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Mathematics: Its Power and Utility

By Karl Smith

10th Edition © 2013
Discipline:Mathematics
Course:Liberal Arts Mathematics
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MATHEMATICS: ITS POWER AND UTILITY, Tenth Edition, combines a unique and practical focus on real-world problem solving allowing even the least-interested or worst-prepared student to appreciate the beauty and value of math while mastering basic concepts and skills they will apply to their daily lives. The first half of the book explores the POWER and historic impact of mathematics and helps students harness that POWER by developing an effective approach to problem solving. The second half builds upon this foundation by exploring the UTLITY and application of math concepts to a wide variety of real-life situations: money management; handling of credit cards; inflation; purchase of a car or home; the effective use of probability, statistics, and surveys; and many other topics of life interest. Unlike many mathematics texts, MATHEMATICS: ITS POWER AND UTILITY, Tenth Edition, assumes a basic working knowledge of arithmetic, making it effective even for students with no exposure to algebra. Completely self-contained chapters make it easy to teach to a customized syllabus or support the precise pace and emphasis that students require.

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About this product

MATHEMATICS: ITS POWER AND UTILITY, Tenth Edition, combines a unique and practical focus on real-world problem solving allowing even the least-interested or worst-prepared student to appreciate the beauty and value of math while mastering basic concepts and skills they will apply to their daily lives. The first half of the book explores the POWER and historic impact of mathematics and helps students harness that POWER by developing an effective approach to problem solving. The second half builds upon this foundation by exploring the UTLITY and application of math concepts to a wide variety of real-life situations: money management; handling of credit cards; inflation; purchase of a car or home; the effective use of probability, statistics, and surveys; and many other topics of life interest. Unlike many mathematics texts, MATHEMATICS: ITS POWER AND UTILITY, Tenth Edition, assumes a basic working knowledge of arithmetic, making it effective even for students with no exposure to algebra. Completely self-contained chapters make it easy to teach to a customized syllabus or support the precise pace and emphasis that students require.

The first half of the book, "The Power of Math," develops some ideas in arithmetic, algebra, and geometry. The second half of the book, "The Utility of Math," develops the ideas around mathematics that students will use outside of the classroom.

Each chapter opener helps students anticipate upcoming topics. Topics included in "The Power of Math" or "The Utility of Math" section openers are identified. A list of essential ideas tells students what they need to know after they have worked through the chapter.

Each section of the book begins with an introductory box called either "The Power of Math" or "The Utility of Math." These introductory boxes are designed to get students to THINK about how the material in the section relates to their life. The first few problems at the end of every section are also designed to engage students in this way.

Throughout this book, notes explain steps or offer hints about what students should look for as they read.

Table of contents

Chapters

Cover Page
Title Page
Copyright Page
Introduction
Dedication
Preface
Acknowledgments
Part 1. Foundations
Part 2. Applications

Part 1. Foundations

Chapter 1. Arithmetic, Calculators, and Problem Solving
Preview this section ↗
1.1. Math Anxiety ↗
Hints for Success ↗
Writing Mathematics ↗
1.1. Problem Set ↗
1.2. Formulating the Problem ↗
Order of Operations ↗
Simplify a Numerical Expression ↗
Pólya’s Problem-Solving Method ↗
1.2. Problem Set ↗
1.3. Fractions and Decimals ↗
Division by Zero—No, No, No! ↗
Definition of Fraction ↗
Decimal Fractions ↗
Fractions to Decimals ↗
Estimating Fractions ↗
1.3. Problem Set ↗
1.4. Rounding and Estimation ↗
Understanding Large Numbers ↗
Rounding Numbers ↗
Estimation ↗
1.4. Problem Set ↗
1.5. Exponents and Prime Factorization ↗
Exponents ↗
Scientific Notation ↗
Extended Order of Operations ↗
Factoring ↗
Prime Numbers ↗
1.5. Problem Set ↗
1.6. Common Fractions ↗
Reducing Fractions ↗
Multiplying Fractions ↗
Dividing Fractions ↗
Decimals to Fractions ↗
1.6. Problem Set ↗
1.7. Adding and Subtracting Fractions ↗
Common Denominators ↗
Lowest Common Denominator ↗
Procedure for Adding and Subtracting Fractions ↗
1.7. Problem Set ↗
1.8. Hindu-Arabic Numeration System ↗
History of Numeration ↗
Meaning of Numbers ↗
Expanded Notation ↗
1.8. Problem Set ↗
1.9. Different Numeration Systems ↗
Number of Symbols ↗
Change from Some Base to Base Ten ↗
Change from Base 10 to Some Base ↗
1.9. Problem Set ↗
Important Terms ↗
Learning Outcomes ↗
Self-Test ↗
Study Hints for the Self-Test ↗
Chapter 1 Review Questions ↗
Chapter 2. Sets of Numbers
2.1. Symbol Shock
Understanding Variables
Translating Algebra/English
Evaluating
2.1. Problem Set
2.2. Adding of Integers
Signed Numbers
Number Lines
Absolute Value
Adding Integers
2.2. Problem Set
2.3. Subtraction of Integers
Subtracting Integers
Minus/Negative/Opposite
2.3. Problem Set
2.4. Multiplication of Integers
Multiplying Integers
Evaluating Algebraic Expressions
2.4. Problem Set
2.5. Division of Integers
Dividing Integers
Average
2.5. Problem Set
2.6. Rational and Irrational Numbers
Sets of Numbers
Rational Numbers
Pythagorean Theorem
Irrational Numbers
Real Numbers
2.6. Problem Set
Important Terms
Learning Outcomes
Self-Test
Study Hints for the Self-Test
Chapter 2 Review Questions
Chapter 3. Introduction to Algebra
3.1. Polynomials
Terminology
Multiplication with Variables
Classifying Polynomials
3.1. Problem Set
3.2. Similar Terms
3.2. Problem Set
3.3. Simplification
Adding/Subtracting Polynomials
Simplifying Polynomials
3.3. Problem Set
3.4. Equations
Types of Equations
Fundamental Procedures
Properties of Equations
3.4. Problem Set
3.5. Solving Equations
Basic Equation Properties
Simplify Before Solving
Handling Variables
3.5. Problem Set
3.6. Problem Solving with Algebra
Literal Equations
Number Problems
Consecutive Number Problems
Miles-Per-Gallon Problems
Price Comparison Problems
Unclassified Problems
3.6. Problem Set
3.7. Inequalities
Inequality Symbols
Solving an Inequality
3.7. Problem Set
Important Terms
Learning Outcomes
Self-Test
Study Hints for the Self-Test
Chapter 3 Review Questions
Chapter 4. Percents and Problem Solving
4.1. Ratio and Proportion
Ratio
Proportion
4.1. Problem Set
4.2. Problem Solving with Proportions
Missing Terms
Cross-Product Method
Applied Problems
4.2. Problem Set
4.3. Percent
Definition of Percent
Percents as Fractions and Decimals
Converting Fractions, Decimals, and Proportions
4.3. Problem Set
4.4. Problem Solving with Percents
Unit-Fraction-Conversion Method
Estimation
The Percent Problem
Problem Solving with Percents
4.4. Problem Set
Important Terms
Learning Outcomes
Self-Test
Study Hints for the Self-Test
Chapter 4 Review Questions
Chapter 5. Introduction to Geometry
5.1. Euclidean Geometry
Foundations
Euclid’s Postulates (Traditional Geometry)
Transformational Geometry
5.1. Problem Set
5.2. Angles and Polygons
Naming Angles
Constructing Angles
Classifying Angles
Classifying Pairs of Angles
Perpendicular and Parallel Lines
Classifying Polygons
5.2. Problem Set
5.3. Triangles
Classifying Triangles
Congruent Triangles
Angles of a Triangle
5.3. Problem Set
5.4. Similar Triangles
Similar Triangles and Corresponding Parts
Problem Solving with Similar Triangles
Pythagorean Theorem
5.4. Problem Set
Important Terms
Essential Ideas
Learning Outcomes
Self-Test
Study Hints for the Self-Test
Chapter 5 Review Questions
Chapter 6. Measurement and Problem Solving
6.1. Precision, Accuracy, and Estimation
Precision versus Accuracy
Estimation
Measurement Systems
Metric Measurement Prefixes
Measuring Length
6.1. Problem Set
6.2. Perimeter
Measuring Distance Around a Polygon
Measuring Distance Around a Circle
6.2. Problem Set
6.3. Area
Square Unit Measurements
Areas of Rectangles and Squares
Areas of Parallelograms
Areas of Triangles
Areas of Trapezoids
Areas of Circles
Applications
6.3. Problem Set
6.4. Volume and Capacity
Measuring Volumes of Cubes and Boxes
Measuring Capacity
6.4. Problem Set
6.5. Miscellaneous Measurements
Measuring Volumes of Solids
Mass
Temperature
6.5. Problem Set
6.6. Converting Units
Metric Measurement Conversions
U.S. Measurement Conversion
U.S.-Metric Conversions
6.6. Problem Set
Important Terms
Learning Outcomes
Self-Test
Study Hints for the Self-Test
Chapter 6 Review Questions

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