# Using & Understanding Mathematics: A Quantitative Reasoning Approach, 7th edition

Published by Pearson (January 18, 2018) © 2019

**Jeffrey O. Bennett**University of Colorado Boulder**William L. Briggs**University of Colorado Denver

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For courses in Liberal Arts Mathematics and Quantitative Literacy.

### Mathematics for college, career and life

Through their proven success as trailblazers in Quantitative Reasoning, Jeff Bennett and Bill Briggs' **Using & Understanding Mathematics: A Quantitative Reasoning Approach, 7th Edition **prepares students for the mathematics they will encounter in college courses, their future careers and life in general. Its quantitative reasoning approach helps students build the skills required to understand major issues in everyday life, and compels them to acquire the problem-solving tools needed to think critically about quantitative issues in contemporary society.

### Hallmark features of this title

**Chapter Overviews**include a multiple-choice question connecting content with the book's themes of college, career and life.**Now Try**exercise references appear after every example and direct students to a specific exercise.**Think About It**is designed to encourage deeper understanding of topics such as proof of the Pythagorean Theorem and Zeno's paradox.**Brief Reviews**summarize key skills that may require a refresher to support success in the section. These appear wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.**Using Technology**boxes appear throughout to highlight technologies such as Excel, graphing calculators, apps and websites that can be used for the corresponding concept.

### New and updated features of this title

**Updated data**throughout reflects the most current information and events. Examples include health insurance, demographic data, and the federal budget.**A new 3-step strategy, Understand - Solve - Explain**, in Ch. 2 (Approaches to Problem Solving): This change moves away from the Polya-based 4-step method to simplify problem solving, encouraging students to put it into practice more easily.**Extensively revised Ch. 4 (Managing Money)**includes the most current financial information regarding loans, taxes and budgets.**New Caution! feature:**These short notes are found throughout and highlight common errors.**New and revised In Your World**boxes continue the focus on topics that students are likely to encounter in the world around them, whether in the news, consumer decisions or political discussions.- A printed
**Activity Manual**is also available for those who wish to do more activities in the course. It is correlated to the textbook and activities can be completed by students individually or in a group.

### Features of MyLab Math for the 7th Edition

**A new series of example-based videos**is accompanied by assessment questions that enable instructors to gauge student understanding.**New Dynamic Concept videos**focus on some of the most interesting and challenging concepts to help students gain a deeper understanding, using engaging visual lightboard functionality.**New When Will I Ever Use This?**videos demonstrate how various math concepts are utilized in various jobs and careers.**New****Interactive Concept Videos**discuss a concept in depth, then ask students to try a problem on their own. Incorrect answers are followed by further explanation, taking into consideration what may have led to the student selecting that particular answer.**New Animations**let students interact with the math in a visual, tangible way. These animations allow students to explore and manipulate the mathematical concepts, leading to more durable understanding.**New StatCrunch**^{® }**Integration:**This powerful web-based statistical software allows users to collect data, perform analyses and generate compelling results. For this edition, StatCrunch questions have been added to relevant Technology Exercises and access to the software has been integrated into the MyLab Math course**.**

### I. LOGIC AND PROBLEM SOLVING

**1. Thinking Critically**- Activity: Bursting Bubble
**1A. Living in the Media Age**- In Your World: Fact Checking on the Web
**1B. Propositions and Truth Values****1C. Sets and Venn Diagrams**- Brief Review: Sets of Numbers
**1D. Analyzing Arguments**- Mathematical Insight: Deductive Proof of the Pythagorean Theorem
**1E. Critical Thinking in Everyday Life**- In Your World: Beware of “Up to” Deals

**2. Approaches to Problem Solving**- Activity: Global Melting
**2A. Understand, Solve, and Explain**- Brief Review: Common Fractions
- Brief Review: Decimal Fractions
- Using Technology: Currency Exchange Rates
- In Your World: Changing Money in Foreign Countries
**2B. Extending Unit Analysis**- In Your World: Gems and Gold Jewelry
- Brief Review: Powers of 10
- Using Technology: Metric Conversions
- In Your World: Save Money and Save the Earth
**2C. Problem-Solving Hints**- Mathematical Insight: Zeno’s Paradox

### II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE

**3. Numbers in the Real World**- Activity: Big Numbers
**3A. Uses and Abuses of Percentages**- Brief Review: Percentages
- Brief Review: What Is a Ratio?
**3B. Putting Numbers in Perspective**- Brief Review: Working with Scientific Notation
- Using Technology: Scientific Notation
**3C. Dealing with Uncertainty**- Brief Review: Rounding
- Using Technology: Rounding in Excel
**3D. Index Numbers: The CPI and Beyond**- Using Technology: The Inflation Calculator
- In Your World: The Chained CPI and the Federal Budget
**3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More**

**4. Managing Money**- Activity: Student Loans
**4A. Taking Control of Your Finances****4B. The Power of Compounding**- Brief Review: Powers and Roots
- Using Technology: Powers
- Using Technology: The Compound Interest Formula
- Using Technology: The Compound Interest Formula for Interest Paid More Than Once a Year
- Using Technology: APY in Excel
- Using Technology: Powers of e
- Brief Review: Four Basic Rules of Algebra
- In Your World: Effects of Low Interest Rates
**4C. Savings Plans and Investments**- Mathematical Insight: Derivation of the Savings Plan Formula
- Using Technology: The Savings Plan Formula
- Using Technology: Fractional Powers (Roots)
- In Your World: Building a Portfolio
**4D. Loan Payments, Credit Cards, and Mortgages**- Using Technology: The Loan Payment Formula (Installment Loans)
- Mathematical Insight: Derivation of the Loan Payment Formula
- Using Technology: Principal and Interest Portions of Loan Payments
- In Your World: Avoiding Credit Card Trouble
- In Your World: Choosing or Refinancing a Loan
**4E. Income Taxes****4F. Understanding the Federal Budget**

### III. PROBABILITY AND STATISTICS

**5. Statistical Reasoning**- Activity: Cell Phones and Driving
**5A. Fundamentals of Statistics**- Using Technology: Random Numbers
**5B. Should You Believe a Statistical Study?**- In Your World: The Gun Debate: Defensive Gun Use
**5C. Statistical Tables and Graphs**- Using Technology: Frequency Tables in Excel
- Using Technology: Bar Graphs and Pie Charts in Excel
- Using Technology: Line Charts in Excel
**5D. Graphics in the Media**- Using Technology: Graphs with Multiple Data Sets
**5E. Correlation and Causality**- Using Technology: Scatterplots in Excel

**6. Putting Statistics to Work**- Activity: Are We Smarter Than Our Parents?
**6A. Characterizing Data**- Using Technology: Mean, Median, and Mode in Excel
**6B. Measures of Variation**- Using Technology: Standard Deviation in Excel
**6C. The Normal Distribution**- Using Technology: Standard Scores and Percentiles in Excel
**6D. Statistical Inference**- In Your World: Is Polling Reliable?

**7. Probability: Living With The Odds**- Activity: Lotteries
**7A. Fundamentals of Probability**- Brief Review: The Multiplication Principle
**7B. Combining Probabilities****7C. The Law of Large Numbers****7D. Assessing Risk**- In Your World: Terrorism, Risk, and Human Psychology
**7E. Counting and Probability**- Using Technology: Factorials
- Brief Review: Factorials
- Using Technology: Permutations
- Using Technology: Combinations

### IV. MODELING

**8. Exponential Astonishment**- Activity: Towers of Hanoi
**8A. Growth: Linear vs. Exponential****8B. Doubling Time and Half-Life**- Using Technology: Logarithms
- Brief Review: Logarithms
**8C. Real Population Growth**- In Your World: Choosing Our Fate
**8D. Logarithmic Scales: Earthquakes, Sounds, and Acids**- In Your World: Ocean Acidification

**9. Modeling Our World**- Activity: Climate Modeling
**9A. Functions: The Building Blocks of Mathematical Models**- Brief Review: The Coordinate Plane
**9B. Linear Modeling**- Using Technology: Graphing Functions
- In Your World: Algebra’s Baghdad Connection
**9C. Exponential Modeling**- Brief Review: Algebra with Logarithms
- Mathematical Insight: Doubling Time and Half-Life Formulas
- In Your World: Changing Rates of Change

**10. Modeling With Geometry**- Activity: Eyes in the Sky
**10A. Fundamentals of Geometry**- Mathematical Insight: Archimedes and Pi
- In Your World: Plato, Geometry, and Atlantis
**10B. Problem Solving with Geometry****10C. Fractal Geometry**

### V. FURTHER APPLICATIONS

**11. Mathematics and The Arts**- Activity: Digital Music Files
- 11A. Mathematics and Music
- In Your World: Music Just for You
- 11B. Perspective and Symmetry
- 11C. Proportion and the Golden Ratio

**12. Mathematics and Politics**- Activity: Partisan Redistricting
**12A. Voting: Does the Majority Always Rule?**- In Your World: Counting Votes - Not as Easy as It Sounds
**12B. Theory of Voting**- In Your World: The Electoral College and the Presidency
**12C. Apportionment: The House of Representatives and Beyond****12D. Dividing the Political Pie**

#### Credits

#### Answers to Quick Quizzes and Odd-Numbered Exercises

#### Index

### About our authors

**Jeffrey Bennett **specializes in mathematics and science education. He has taught at every level from pre-school through graduate school, including more than 50 college courses in mathematics, physics, astronomy, and education. His work on **Using and Understanding Mathematics **began in 1987, when he helped create a new mathematics course for the University of Colorado's core curriculum. Variations on this course, with its quantitative reasoning approach, are now taught at hundreds of colleges nationwide. In addition to his work in mathematics, Dr. Bennett (whose PhD is in astrophysics) has written leading college-level textbooks in astronomy, statistics, and astrobiology, as well as books for the general public. He also proposed and developed both the Colorado Scale Model Solar System on the University of Colorado at Boulder campus and the Voyage Scale Model Solar System, a permanent, outdoor exhibit on the National Mall in Washington, DC. He has recently begun writing science books for children, including the award-winning **Max Goes to the Moon** and **Max Goes to Mars.** When not working, he enjoys swimming as well as hiking the trails of Boulder, Colorado with his family.

**William L. Briggs **has been on the mathematics faculty at the University of Colorado at Denver for 22 years. He teaches numerous courses within the undergraduate and graduate curriculum, and has special interest in teaching calculus, differential equations, and mathematical modeling. He developed the quantitative reasoning course for liberal arts students at University of Colorado at Denver supported by his textbook **Using and Understanding Mathematics**. He has written 2 other tutorial monographs, “The Multigrid Tutorial” and “The DFT: An Owner's Manual for the Discrete Fourier Transform,” as well as **Ants, Bikes, Clocks**, a mathematical problem-solving text for undergraduates. He is a University of Colorado President's Teaching Scholar, an Outstanding Teacher awardee of the Rocky Mountain Section of the MAA, and the recipient of a Fulbright Fellowship to Ireland. Bill lives with his wife Julie and their Gordon setter Seamus in Boulder, Colorado. He loves to bake bread, run trails and rock climb in the mountains near his home.

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