Scottsdale Community College Basic Arithmetic Student Workbook Development Team Donna Gaudet Amy Volpe Jenifer Bohart First Edition December, 2012 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. ii A NOTE ABOUT THIS WORKBOOK This workbook was created through the efforts of three instructors at Scottsdale Community College in Scottsdale, Arizona. Any individual may download and utilize a digital copy of this workbook for free. The Creative Commons licensing of this text allows others to freely use, modify, or remix any of the information presented here. Contact Donna Gaudet at [email protected] if you are an instructor that wishes to teach with these materials or adapt and edit them for teaching. This workbook does not contain beautiful graphics, hundreds of problems or 4-color printing. Those things are wonderful to have but also very expensive. This workbook does have lessons that were carefully and thoughtfully crafted to lead students on a path to understanding numbers and arithmetic. As you work through the text, you may find errors. If you do, please contact Donna Gaudet at the email address above and provide specific information about the error and where it is located. The information presented in the text is a work in progress and will evolve with the input of students and other users. We look forward to your feedback! iii WORKOOK & SUPPORTING COMPONENTS This workbook is designed to lead students through a basic understanding of numbers and arithmetic. The included curriculum is broken into twelve lessons (see Table of Contents page for lesson titles). Each lesson includes the following components: MINILESSON • The MiniLesson is the main instructional component for each lesson. • Ideas are introduced with practical situations. • Example problems (marked with a star) are to be completed by watching video links and taking notes/writing down the problem as written by the instructor. • You Try problems help reinforce lesson concepts and should be worked in the order they appear showing as much work as possible. Answers can be checked in Appendix A. PRACTICE PROBLEMS • These problems can be found at the end of each lesson. If you are working through this material on your own, the recommendation is to work all those problems. If you are using this material as part of a formal class, your instructor will provide guidance on which problems to complete. Your instructor will also provide information on accessing answers/solutions for these problems. ASSESS YOUR LEARNING • The last part of each lesson is a short assessment. If you are working through this material on your own, use these assessments to test your understanding of the lesson concepts. Take the assessments without the use of the book or your notes and then check your answers. If you are using this material as part of a formal class, your instructor will provide guidance on which problems to complete. Your instructor will also provide information on accessing answers/solutions for these problems. ONLINE HOMEWORK ASSESSMENT SYSTEM • If you are using these materials as part of a formal class and your class utilizes an online homework/assessment system, your instructor will provide information as to how to access and use that system in conjunction with this workbook. iv TABLE OF CONTENTS LESSON 1 – WHOLE NUMBERS ................................................................................................................ 1 MINILESSON ............................................................................................................................................ 3 PRACTICE PROBLEMS ......................................................................................................................... 11 ASSESS YOUR LEARNING .................................................................................................................. 15 LESSON 2 – INTRODUCTION TO FRACTIONS ..................................................................................... 17 MINILESSON .......................................................................................................................................... 19 PRACTICE PROBLEMS ......................................................................................................................... 27 ASSESS YOUR LEARNING .................................................................................................................. 33 LESSON 3 – FRACTION ADDITION & SUBTRACTION ........................................................................ 35 MINILESSON .......................................................................................................................................... 37 PRACTICE PROBLEMS ......................................................................................................................... 47 ASSESS YOUR LEARNING .................................................................................................................. 51 LESSON 4 – FRACTION MULTIPLICATION & DIVISION .................................................................... 53 MINILESSON .......................................................................................................................................... 55 PRACTICE PROBLEMS ......................................................................................................................... 65 ASSESS YOUR LEARNING .................................................................................................................. 69 LESSON 5 - DECIMALS ............................................................................................................................. 71 MINILESSON .......................................................................................................................................... 73 PRACTICE PROBLEMS ......................................................................................................................... 81 ASSESS YOUR LEARNING .................................................................................................................. 85 LESSON 6 - PERCENTS .............................................................................................................................. 87 MINILESSON .......................................................................................................................................... 89 PRACTICE PROBLEMS ......................................................................................................................... 99 ASSESS YOUR LEARNING ................................................................................................................ 103 LESSON 7 – RATIOS, RATES, & PROPORTIONS ................................................................................. 105 MINILESSON ........................................................................................................................................ 107 PRACTICE PROBLEMS ....................................................................................................................... 113 ASSESS YOUR LEARNING ................................................................................................................ 119 LESSON 8 - STATISTICS .......................................................................................................................... 121 MINILESSON ........................................................................................................................................ 123 PRACTICE PROBLEMS ....................................................................................................................... 131 ASSESS YOUR LEARNING ................................................................................................................ 135 LESSON 9 – UNITS & CONVERSIONS .................................................................................................. 137 MINILESSON ........................................................................................................................................ 139 PRACTICE PROBLEMS ....................................................................................................................... 147 ASSESS YOUR LEARNING ................................................................................................................ 155 LESSON 10 – GEOMETRY I: PERIMETER & AREA ............................................................................ 157 MINILESSON ........................................................................................................................................ 159 PRACTICE PROBLEMS ....................................................................................................................... 173 ASSESS YOUR LEARNING ................................................................................................................ 181 LESSON 11 – GEOMETRY II: VOLUME & TRIANGLES ..................................................................... 183 MINILESSON ........................................................................................................................................ 185 PRACTICE PROBLEMS ....................................................................................................................... 197 ASSESS YOUR LEARNING ................................................................................................................ 203 LESSON 12 – SIGNED NUMBERS .......................................................................................................... 205 MINILESSON ........................................................................................................................................ 207 PRACTICE PROBLEMS ....................................................................................................................... 215 ASSESS YOUR LEARNING ................................................................................................................ 221 APPENDIX A: ANSWERS TO YOU-TRY PROBLEMS ......................................................................... 223   v vi Basic Arithmetic Lesson 1 – Whole Numbers LESSON 1 – WHOLE NUMBERS INTRODUCTION We will begin our study of Basic Arithmetic by learning about whole numbers. Whole numbers are the numbers used most often for counting and computation in everyday life. The table below shows the specific whole-number related objectives that are the achievement goal for this lesson. Read through them carefully now to gain initial exposure to the terms and concept names for the lesson. Refer back to the list at the end of the lesson to see if you can perform each objective. Lesson Objective Related Examples Identify the place value of a digit or digits in a given number. 1, YT7 Read and write whole numbers. 2, YT4 Round whole numbers to a given place. 3, YT5, YT6 Rewrite an exponential expression in factored form. 8 Compute numerical expressions using exponents. 12, 13, YT14 Use correct order of operations to evaluate numerical expressions. 9, 10, 11, YT15 Solve whole number applications with a problem-solving process 16, YT17 KEY TERMS The key terms listed below will help you keep track of important mathematical words and phrases that are part of this lesson. Look for these words and circle or highlight them along with their definition or explanation as you work through the MiniLesson. • Whole Numbers • Number Line • Place Value • Round Whole Numbers • Exponent • Power • Factor • Factored Form • Mathematical Operations • Order of Operations (PEMDAS) • Solution Work Flow • Complete Solution • Disjointed Solution • Problem Solving Process 1 Basic Arithmetic Lesson 1 – Whole Numbers LESSON CHECKLIST Use this page to track required components for your class and your progress on each one. Required? Component Comments Due Score Y or N Mini-Lesson Online Homework Online Quiz Online Test Practice Problems Lesson Assessment 2 Basic Arithmetic Lesson 1 – Whole Numbers MINILESSON WHOLE NUMBERS, PLACE VALUE, AND ROUNDING Whole numbers are often referred to as “the counting numbers plus the number 0”. The first few whole numbers are written as: 0, 1, 2, 3, 4, 5, 6, 7, … We can place a representative set of these on a number line as follows: Note that the arrows on the number line indicate that the numbers continue in both directions. We will learn in Lesson 12 about numbers to the left of 0! We read whole numbers from left to right. To do this correctly, we need to know the place value of each digit in the number. The table below illustrates place values through the Billions place. You can use this table to help you properly identify number names. Example 1: Place each number in the chart above. What place value does the digit “0” occupy in each number? a. 25,032 b. 105,243 c. 12, 340,412 Example 2: Write each whole number below in words. a. 275,345,201 b. 502,013 3 Basic Arithmetic Lesson 1 – Whole Numbers To round a number means to approximate that number by replacing it with another number that is “close” in value. Rounding is often used when estimating. For example, if I wanted to add 41 and 37, I could round each number to the nearest ten (40 and 40) then add to estimate the sum at 80. When rounding, the analogy of a road may help you decide which number you are closer to. See the image below. The numbers 43, 45, and 46 are all rounded to the nearest tens place. Note that a number in the middle of the “road” is rounded up. Example 3: a. Round 40,963 to the nearest tens place. b. Round 40,963 to the nearest hundreds place. c. Round 40,963 to the nearest thousand d. Round 40,963 to the nearest ten thousand YOU TRY 4. Write the number 12,304,652 using words. ____________________________________________________________________ 5. Round 12,304,652 to the nearest million. ______________________________ 6. Round 12,304,652 to the nearest hundred. _______________________________ 7. What place does the digit 3 occupy in the number 12,304,652? _________________ 4