Arithmetic 4 Success: A Simple Yet Thorough Review of Arithmetic
Edition: 7
Copyright: 2017
Pages: 910
Edition: 7
Copyright: 2017
Pages: 912
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A Math Foundation for Success in Life and in STEM
Arithmetic 4 Success enables students to finally understand arithmetic concepts and applications that provide a foundation for success in STEM disciplines (Science, Technology, Engineering, and Math). The book begins with practical word “puzzles” that focus on situations common in everyday life.
Critical thinking skills, problem-solving skills, common fraction concepts, and properties of “1” are emphasized throughout the book.
- Promotes the feeling that math is fun! Exercises are called “puzzles” instead of “problems.”
- Facilitates the development of number sense and “head math! “Puzzles” contain carefully selected compatible numbers.
- Reduces math anxiety! Students discover most word puzzles can be solved using ONLY three math concepts: unit analysis, proportions, and formulas.
- Limits one concept per-page! The concept to be learned is clearly written in large lettering at the top of each page.
- Is student friendly! Mnemonics and analogies help students remember vocabulary and concepts presented. For example, the proportion algorithm is remembered as the “heart method.” Numerous check quizzes, reviews, and check tests help students monitor their progress.
- Helps students focus! Boxes and arrows are used to capture and direct the student’s attention. The book is offered in a loose-leaf binder format to enable students to place explanations and examples side-by-side with exercises.
- Offers encouragement and hope for students who have struggled! Students see a variety of short, motivational biographies in which struggles become successes because determined people DO NOT give up. Short encouraging quotes (often humorous) appear throughout the answer keys.
- Emphasizes applications that promote critical thinking! Word puzzles describe situations in which several facts are given. From these, students make organized lists and identify relevant information needed to answer the question.
- Is instructor friendly! Ancillary materials are available for adopting instructors.
- Promotes an awareness and interest in STEM disciplines! After applying unit analysis, proportions, and formulas to everyday-life puzzles, students are given introductory applications that are part of a variety of STEM disciplines. These include: chemistry, engineering, nursing, radiology, and automotive technology.
- Provides a connection between arithmetic and algebra! Introduces algebra as a language of “letters, numbers, and symbols”, a mystery game that applies arithmetic concepts to unknown numbers.
Chapter 7 is intended to introduce students to STEM careers and help them realize they are learning important arithmetic concepts essential for success. As confidence builds, many students realize a STEM career is possible for them.
The last chapter is intended to help students begin to understand the connection between arithmetic and algebra. They quickly recognize the importance of arithmetic as they use signed numbers and solve basic algebraic equations that include common fractions and decimal fractions.
As previous failures become successes, self-doubt is replaced by elevated self-esteem. Arithmetic 4 Success is guiding students down pathways of success that encourages them to consider STEM careers.
Notes: 1. PART I contains explanations and examples of the “puzzle” exercises
which are found in Part II.
2. PART II contains practice puzzles, check quizzes, and check tests.
These are referenced to corresponding explanations in PART I.
Foreword: What Others Say About Arithmetic 4 Success
Preface: Why This Book Was Written
Introduction: What You Can Expect to Find in This Book
How Arithmetic 4 Success is Organized
Table of Contents
Five Principles that Maximize Learning, Retention, and Transfer
Acknowledgments
Whole Number Review Quiz
Common Fraction Review Quiz
Review of Basic Concepts:
Math Symbols
Subtraction, Zeros, and Short Cuts
Basic Multiplication
Zeros, Multiplication, and Short Cuts
Basic Division
Exponents and Roots
Grouping Symbols
Order of Operations
Basic Geometry Formulas and When to Use Them
Review of Basic Geometry Formulas
Review of Statistics
“Never, Never, Never Give Up!”: Winston Churchill
Someone to Think About: Marie Curie
PART I: Explanations and Examples
Chapter 1: Common Fractions
Someone to Think About: Abraham Lincoln
A Basic Vocabulary for Fractions
The Meaning of a Fraction
Improper Fractions and Mixed Numbers
Properties of One
Equivalent Fractions
Factors and Rules of Divisibility
Prime Factors and Prime Factorization
Reducing Fractions to Lowest Terms
Using Prime Factorization to Determine the GCF
The GCF and Euclid’s Algorithm
Using Prime Factorization for Finding the LCM
Comparing Fractions with Unlike Denominators
Estimating Fractions
Adding and Subtracting Like Fractions
Adding and Subtracting Unlike Fractions
Adding Like Fractions That Use Carrying
Subtracting Like Fractions That Use Borrowing
Using Addition and Subtraction of Fractions in Everyday Life
Using Estimation to Check for Reasonableness
Multiplication of Fractions
Pre-reducing When Multiplying Fractions
When “of” Means Multiply
Mental Math and Multiple Step Puzzles
Division of Common Fractions
Finding the Average of Fractions and Mixed Numbers
Powers and Roots
How Grouping Symbols Are Used
Order of Operations
Distributive Property of Multiplication
Complex Fractions
Using the Distributive Property to Eliminate Denominators
Formulas for Geometric Figures
Using Diagrams to Understand Puzzles
Using Easier Numbers
Using Common Fractions in Geometric Figures
Temperature Formulas
Chapter 1 Review: Common Fractions
Chapter 2: Decimal Fractions
Someone to Think About: Joanne Rowling
The Meaning of a Decimal Fraction
Understanding Place Values of Decimal Fractions
Four Ways to Write Decimal Fractions
Rounding Off Decimal Fractions
Comparing Decimal Fractions
Adding and Subtracting Decimal Fractions
Multiplying Decimal Fractions
Dividing Decimal Fractions
Using Critical Thinking with Multiple Choice Questions
Estimating Sums, Differences, Products, and Quotients
Review Basic Concepts in Statistics
Using Lists and Charts to Determine Minimal Grade Needed
Using Charts to Determine Grade Point Average
Banking Vocabulary
Reconciling an Interest Bearing Checking Account
Savings Accounts
Statistics in Everyday Life: Banking
Interpreting Bar Graphs
Converting Common Fractions into Decimal Fractions
Complex Decimal Fractions
Mental Math, Divisibility Rules, and Reducing
Puzzles That Use Both Decimal Fractions and Common Fractions
Short Cuts when Multiplying and Dividing Decimal Fractions by Exponents of Ten
Converting Decimal Fractions to and from Combination and Standard Forms
Simplifying Ratios by Eliminating the Decimal Point
Scientific Notation
Writing Numbers in Exponential Form
Powers of Decimal Fractions
Estimating Roots of Decimal Fractions
Comparing Numbers
Order of Operations
Chapter 2 Review: Decimal Fractions
Chapter 3: Unit Analysis, Measurement, Accuracy, and Precision
Someone to Think About: Ludwig Van Beethoven
An Introduction to Unit Analysis
Conversion Tables
Concepts of “1” Used in Unit Analysis
Steps Used in Unit Analysis
Using Unit Analysis for Multiple Conversions
Using Unit Analysis to Add or Subtract Denominate Numbers
Chapter 3: Unit Analysis, Measurement, Accuracy, and Precision (continued)
Using Unit Analysis to Add and Multiply Denominate Numbers
Using Unit Analysis When Subtracting and Dividing Denominate Numbers
Measuring Time: the 24 Hour Clock
Rounding Numbers: How Close Is Close Enough?
Exact Numbers and Approximations
Accuracy. Precision, and Significant Digits
Rounding Off to the Least Precise or the Least Accurate Number
Using Accuracy with Multiplication and Division
Using Precision with Addition and Subtraction
Using Accuracy and Precision Together
Accuracy and Precision and the Fraction Bar
Converting Units of Measure and Rounding
The Metric System
Learning to Think in Metrics
Converting within the Metric System
Converting between English Units and Metric Units
Temperature Comparisons
Temperature Conversions
Chapter 3 Review: Unit Analysis, Accuracy, Precision, and Measurement
Chapter 4: Ratios, Rates, and Unit Analysis in Everyday Life
Someone to Think About: Clayton Turner
The Meaning of a Ratio
Writing Ratios in Fraction Form
Writing Rates as Fractions
Unit Rates
Using Unit Rates to Calculate Hourly Earnings
Calculating Salaries and Pay Periods with Unit Analysis
Calculating Gross Pay and Net Pay
Finance Charges, Payments, and Total Costs
Making Payments
Converting Unit Rates between Dollar and Cent Form
Better Buys and Unit Rates
Concrete Concepts and Abstract Concepts
Using Abstract Conversion Factors in Unit Analysis
Working Backwards When Using Unit Analysis
Using Unit Analysis in Everyday Life: Gardening
Using Unit Analysis So Formulas May Be Used
Using Unit Analysis to Answer Distance Questions
Using Unit Analysis to Do Multiple Conversions
Unit Analysis, Multiple Steps, and Working Backwards
Chapter 4 Review: Ratios, Rates, and Unit Analysis
Chapter 5: Ratios, Proportion, and Percent
Someone to Think About: Oprah Winfrey
Review of Rates and Ratios
Recognizing a Proportion
Using the “Heart Method” to Solve Proportions
Pre-reducing and Checking Proportions
Translating Words into Rates, Proportions, and Unit Fractions
More Rates, Proportions, and Unit Analysis
Proportions, Unit Analysis, and Fractions
Reasonable Rounding Off
Using Ratios in Proportions and When Using Unit Analysis
Similar Figures
Using a Proportion to Solve Similar Figures
Drawing Diagrams to Evaluate Information
An Introduction into Percents
Converting Percents to Common Fractions
Converting Complex Percents to Fractions
Using the “Heart Method” to Convert Fractions into Percents
Converting Mixed Numbers to Percents
Converting Fractions to Percents in Complex Form
Converting from a Decimal Fraction to a Percent
Converting Complex Decimals to Percents
Converting Percents to Decimal Fractions
Using Proportions to Solve Percent Puzzles
Understanding “of” in Percent Puzzles
Complex Percents and Their Equivalents
Evaluating Information and Drawing Conclusions
Examples Relating to “of” in “%” Puzzles
Preview of “Type A” and “Type B” Word Puzzles
Word Puzzles That Are Solved as Proportions: Type “A” (No Increase or Decrease)
Word Puzzles That Are Solved as Proportions: Type “B” (% of Increase or % of Decrease)
Calculating Multiple Markdowns
Type “B” Word Puzzles: Increases and Decreases
Interpreting Graphs
Multiple Line Graphs
Multiple Bar Graphs
Circle Graphs
Three Ways to Determine a Percentage
Type “C” Percent Puzzles: “% of”, “% of”
Type “D”: Percent Puzzles That Use Formulas
Calculating Interest (Simple and Compound
Calculating Monthly Payments
Summary of Percent Puzzles That Are NOT Proportions
Chapter 5 Review: Ratios, Proportion, and Percent
Chapter 6: Geometric Formulas
Someone to Think About: Corrie ten Boom
Formulas and Order of Operations
Perimeter of a Triangle
Finding the Area of a Triangle
Finding the Area of a Parallelogram
Finding the Area of a Trapezoid
Area and Volume of Rectangular Objects
Perimeter and Surface Area of Rectangular Shapes
Finding Perimeter and Area Using Mixed Units
Using Algebra to Find an Unknown Part of a Polygon
Finding Area and Perimeter of a Composite Figure
Recognizing Clues When Information Is NOT Stated
Area and Circumference of a Circle
Area and Perimeter of Part of a Circle
More Two-Dimensional Composite Figures
Mixed Units and Two-Dimensional Figures
Plane Composite Figures
Volume and Surface Area of Three-Dimensional Figures
A Triangular Prism
A Square Pyramid
A Cylinder
A Sphere
A Cone
Understanding Formulas
Calculating the Volume of a Composite Figure
Chapter 6 Review: Geometric Formulas
Chapter 7: An Introduction to STEM Applications
Something to Think About: STEM Professionals Needed
An Introduction to STEM
Review of Significant Digits
Very Small and Very Large Numbers
Scientific Notation
Review of Basic Measurement Conversions
Unit Analysis in Automotive Technology:
Conversions in Automotive Technology: Tires
Creating Conversion Factors
When Mixed Units Are Given
Unit Analysis in Automotive Technology
Charts, Unit Analysis, and Buying a Vehicle
Converting to an Equivalent Rate
Unit Analysis in Engineering, Chemistry, and Physics:
STEM in the Space Program
Using Unit Analysis to Determine RPM of a Tire
Miscellaneous Abbreviations and Conversion Factors
Unit Analysis in Engineering and Dams
Unit Analysis in Chemistry and Engineering: Water Purification
Different Ways to Write Numbers
Calculating Water Flow Rates
Calculating Feed Rates
Calculating Detention Time in a Chamber
Calculating Volume of Cylindrical Tanks
Rates That Use Complex Fractions
Using Unit Analysis and Scientific Notation Together
Unit Analysis in Nursing:
The Specialized Language of Medicine
Converting to Military Time
Converting between “Micro” and “Milli” Units
Unit Analysis in Nursing
Working Forwards and Backwards
Dosage Calculations
Calculating IV Flow Rates
Calculating IV Flow Rates and Drip Rates
Calculating Infusion Completion Times
Dosage Calculations Based on Body Weight
Calculating Amount of Vaccine Needed
Ratios, Rates and Proportions:
Review of Ratios, Rates, and Proportions
Drawing Diagrams to Evaluate Information
A Choice: To Use Unit Analysis or a Proportion
Chemical Compounds and Ratios
Chemistry and Medication Percent Calculations
Calculating Percent of Increase (or Decrease)
STEM Formulas:
Multiplication and Grouping Symbols
Temperature Scales Used in STEM
The “Plus or Minus” Symbol “±”
Tolerance Intervals and Margin of Error
“T” Tables and Subscripts in Formulas
Nested Grouping Symbols
Formulas with Embedded Grouping Symbols
Cautions About Embedded Grouping Symbols
Writing Variations of Formulas
Manipulating a Formula to Solve for a Variable
Math Laws and Variations of Formulas
Chapter 7 Review: Basic Concepts Used in STEM
Chapter 8: An Introduction to Algebra: Signed Numbers and Equations
Something to Think About: The Brain
What Is Algebra?
Basic Vocabulary
The Number Line
The Horizontal Number Line and Signed Numbers
The Rules of Multiplication (and Division) of Signed Numbers
The Rules of Addition of Integers
Symbols Used for Multiplication
Signed Common Fractions and Decimal Fractions
The Rules of Addition of Integers Use Analogy: THINK MONEY!
Using the Order of Operations
Making Addition and Subtraction of Integers Easier
Additive Inverses
Using the Multiplicative Identity of “1”
Identifying Clusters of Multiplication
The Associative and Commutative Properties of Mathematics
Nested (or Embedded) Grouping Symbols
Fraction Bars and Signs as Grouping Symbols
Review of Order of Operations
Substitution
Getting Ready to Solve Equations
Punctuation Symbols in Mathematics
Misunderstandings in Mathematics
Using Inverses to Solve Equations
Phrases, Sentences, and Verbs in Algebra
Solving Algebraic Equations That Contain Common Fractions and Decimal Fractions
Signed Fractions That Require Carrying and Borrowing
Chapter 8 Review
Index
Part II: Practice Puzzles
When Using this Book to Prepare for a Qualifying Exam
Table of Contents for Part II Quizzes, Reviews, and Check Tests
Whole Number Refresher Practice Sheets
Part III: Answers to Practice Puzzles and Appendix
Appendix 1: Common Equivalents
Appendix 2: Abbreviations and Formulas Commonly Used In STEM
Appendix 3: Equivalents Used in Nursing
Appendix 4: Perimeter and Area of Two-Dimensional Figures
Appendix 5: Volume and Surface Area of Three-Dimensional Figures
Success Stories:
Winston Churchill (Prime Minister of England)
Marie Curie (inventor of radium)
Abraham Lincoln (U.S. President)
Joanne Rowling (author of Harry Potter series)
Ludwig Van Beethoven (composer-musician)
Jessica Bansen (teacher for disabled students)
Clayton Turner (artist)
Oprah Winfrey (television personality)
Corrie ten Boom (survivor of Holocaust)
Fotini Alfieris (coordinator of Multiple Sclerosis)
Ronan Tynan (physician, musician, singer)
Index
Rosemarie Bezerra-Nader was raised on a dairy farm in rural Lemoore, California. Although neither parent ever attended high school, James and Mary Bezerra placed a high value on education as a means of improving one’s quality of life; they instilled a very strong ambition and work ethic in each of their four children. Rosemarie is married to Fareed Nader, a Geomatics engineering Professor Emeritus at California State University, Fresno (CSUF). They support and encourage each other’s passion for teaching.
Rosemarie has had a wide variety of teaching experiences:
5 summers
as a K-3 teacher in dairy-farming communities
5 years
as a 4th and 5th grade teacher in a Central California community where children were members of
multigenerational dairy-farming families, migrant families, and military families.
12 years
as a 7th-9th grade teacher in large urban and suburban communities where she taught math, English, critical
thinking, and peer counseling.
25 years
as an adjunct instructor at California State University, Fresno where she taught professional development
and test prep classes for teachers in math, critical thinking, and English. At CSUF, she also taught bulletin
board classes for teachers and beginning guitar.
1990 - the present
as a developmental math instructor at Fresno City College in Fresno, California where she also taught
reading, critical thinking, and decision-making classes.
In a fast-paced, ever-changing world, Rosemarie is committed to teaching people to “learn how to learn.” Math is the subject she enjoys using to do this. Rosemarie enjoys the challenge and rewards in teaching people who doubt their abilities. Developmental math is the subject she enjoys teaching most.
Throughout her varied teaching experience, Rosemarie has integrated the development of critical thinking skills and problem-solving strategies. She strongly feels these are the keys that unlock the doors to learning retention, and transfer across the curriculum for all age groups.
Rosemarie traveled widely within the United States as a consultant in how to integrate critical thinking into an existing curriculum.
She has written three developmental books:
Arithmetic For Success
The Bridge Between Arithmetic and Algebra
Mastering Whole Numbers, the Express Way
In her “spare time”, Rosemarie enjoys singing, playing piano, ballroom dancing, sewing, and spending time playing with her two canine “kids.”
Winston Churchill is her favorite character in history. Rosemarie ends every motivational biography with a message to students: This message is Churchill's famous quote to:
“Never, never, never give up!”
"Arithmetic 4 Success promotes student understanding and success while decreasing math anxiety. The compact, one concept per page format and the clear, concise, and thorough explanations use visual aids and dialogue boxes to appeal to multiple learning modalities. The book’s system of cross referencing enables students to easily and quickly find explanations and examples in Part I that directly correlate with ‘puzzles’ in Part II. The use of real world ‘puzzles’ gives math relevance as it bridges the gap between math and everyday life. The relaxed style the author used in Arithmetic 4 Success builds confidence in students, especially those who have struggled with math."
Instructor - Administrator for Grades 7 – 12
"The methods taught in Arithmetic 4 Success changed my life and enabled me to have the career I have today. The blending of critical thinking skills with concise explanations and careful sequencing helped me make connections and remember concepts. The solid foundation in math that resulted enabled me to complete my bachelor’s degree, pass the GRE, and earn a master’s degree. The high school math phobia that haunted me for 20 years of my adult life was replaced with confidence and an understanding of math that I use every day."
-- Linda Kane, Fresno City College Instructor
Learning Disabilities Specialists- School Psychologist
"The visual methods used in Arithmetic 4 Success enabled me to understand and pass the arithmetic portion of the California Real Estate Licensing Exam. I still remember and use the “heart method” for setting up percent problems."
"The application of concepts emphasized in Arithmetic 4 Success bridge the gap left by traditional math classes. In a step-by–step, easy to understand manner, the author develops the concept of dimensional analysis as an extension of common fractions. This understanding and the ability to apply accuracy and precision will help students pass math-science dependent tests like the State of California Water Certification Test and the California Wastewater Certification test. Even before earning a community college degree, individuals can quality for career path positions in a variety of industries where they can receive on-the-job training; examples include positions within municipal water and waste-water utilities. Math has been the gatekeeper to these positions. Most of the math concepts needed to pass these tests can be found in Arithmetic 4 Success."
-- Robert Moorhead, BS & MBA
Water Technology & Educational Services (owner)
Community College Water Certification Instructor
Director of Fresno Purification Plant (semi retired)
Municipal System Laboratory Director, Senior Chemist
Find Student Testimonials Featured in JOURNAL OF THE FACULTY ASSOCIATION OF CALIFORNIA COMMUNITY COLLEGES | FALL 2019
A Math Foundation for Success in Life and in STEM
Arithmetic 4 Success enables students to finally understand arithmetic concepts and applications that provide a foundation for success in STEM disciplines (Science, Technology, Engineering, and Math). The book begins with practical word “puzzles” that focus on situations common in everyday life.
Critical thinking skills, problem-solving skills, common fraction concepts, and properties of “1” are emphasized throughout the book.
- Promotes the feeling that math is fun! Exercises are called “puzzles” instead of “problems.”
- Facilitates the development of number sense and “head math! “Puzzles” contain carefully selected compatible numbers.
- Reduces math anxiety! Students discover most word puzzles can be solved using ONLY three math concepts: unit analysis, proportions, and formulas.
- Limits one concept per-page! The concept to be learned is clearly written in large lettering at the top of each page.
- Is student friendly! Mnemonics and analogies help students remember vocabulary and concepts presented. For example, the proportion algorithm is remembered as the “heart method.” Numerous check quizzes, reviews, and check tests help students monitor their progress.
- Helps students focus! Boxes and arrows are used to capture and direct the student’s attention. The book is offered in a loose-leaf binder format to enable students to place explanations and examples side-by-side with exercises.
- Offers encouragement and hope for students who have struggled! Students see a variety of short, motivational biographies in which struggles become successes because determined people DO NOT give up. Short encouraging quotes (often humorous) appear throughout the answer keys.
- Emphasizes applications that promote critical thinking! Word puzzles describe situations in which several facts are given. From these, students make organized lists and identify relevant information needed to answer the question.
- Is instructor friendly! Ancillary materials are available for adopting instructors.
- Promotes an awareness and interest in STEM disciplines! After applying unit analysis, proportions, and formulas to everyday-life puzzles, students are given introductory applications that are part of a variety of STEM disciplines. These include: chemistry, engineering, nursing, radiology, and automotive technology.
- Provides a connection between arithmetic and algebra! Introduces algebra as a language of “letters, numbers, and symbols”, a mystery game that applies arithmetic concepts to unknown numbers.
Chapter 7 is intended to introduce students to STEM careers and help them realize they are learning important arithmetic concepts essential for success. As confidence builds, many students realize a STEM career is possible for them.
The last chapter is intended to help students begin to understand the connection between arithmetic and algebra. They quickly recognize the importance of arithmetic as they use signed numbers and solve basic algebraic equations that include common fractions and decimal fractions.
As previous failures become successes, self-doubt is replaced by elevated self-esteem. Arithmetic 4 Success is guiding students down pathways of success that encourages them to consider STEM careers.
Notes: 1. PART I contains explanations and examples of the “puzzle” exercises
which are found in Part II.
2. PART II contains practice puzzles, check quizzes, and check tests.
These are referenced to corresponding explanations in PART I.
Foreword: What Others Say About Arithmetic 4 Success
Preface: Why This Book Was Written
Introduction: What You Can Expect to Find in This Book
How Arithmetic 4 Success is Organized
Table of Contents
Five Principles that Maximize Learning, Retention, and Transfer
Acknowledgments
Whole Number Review Quiz
Common Fraction Review Quiz
Review of Basic Concepts:
Math Symbols
Subtraction, Zeros, and Short Cuts
Basic Multiplication
Zeros, Multiplication, and Short Cuts
Basic Division
Exponents and Roots
Grouping Symbols
Order of Operations
Basic Geometry Formulas and When to Use Them
Review of Basic Geometry Formulas
Review of Statistics
“Never, Never, Never Give Up!”: Winston Churchill
Someone to Think About: Marie Curie
PART I: Explanations and Examples
Chapter 1: Common Fractions
Someone to Think About: Abraham Lincoln
A Basic Vocabulary for Fractions
The Meaning of a Fraction
Improper Fractions and Mixed Numbers
Properties of One
Equivalent Fractions
Factors and Rules of Divisibility
Prime Factors and Prime Factorization
Reducing Fractions to Lowest Terms
Using Prime Factorization to Determine the GCF
The GCF and Euclid’s Algorithm
Using Prime Factorization for Finding the LCM
Comparing Fractions with Unlike Denominators
Estimating Fractions
Adding and Subtracting Like Fractions
Adding and Subtracting Unlike Fractions
Adding Like Fractions That Use Carrying
Subtracting Like Fractions That Use Borrowing
Using Addition and Subtraction of Fractions in Everyday Life
Using Estimation to Check for Reasonableness
Multiplication of Fractions
Pre-reducing When Multiplying Fractions
When “of” Means Multiply
Mental Math and Multiple Step Puzzles
Division of Common Fractions
Finding the Average of Fractions and Mixed Numbers
Powers and Roots
How Grouping Symbols Are Used
Order of Operations
Distributive Property of Multiplication
Complex Fractions
Using the Distributive Property to Eliminate Denominators
Formulas for Geometric Figures
Using Diagrams to Understand Puzzles
Using Easier Numbers
Using Common Fractions in Geometric Figures
Temperature Formulas
Chapter 1 Review: Common Fractions
Chapter 2: Decimal Fractions
Someone to Think About: Joanne Rowling
The Meaning of a Decimal Fraction
Understanding Place Values of Decimal Fractions
Four Ways to Write Decimal Fractions
Rounding Off Decimal Fractions
Comparing Decimal Fractions
Adding and Subtracting Decimal Fractions
Multiplying Decimal Fractions
Dividing Decimal Fractions
Using Critical Thinking with Multiple Choice Questions
Estimating Sums, Differences, Products, and Quotients
Review Basic Concepts in Statistics
Using Lists and Charts to Determine Minimal Grade Needed
Using Charts to Determine Grade Point Average
Banking Vocabulary
Reconciling an Interest Bearing Checking Account
Savings Accounts
Statistics in Everyday Life: Banking
Interpreting Bar Graphs
Converting Common Fractions into Decimal Fractions
Complex Decimal Fractions
Mental Math, Divisibility Rules, and Reducing
Puzzles That Use Both Decimal Fractions and Common Fractions
Short Cuts when Multiplying and Dividing Decimal Fractions by Exponents of Ten
Converting Decimal Fractions to and from Combination and Standard Forms
Simplifying Ratios by Eliminating the Decimal Point
Scientific Notation
Writing Numbers in Exponential Form
Powers of Decimal Fractions
Estimating Roots of Decimal Fractions
Comparing Numbers
Order of Operations
Chapter 2 Review: Decimal Fractions
Chapter 3: Unit Analysis, Measurement, Accuracy, and Precision
Someone to Think About: Ludwig Van Beethoven
An Introduction to Unit Analysis
Conversion Tables
Concepts of “1” Used in Unit Analysis
Steps Used in Unit Analysis
Using Unit Analysis for Multiple Conversions
Using Unit Analysis to Add or Subtract Denominate Numbers
Chapter 3: Unit Analysis, Measurement, Accuracy, and Precision (continued)
Using Unit Analysis to Add and Multiply Denominate Numbers
Using Unit Analysis When Subtracting and Dividing Denominate Numbers
Measuring Time: the 24 Hour Clock
Rounding Numbers: How Close Is Close Enough?
Exact Numbers and Approximations
Accuracy. Precision, and Significant Digits
Rounding Off to the Least Precise or the Least Accurate Number
Using Accuracy with Multiplication and Division
Using Precision with Addition and Subtraction
Using Accuracy and Precision Together
Accuracy and Precision and the Fraction Bar
Converting Units of Measure and Rounding
The Metric System
Learning to Think in Metrics
Converting within the Metric System
Converting between English Units and Metric Units
Temperature Comparisons
Temperature Conversions
Chapter 3 Review: Unit Analysis, Accuracy, Precision, and Measurement
Chapter 4: Ratios, Rates, and Unit Analysis in Everyday Life
Someone to Think About: Clayton Turner
The Meaning of a Ratio
Writing Ratios in Fraction Form
Writing Rates as Fractions
Unit Rates
Using Unit Rates to Calculate Hourly Earnings
Calculating Salaries and Pay Periods with Unit Analysis
Calculating Gross Pay and Net Pay
Finance Charges, Payments, and Total Costs
Making Payments
Converting Unit Rates between Dollar and Cent Form
Better Buys and Unit Rates
Concrete Concepts and Abstract Concepts
Using Abstract Conversion Factors in Unit Analysis
Working Backwards When Using Unit Analysis
Using Unit Analysis in Everyday Life: Gardening
Using Unit Analysis So Formulas May Be Used
Using Unit Analysis to Answer Distance Questions
Using Unit Analysis to Do Multiple Conversions
Unit Analysis, Multiple Steps, and Working Backwards
Chapter 4 Review: Ratios, Rates, and Unit Analysis
Chapter 5: Ratios, Proportion, and Percent
Someone to Think About: Oprah Winfrey
Review of Rates and Ratios
Recognizing a Proportion
Using the “Heart Method” to Solve Proportions
Pre-reducing and Checking Proportions
Translating Words into Rates, Proportions, and Unit Fractions
More Rates, Proportions, and Unit Analysis
Proportions, Unit Analysis, and Fractions
Reasonable Rounding Off
Using Ratios in Proportions and When Using Unit Analysis
Similar Figures
Using a Proportion to Solve Similar Figures
Drawing Diagrams to Evaluate Information
An Introduction into Percents
Converting Percents to Common Fractions
Converting Complex Percents to Fractions
Using the “Heart Method” to Convert Fractions into Percents
Converting Mixed Numbers to Percents
Converting Fractions to Percents in Complex Form
Converting from a Decimal Fraction to a Percent
Converting Complex Decimals to Percents
Converting Percents to Decimal Fractions
Using Proportions to Solve Percent Puzzles
Understanding “of” in Percent Puzzles
Complex Percents and Their Equivalents
Evaluating Information and Drawing Conclusions
Examples Relating to “of” in “%” Puzzles
Preview of “Type A” and “Type B” Word Puzzles
Word Puzzles That Are Solved as Proportions: Type “A” (No Increase or Decrease)
Word Puzzles That Are Solved as Proportions: Type “B” (% of Increase or % of Decrease)
Calculating Multiple Markdowns
Type “B” Word Puzzles: Increases and Decreases
Interpreting Graphs
Multiple Line Graphs
Multiple Bar Graphs
Circle Graphs
Three Ways to Determine a Percentage
Type “C” Percent Puzzles: “% of”, “% of”
Type “D”: Percent Puzzles That Use Formulas
Calculating Interest (Simple and Compound
Calculating Monthly Payments
Summary of Percent Puzzles That Are NOT Proportions
Chapter 5 Review: Ratios, Proportion, and Percent
Chapter 6: Geometric Formulas
Someone to Think About: Corrie ten Boom
Formulas and Order of Operations
Perimeter of a Triangle
Finding the Area of a Triangle
Finding the Area of a Parallelogram
Finding the Area of a Trapezoid
Area and Volume of Rectangular Objects
Perimeter and Surface Area of Rectangular Shapes
Finding Perimeter and Area Using Mixed Units
Using Algebra to Find an Unknown Part of a Polygon
Finding Area and Perimeter of a Composite Figure
Recognizing Clues When Information Is NOT Stated
Area and Circumference of a Circle
Area and Perimeter of Part of a Circle
More Two-Dimensional Composite Figures
Mixed Units and Two-Dimensional Figures
Plane Composite Figures
Volume and Surface Area of Three-Dimensional Figures
A Triangular Prism
A Square Pyramid
A Cylinder
A Sphere
A Cone
Understanding Formulas
Calculating the Volume of a Composite Figure
Chapter 6 Review: Geometric Formulas
Chapter 7: An Introduction to STEM Applications
Something to Think About: STEM Professionals Needed
An Introduction to STEM
Review of Significant Digits
Very Small and Very Large Numbers
Scientific Notation
Review of Basic Measurement Conversions
Unit Analysis in Automotive Technology:
Conversions in Automotive Technology: Tires
Creating Conversion Factors
When Mixed Units Are Given
Unit Analysis in Automotive Technology
Charts, Unit Analysis, and Buying a Vehicle
Converting to an Equivalent Rate
Unit Analysis in Engineering, Chemistry, and Physics:
STEM in the Space Program
Using Unit Analysis to Determine RPM of a Tire
Miscellaneous Abbreviations and Conversion Factors
Unit Analysis in Engineering and Dams
Unit Analysis in Chemistry and Engineering: Water Purification
Different Ways to Write Numbers
Calculating Water Flow Rates
Calculating Feed Rates
Calculating Detention Time in a Chamber
Calculating Volume of Cylindrical Tanks
Rates That Use Complex Fractions
Using Unit Analysis and Scientific Notation Together
Unit Analysis in Nursing:
The Specialized Language of Medicine
Converting to Military Time
Converting between “Micro” and “Milli” Units
Unit Analysis in Nursing
Working Forwards and Backwards
Dosage Calculations
Calculating IV Flow Rates
Calculating IV Flow Rates and Drip Rates
Calculating Infusion Completion Times
Dosage Calculations Based on Body Weight
Calculating Amount of Vaccine Needed
Ratios, Rates and Proportions:
Review of Ratios, Rates, and Proportions
Drawing Diagrams to Evaluate Information
A Choice: To Use Unit Analysis or a Proportion
Chemical Compounds and Ratios
Chemistry and Medication Percent Calculations
Calculating Percent of Increase (or Decrease)
STEM Formulas:
Multiplication and Grouping Symbols
Temperature Scales Used in STEM
The “Plus or Minus” Symbol “±”
Tolerance Intervals and Margin of Error
“T” Tables and Subscripts in Formulas
Nested Grouping Symbols
Formulas with Embedded Grouping Symbols
Cautions About Embedded Grouping Symbols
Writing Variations of Formulas
Manipulating a Formula to Solve for a Variable
Math Laws and Variations of Formulas
Chapter 7 Review: Basic Concepts Used in STEM
Chapter 8: An Introduction to Algebra: Signed Numbers and Equations
Something to Think About: The Brain
What Is Algebra?
Basic Vocabulary
The Number Line
The Horizontal Number Line and Signed Numbers
The Rules of Multiplication (and Division) of Signed Numbers
The Rules of Addition of Integers
Symbols Used for Multiplication
Signed Common Fractions and Decimal Fractions
The Rules of Addition of Integers Use Analogy: THINK MONEY!
Using the Order of Operations
Making Addition and Subtraction of Integers Easier
Additive Inverses
Using the Multiplicative Identity of “1”
Identifying Clusters of Multiplication
The Associative and Commutative Properties of Mathematics
Nested (or Embedded) Grouping Symbols
Fraction Bars and Signs as Grouping Symbols
Review of Order of Operations
Substitution
Getting Ready to Solve Equations
Punctuation Symbols in Mathematics
Misunderstandings in Mathematics
Using Inverses to Solve Equations
Phrases, Sentences, and Verbs in Algebra
Solving Algebraic Equations That Contain Common Fractions and Decimal Fractions
Signed Fractions That Require Carrying and Borrowing
Chapter 8 Review
Index
Part II: Practice Puzzles
When Using this Book to Prepare for a Qualifying Exam
Table of Contents for Part II Quizzes, Reviews, and Check Tests
Whole Number Refresher Practice Sheets
Part III: Answers to Practice Puzzles and Appendix
Appendix 1: Common Equivalents
Appendix 2: Abbreviations and Formulas Commonly Used In STEM
Appendix 3: Equivalents Used in Nursing
Appendix 4: Perimeter and Area of Two-Dimensional Figures
Appendix 5: Volume and Surface Area of Three-Dimensional Figures
Success Stories:
Winston Churchill (Prime Minister of England)
Marie Curie (inventor of radium)
Abraham Lincoln (U.S. President)
Joanne Rowling (author of Harry Potter series)
Ludwig Van Beethoven (composer-musician)
Jessica Bansen (teacher for disabled students)
Clayton Turner (artist)
Oprah Winfrey (television personality)
Corrie ten Boom (survivor of Holocaust)
Fotini Alfieris (coordinator of Multiple Sclerosis)
Ronan Tynan (physician, musician, singer)
Index
Rosemarie Bezerra-Nader was raised on a dairy farm in rural Lemoore, California. Although neither parent ever attended high school, James and Mary Bezerra placed a high value on education as a means of improving one’s quality of life; they instilled a very strong ambition and work ethic in each of their four children. Rosemarie is married to Fareed Nader, a Geomatics engineering Professor Emeritus at California State University, Fresno (CSUF). They support and encourage each other’s passion for teaching.
Rosemarie has had a wide variety of teaching experiences:
5 summers
as a K-3 teacher in dairy-farming communities
5 years
as a 4th and 5th grade teacher in a Central California community where children were members of
multigenerational dairy-farming families, migrant families, and military families.
12 years
as a 7th-9th grade teacher in large urban and suburban communities where she taught math, English, critical
thinking, and peer counseling.
25 years
as an adjunct instructor at California State University, Fresno where she taught professional development
and test prep classes for teachers in math, critical thinking, and English. At CSUF, she also taught bulletin
board classes for teachers and beginning guitar.
1990 - the present
as a developmental math instructor at Fresno City College in Fresno, California where she also taught
reading, critical thinking, and decision-making classes.
In a fast-paced, ever-changing world, Rosemarie is committed to teaching people to “learn how to learn.” Math is the subject she enjoys using to do this. Rosemarie enjoys the challenge and rewards in teaching people who doubt their abilities. Developmental math is the subject she enjoys teaching most.
Throughout her varied teaching experience, Rosemarie has integrated the development of critical thinking skills and problem-solving strategies. She strongly feels these are the keys that unlock the doors to learning retention, and transfer across the curriculum for all age groups.
Rosemarie traveled widely within the United States as a consultant in how to integrate critical thinking into an existing curriculum.
She has written three developmental books:
Arithmetic For Success
The Bridge Between Arithmetic and Algebra
Mastering Whole Numbers, the Express Way
In her “spare time”, Rosemarie enjoys singing, playing piano, ballroom dancing, sewing, and spending time playing with her two canine “kids.”
Winston Churchill is her favorite character in history. Rosemarie ends every motivational biography with a message to students: This message is Churchill's famous quote to:
“Never, never, never give up!”
"Arithmetic 4 Success promotes student understanding and success while decreasing math anxiety. The compact, one concept per page format and the clear, concise, and thorough explanations use visual aids and dialogue boxes to appeal to multiple learning modalities. The book’s system of cross referencing enables students to easily and quickly find explanations and examples in Part I that directly correlate with ‘puzzles’ in Part II. The use of real world ‘puzzles’ gives math relevance as it bridges the gap between math and everyday life. The relaxed style the author used in Arithmetic 4 Success builds confidence in students, especially those who have struggled with math."
Instructor - Administrator for Grades 7 – 12
"The methods taught in Arithmetic 4 Success changed my life and enabled me to have the career I have today. The blending of critical thinking skills with concise explanations and careful sequencing helped me make connections and remember concepts. The solid foundation in math that resulted enabled me to complete my bachelor’s degree, pass the GRE, and earn a master’s degree. The high school math phobia that haunted me for 20 years of my adult life was replaced with confidence and an understanding of math that I use every day."
-- Linda Kane, Fresno City College Instructor
Learning Disabilities Specialists- School Psychologist
"The visual methods used in Arithmetic 4 Success enabled me to understand and pass the arithmetic portion of the California Real Estate Licensing Exam. I still remember and use the “heart method” for setting up percent problems."
"The application of concepts emphasized in Arithmetic 4 Success bridge the gap left by traditional math classes. In a step-by–step, easy to understand manner, the author develops the concept of dimensional analysis as an extension of common fractions. This understanding and the ability to apply accuracy and precision will help students pass math-science dependent tests like the State of California Water Certification Test and the California Wastewater Certification test. Even before earning a community college degree, individuals can quality for career path positions in a variety of industries where they can receive on-the-job training; examples include positions within municipal water and waste-water utilities. Math has been the gatekeeper to these positions. Most of the math concepts needed to pass these tests can be found in Arithmetic 4 Success."
-- Robert Moorhead, BS & MBA
Water Technology & Educational Services (owner)
Community College Water Certification Instructor
Director of Fresno Purification Plant (semi retired)
Municipal System Laboratory Director, Senior Chemist
Find Student Testimonials Featured in JOURNAL OF THE FACULTY ASSOCIATION OF CALIFORNIA COMMUNITY COLLEGES | FALL 2019