VIEWING LIFE MATHEMATICALLY A Pathway to Quantitative Literacy GUIDED NOTEBOOK + Integrated Review SECOND EDITION Annotated Instructor’s Edition - Not for SaleEditor: Barbara Miller Assistant Editors: Jolie Even, S. Rebecca Johnson Creative Services Manager: Trudy Tronco Cover Design: Patrick Thompson Composition and Answer Key Assistance: Quant Systems India Pvt. Ltd. A division of Quant Systems, Inc. 546 Long Point Road Mount Pleasant, SC 29464 Copyright © 2022 by Hawkes Learning / Quant Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 978-1-64277-492-4 AIE ISBN: 978-1-64277-498-6Table of Contents Preface Math Knowledge Required for Math@Work Career Explorations . . . . . . . . . . . . . . . . . . .vi How to Use the Guided Notebook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Strategies for Academic Success How to Read a Math Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Tips for Success in a Math Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Tips for Improving Math Test Scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Practice, Patience, and Persistence! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Note Taking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi Do I Need a Math Tutor? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xvii Tips for Improving Your Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Overcoming Anxiety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Online Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx Preparing for a Final Math Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi Managing Your Time Effectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii CHAPTER 1.R Review Concepts for Critical Thinking and Problem Solving 1.R.1 Introduction to Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.R.2 Rounding and Estimating Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.R.3 Exponents and Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.R.4 Problem Solving with Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.R.5 Translating English Phrases and Algebraic Expressions . . . . . . . . . . . . . . . . . . . . 27 1.R.6 Solving Linear Equations: ax + b = c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 CHAPTER 2.R Review Concepts for Set Theory 2.R.1 Introduction to Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.R.2 Addition with Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.R.3 Subtraction with Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.R.4 Multiplication, Division, and Order of Operations with Integers . . . . . . . . . . . . . . . 57CHAPTER 4.R Review Concepts for Ratios, Percentages, Rates, and Proportionality 4.R.1 Introduction to Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.R.2 Introduction to Decimal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.R.3 Multiplication and Division with Decimal Numbers. . . . . . . . . . . . . . . . . . . . . . . 79 4.R.4 Basics of Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.R.5 Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 CHAPTER 5.R Review Concepts for Algebra: Equations, Inequalities, and Functions 5.R.1 Operations with Real Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.R.2 Simplifying Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.R.3 Solving One-Step Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.R.4 Solving Multistep Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.R.5 Solving Linear Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 5.R.6 The Quadratic Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.R.7 The Cartesian Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.R.8 Graphing Linear Equations in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.R.9 Introduction to Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 CHAPTER 6.R Review Concepts for Finance 6.R.1 Estimating and Order of Operations with Decimal Numbers . . . . . . . . . . . . . . . . 159 6.R.2 Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 6.R.3 Reading Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 CHAPTER 7.R Review Concepts for Numeration and Measurement Systems 7.R.1 The Decimal System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.R.2 Addition and Subtraction with Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . 185 7.R.3 Multiplication with Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 7.R.4 Division with Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 iv Preface Table of ContentsCHAPTER 8.R Review Concepts for Number Theory 8.R.1 Tests for Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 8.R.2 Prime Numbers and Prime Factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 CHAPTER 9.R Review Concepts for Geometry 9.R.1 Angles and Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9.R.2 Square Roots and the Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . 231 9.R.3 Evaluating Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 9.R.4 Working with Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 CHAPTER 10.R Review Concepts for Probability 10.R.1 Multiplication and Division with Fractions and Mixed Numbers . . . . . . . . . . . . . . 251 10.R.2 Least Common Multiple (LCM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 10.R.3 Addition and Subtraction with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.R.4 Decimal Numbers and Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 10.R.5 Determining Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 CHAPTER 11.R Review Concepts for Statistics 11.R.1 Bar Graphs, Pictographs, Circle Graphs, and Line Graphs . . . . . . . . . . . . . . . . . 283 11.R.2 Constructing Graphs from Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 11.R.3 The Cartesian Coordinate System, Scatter Plots, and Linear Equations. . . . . . . . . . 297 11.R.4 Slope-Intercept Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 11.R.5 Evaluating Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Math @ Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 v Table of Contents PrefaceMath Knowledge Required for Math@Work Career Explorations The following table summarizes the math knowledge required for each Math@Work career exploration. Use this table to determine when you are ready to explore each career. Math@Work Career Whole Numbers Fr actions IntegersDecimal Numbers Av er ages Per cents Simple Inter est RatiosPr opor tions Geometr y StatisticsGr aphing Linear E quations Systems of E quations Mixtur e Pr oblems Scientific Notation Gr eatest Common F act or Rational Expr essions Radicals Basic Inventory Management check Hospitality Management check checkcheck Bookkeeper check Pediatric Nurse checkcheck check Architecture checkcheck Statistician: Quality Control checkcheck check Dental Assistant checkcheckcheck Financial Advisor checkcheck checkcheck Market Research Analyst checkcheck Chemistry checkcheck check Astronomy checkcheck Math Education checkcheck Physics checkcheck Forensic Scientist checkcheckcheck Other Careers in Mathematics vi Preface Math Knowledge Required for Math@Work Career Explorations Support If you have questions or comments we can be contacted as follows: 24/7 Chat: chat.hawkeslearning.com Phone: (843) 571-2825 E-mail: support@hawkeslearning.com Web: hawkeslearning.com Our support hours are 8:00 a.m. to 10:00 p.m. (ET), Monday through Friday. vii Support Prefaceviii Preface How to Use the Guided Notebook How to Use the Guided Notebook There are a variety of elements in this Guided Notebook that will help you on your way to mastering each topic. Here is a rundown of how to use the elements as you work through this notebook. Fill-in-the-Blanks 1. When there is an incomplete sentence, you will need to write in the missing word(s). The missing words can be found by reading through the Learn screens. Boxed Content Definitions and procedures are highlighted within a box, like the ones shown here. The missing content will vary from box to box. Sometimes an entire definition is missing and sometimes only part of a sentence is missing. Here are two examples of the box variations. Definition First term to define: Write the definition here. Second term to define: If there is another term, define it the same way as above. DEFINITION • Terms Related to Probability Outcome An individual result of an experiment. Sample Space The set of all possible outcomes of an experiment. Event Some (or all) of the outcomes from the sample space. DEFINITIONix How to Use the Guided Notebook Preface Properties and Procedure boxes are completed in a similar way: Commutative Property of Multiplication The order of the numbers in multiplication can be reversed without changing the product. For example, 3 ∙ 4 = 12 and 4 ∙ 3 = 12. PROPERTIES Subtracting Whole Numbers 1. Write the numbers vertically so that the place values are lined up in columns. 2. Subtract only the digits with the same place value. 3. Check by adding the difference to the subtrahend. The sum must be the minuend. PROCEDURE Ť Watch and Work For each Watch and Work, you will need to watch the corresponding video in Learn mode and follow along while completing the example in the space provided. Example 5 Multiplying Whole Numbers Multiply: 12 ⋅ 35 Solution The standard form of multiplication is used here to find the product 12 ⋅ 35. 1 1 2 × 3 5 6 0 12 ∙ 5 = 60 36 0 12 ∙ 30 = 360 42 0 Product X Now You Try It! After working along with the example video, work through a similar exercise on your own in the space provided. Example A Multiplying Whole Numbers Multiply: 25 42 × 1050Next >