercises • ………………………………………………………………. 54
Chapter 1 Test • …………………………………………………………………………………. 63
2 Multiplying and Dividing Fractions…………………………………………………………………………. 65
2.1 Basics of Fractions • …………………………………………………………………………… 65
2.2 Mixed Numbers • ……………………………………………………………………………….. 66
2.3 Factors • ……………………………………………………………………………………………. 72
2.4 Writing a Fraction in Lowest Terms • ……………………………………………………. 80
2.5 Multiplying Fractions • ……………………………………………………………………….. 83
2.6 Applications of Multiplication • ……………………………………………………………. 86
2.7 Dividing Fractions • ……………………………………………………………………………. 90
2.8 Multiplying and Dividing Mixed Numbers • ………………………………………….. 93
Chapter 2 Review Exercises • ………………………………………………………………. 98
Chapter 2 Test • …………………………………………………………………………………. 102
3 Adding and Subtracting Fractions…………………………………………………………………………. 105
3.1 Adding and Subtracting Like Fractions • ……………………………………………….. 105
3.2 Least Common Multiples • ………………………………………………………………….. 107
3.3 Adding and Subtracting Unlike Fractions • ……………………………………………. 113
3.4 Adding and Subtracting Mixed Numbers • …………………………………………….. 117
3.5 Order Relations and the Order of Operations • ……………………………………….. 127
Chapter 3 Review Exercises • ………………………………………………………………. 132
Chapter 3 Test • …………………………………………………………………………………. 138
4 Decimals……………………………………………………………………………………………………………….. 141
4.1 Reading and Writing Decimal Numbers • ………………………………………………. 141
4.2 Rounding Decimal Numbers • ……………………………………………………………… 144
4.3 Adding and Subtracting Decimal Numbers • ………………………………………….. 149
4.4 Multiplying Decimal Numbers • …………………………………………………………… 154
4.5 Dividing Decimal Numbers • ……………………………………………………………….. 160
4.6 Fractions and Decimals • …………………………………………………………………….. 169
Chapter 4 Review Exercises • ………………………………………………………………. 174
Chapter 4 Test • …………………………………………………………………………………. 180
5 Ratio and Proportion…………………………………………………………………………………………….. 183
5.1 Ratios • ……………………………………………………………………………………………… 183
5.2 Rates • ………………………………………………………………………………………………. 186
5.3 Proportions • ……………………………………………………………………………………… 190
5.4 Solving Proportions • ………………………………………………………………………….. 193
5.5 Solving Application Problems with Proportions • …………………………………… 199
Chapter 5 Review Exercises • ………………………………………………………………. 205
Chapter 5 Test • …………………………………………………………………………………. 210
6 Percent…………………………………………………………………………………………………………………..213
6.1 Basics of Percent • ……………………………………………………………………………… 213
6.2 Percents and Fractions • ………………………………………………………………………. 217
6.3 Using the Percent Proportion and Identifying the Components
in a Percent Problem • ………………………………………………………………………… 223
6.4 Using Proportions to Solve Percent Problems • ………………………………………. 229
6.5 Using the Percent Equation • ……………………………………………………………….. 236
6.6 Solving Application Problems with Percent • …………………………………………. 241
6.7 Simple Interest • …………………………………………………………………………………. 247
6.8 Compound Interest • …………………………………………………………………………… 252
Chapter 6 Review Exercises • ………………………………………………………………. 256
Chapter 6 Test • …………………………………………………………………………………. 262
7 Geometry……………………………………………………………………………………………………………….265
7.1 Lines and Angles • ……………………………………………………………………………… 265
7.2 Rectangles and Squares • …………………………………………………………………….. 268
7.3 Parallelograms and Trapezoids • ………………………………………………………….. 273
7.4 Triangles • …………………………………………………………………………………………. 275
7.5 Circles • ……………………………………………………………………………………………. 278
7.6 Volume and Surface Area • ………………………………………………………………….. 282
7.7 Pythagorean Theorem • ……………………………………………………………………….. 286
7.8 Congruent and Similar Triangles • ………………………………………………………… 289
Chapter 7 Review Exercises • ………………………………………………………………. 293
Chapter 7 Test • …………………………………………………………………………………. 300
8 Statistics……………………………………………………………………………………………………………….. 303
8.1 Circle Graphs • …………………………………………………………………………………… 303
8.2 Bar Graphs and Line Graphs • ……………………………………………………………… 307
8.3 Frequency Distributions and Histograms • ……………………………………………… 309
8.4 Mean, Median, and Mode • ………………………………………………………………….. 310
Chapter 8 Review Exercises • ………………………………………………………………. 314
Chapter 8 Test • …………………………………………………………………………………. 317
Cumulative Review Exercises (Chapters 1–8) • ………………………………………. 319
9 The Real Number System………………………………………………………………………………………. 325
9.1 Exponents, Order of Operations, and Inequality • …………………………………… 325
9.2 Variables, Expressions, and Equations • ………………………………………………… 329
9.3 Real Numbers and the Number Line • …………………………………………………… 335
9.4 Adding Real Numbers • ………………………………………………………………………. 339
9.5 Subtracting Real Numbers • …………………………………………………………………. 344
9.6 Multiplying and Dividing Real Numbers • …………………………………………….. 349
9.7 Properties of Real Numbers • ……………………………………………………………….. 355
9.8 Simplifying Expressions • ……………………………………………………………………. 359
Chapter 9 Review Exercises • ………………………………………………………………. 363
Chapter 9 Test • …………………………………………………………………………………. 368
10 Equations, Inequalities, and Applications………………………………………………………………..371
10.1 The Addition Property of Equality • ……………………………………………………… 371
10.2 The Multiplication Property of Equality • ………………………………………………. 378
10.3 More on Solving Linear Equations • ……………………………………………………… 384
10.4 An Introduction to Applications of Linear Equations • …………………………….. 395
10.5 Formulas and Additional Applications from Geometry • ………………………….. 407
10.6 Solving Linear Inequalities • ………………………………………………………………… 416
Chapter 10 Review Exercises • …………………………………………………………….. 426
Chapter 10 Test • ……………………………………………………………………………….. 431
11 Graphs of Linear Equations and Inequalities in Two Variables………………………………..435
11.1 Linear Equations in Two Variables; The Rectangular Coordinate System • … 435
11.2 Graphing Linear Equations in Two Variables • ………………………………………. 445
11.3 The Slope of a Line • ………………………………………………………………………….. 456
11.4 Writing and Graphing Equations of Lines • ……………………………………………. 462
11.5 Graphing Linear Inequalities in Two Variables • …………………………………….. 473
Chapter 11 Review Exercises • …………………………………………………………….. 479
Chapter 11 Test • ……………………………………………………………………………….. 486
12 Exponents and Polynomials…………………………………………………………………………………….489
12.1 Adding and Subtracting Polynomials • ………………………………………………….. 489
12.2 The Product Rule and Power Rules for Exponents • ………………………………… 495
12.3 Multiplying Polynomials • …………………………………………………………………… 500
12.4 Special Products • ………………………………………………………………………………. 506
12.5 Integer Exponents and the Quotient Rule • …………………………………………….. 511
12.6 Dividing a Polynomial by a Monomial • ………………………………………………… 516
12.7 Dividing a Polynomial by a Polynomial • ………………………………………………. 519
12.8 An Application of Exponents: Scientific Notation • ………………………………… 524
Chapter 12 Review Exercises • …………………………………………………………….. 529
Chapter 12 Test • ……………………………………………………………………………….. 535
13 Factoring and Applications……………………………………………………………………………………. 539
13.1 Factors; The Greatest Common Factor • ………………………………………………… 539
13.2 Factoring Trinomials • ………………………………………………………………………… 545
13.3 Factoring Trinomials by Grouping • ……………………………………………………… 552
13.4 Factoring Trinomials by Using the FOIL Method • …………………………………. 556
13.5 Special Factoring Techniques • …………………………………………………………….. 563
13.6 A General Approach to Factoring • ………………………………………………………. 570
13.7 Solving Quadratic Equations by Factoring • …………………………………………… 573
13.8 Applications of Quadratic Equations • …………………………………………………… 581
Chapter 13 Review Exercises • …………………………………………………………….. 589
Chapter 13 Test • ……………………………………………………………………………….. 595
14 Rational Expressions and Applications…………………………………………………………………… 599
14.1 The Fundamental Property of Rational Expressions • ……………………………… 599
14.2 Multiplying and Dividing Rational Expressions • ……………………………………. 605
14.3 Least Common Denominators • ……………………………………………………………. 610
14.4 Adding and Subtracting Rational Expressions • ……………………………………… 615
14.5 Complex Fractions • …………………………………………………………………………… 627
14.6 Solving Equations with Rational Expressions • ………………………………………. 633
14.7 Applications of Rational Expressions • ………………………………………………….. 645
14.8 Variation • …………………………………………………………………………………………. 654
Chapter 14 Review Exercises • …………………………………………………………….. 657
Chapter 14 Test • ……………………………………………………………………………….. 666
15 Systems of Linear Equations and Inequalities………………………………………………………….671
15.1 Solving Systems of Linear Equations by Graphing • ……………………………….. 671
15.2 Solving Systems of Linear Equations by Substitution • ……………………………. 680
15.3 Solving Systems of Linear Equations by Elimination • …………………………….. 689
15.4 Applications of Linear Systems • ………………………………………………………….. 698
15.5 Solving Systems of Linear Inequalities • ……………………………………………….. 711
Chapter 15 Review Exercises • …………………………………………………………….. 717
Chapter 15 Test • ……………………………………………………………………………….. 725
16.1 Evaluating Roots • ……………………………………………………………………………… 729
16.2 Multiplying, Dividing, and Simplifying Radicals • ………………………………….. 735
16.4 Rationalizing the Denominator • …………………………………………………………… 745
16.5 More Simplifying and Operations with Radicals • …………………………………… 750
16.6 Solving Equations with Radicals • ………………………………………………………… 756
Chapter 16 Review Exercises • …………………………………………………………….. 766
Chapter 16 Test • ……………………………………………………………………………….. 771
17.1 Solving Quadratic Equations by the Square Root Property • …………………….. 775
17.2 Solving Quadratic Equations by Completing the Square • ………………………… 780
17.4 Graphing Quadratic Equations • …………………………………………………………… 796
17.5 Introduction to Functions • ………………………………………………………………….. 804
Chapter 17 Review Exercises • …………………………………………………………….. 806
Chapter 17 Test • ……………………………………………………………………………….. 813
Cumulative Review Exercises (Chapters 9–17) • …………………………………….. 816
Appendix A Measurement…………………………………………………………………………………………. 827
A.1 Problem Solving with U.S. Measurement Units • ……………………………………. 827
A.2 The Metric System—Length • ……………………………………………………………… 833
A.3 The Metric System—Capacity and Weight (Mass) • ……………………………….. 836
A.4 Metric–U.S. Measurement Conversions and Temperature • ……………………… 841
Appendix B Inductive and Deductive Reasoning ……………………………………………………… 84

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