PATHWAYS to College Mathematics D. FRANKLIN WRIGHT © All Rights Reser ved.Manager of Math Content Development: Chelsey Cooke Project Manager: Emily Christian Editor: Barbara Miller Assistant Editors: Chelsey Cooke, Allison Conger, Adam Flaherty, Lisa Hinton, S. Rebecca Johnson, Nina Waldron, Kara Roché Indexer: Barbara Miller Content Contributors: Sage Bentley, Diane Devanney, L. Robin Hendrix, Penny Hidalgo, Michael W. Lanstrum, Arthur Migala, Barbara Miller, Leonardo Pinheiro, Paula Stickles, Christina L. Thompson, Hao-Nhien Vu, Kellie Zimmer Courseware Developers: Brandon Aiton, Vince Cellini, Adam Flaherty, Kyle Gilstrap, William McCullough Creative Services Manager: Trudy Gove Contributing Designers: Lizbeth Mendoza, Patrick Thompson, Joel Travis Composition and Answer Key Assistance: Quant Systems India Pvt. Ltd. Cover Design: Patrick Thompson A division of Quant Systems, Inc. 546 Long Point Road Mount Pleasant, SC 29464 Copyright © 2021 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. Library of Congress Control Number 2020906258 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 978-1-64277-308-8 AIE ISBN: 978-1-64277-309-5 © All Rights Reser ved.Table of Contents Reser Rights ved. © All Rights ved.Preface Pathways to College Mathematics: Purpose and Style Pathways to College Mathematics is a one-semester developmental-level course designed to give students an alternate path to non-STEM courses such as Quantitative Reasoning and Introductory Statistics. This course streamlines the algebra content from a traditional algebra course to the skills that students on a non-STEM path truly need to be successful in their college math courses. Students will be introduced to several fields of mathematics, including consumer mathematics, logic, probability, and statistics. The goal of this course is to help students 1. learn the fundamental concepts and skills to transition to their next math course, 2. acquire the learning skills necessary for succeeding in their coursework, 3. develop reasoning and problem-solving skills, and 4. achieve satisfaction in learning so that they will be encouraged to continue their education in mathematics. The writing style of this text gives carefully worded, thorough explanations that are direct, easy to understand, and mathematically accurate. The use of color, boldface, subheadings, and shaded boxes helps students understand and reference important topics. Each topic is developed in a straightforward step-by-step manner. Each section contains many detailed examples to lead students successfully through the exercises and help them develop an understanding of the related concepts. This course chapters clearly labeled with specific paths to help student prepare for the different courses they will move on to. Students can begin by building a solid foundation of algebra skills. If a student is moving on to a quantitative reasoning course, they can learn the basics of measurement, geometry, personal finance, sets, and logic. If they are moving on to a statistics course, they can learn the basics of probability and statistics. Each chapter begins with an real-world introduction of the upcoming topic to entice students to learn. At the end of each chapter, there is a project based on another real-world situation to allow students to use the concepts and skills learned in the chapter. Both the chapter introductions and the projects will foster an awareness of how math impacts everyone’s daily life. vii Pathways to College Mathematics: Purpose and Style Preface © All Rights Reser ved.Pathways to College Mathematics: Content Highlights Strategies for Academic Success This section has been included to help students hone their skills in note taking, time management, test taking, and reading. This section also provides tips for improving memory, overcoming test anxiety, and finding a math tutor. Strategies for Academic Success Note Taking Taking notes in class is an important step in understanding new material. While there are several methods for taking notes, every note-taking method can benefit from these general tips. General Tips •Write the date and the course name at the top of each page. •Write the notes in your own words and paraphrase. •Use abbreviations, such as ft for foot, # for number, def for definition, and RHS for right-hand side. •Copy all figures or examples that are presented during the lecture. •Review and rewrite your notes after class. Do this on the same day, if possible. There are many different methods of note taking and it’s always good to explore new methods. A good time to try out new note-taking methods is when you rewrite your class notes. Be sure to try each new method a few times before deciding which works best for you. Presented here are three note-taking methods you can try out. You may even find that a blend of several methods works best for you. Note-Taking Methods Outline An outline consists of several topic headings, each followed by a series of indented bullet points that include subtopics, definitions, examples, and other details. Example: 1. Ratio a. Comparison of two quantities by division. b. Ratio of a to b i. a b ii. a : b iii. a to b c. Can be reduced d. Common units can cancel Split Page The split page method divides the page vertically into two columns with the left column narrower than the right column. Main topics go in the left column and detailed comments go in the right column. The bottom of the page is reserved for a short summary of the material covered. Example: Keywords:Notes: Ratios1. Comparison of two quantities by division 2. a b , a : b, a to b 3. Can reduce 4. Common units can cancel Summary: Ratios are used to compare quantities and units can cancel. Mapping The mapping method is the most visual of the three methods. One common way to create a mapping is to write the main idea or topic in the center and draw lines, from the main idea to smaller ideas or subtopics. Additional branches can be created from the subtopics until all of the key ideas and definitions are included. Using a different color for subtopic can help visually organize the topics. Example: Ratios Main Topic Common units cancel Comparison of quanti- ties by division Can be re- duced a b a : b a to b Questions 1. Find two other note taking methods and describe them. 2. Write five additional abbreviations that you could use while taking notes. viStrategies for Academic Success Note Taking Concept Check Exercises to assess students’ conceptual understanding of topics and important definitions are included in every section. 1. Every square is a rectangle but not every rectangle is a ________. Chapter Projects This feature promotes collaboration and shows students the practical side of mathematics through activities using real-world applications of the concepts taught in the chapter. 735Chapter 9 Project Sweet, Sweet Probability Chapter 9 Project Sweet, Sweet Probability An activity to investigate the probability of how often you really get to eat your favorite M&M color. Probability is integral to the field of statistics. Many companies use probability…make decisions regarding what products they produce and how they produce them. For example, the confectionary division of Mars Inc. uses probability to determine how many M&M’s they will make of each color. The color of M&M’s candies has changed several times and for varied reasons since the candy was introduced in the 1940s. For example, in 1995, Mars Inc. launched an M&M’s Color Campaign, which was a contest that introduced three new colors (purple, blue, and pink) to the public while asking the public to pick one of those colors to replace the tan M&M (blue won). Mars Inc. used to publish the color distribution on their website but no longer does. Let’s investigate the proportions used. Assume you open a bag of regular M&M’s and count the frequency of each color. Your results are shown in the table below. ColorFrequency Red10 Orange8 Yellow12 Green9 Blue3 Brown6 Use the data from the table above to answer the following questions. 1. What type of probability is being used for this investigation? Explain your answer. 2. IfoneM&Misrandomlyselected,findthe probability of selecting a red M&M. 3. IfoneM&Misrandomlyselected,findthe probability of selecting a blue M&M. 4. IfoneM&Misrandomlyselected,findthe probability of selecting a pink M&M. 5. IfoneM&Misrandomlyselected,findthe probability of selecting an M&M that is not brown. 6. IfoneM&Misrandomlyselected,findthe probability of selecting an orange or a yellow M&M. a. P(orange or yellow) = b. Is this event mutually exclusive? Explain your answer. 7. IfoneM&Misrandomlyselected,find the probability of selecting a red or an orange M&M. a. P(red or orange) = b. Is this event mutually exclusive? Explain your answer. Applications Real world application problems have been included throughout the text to challenge students to apply the concepts taught in the lesson. Connections Each chapter begins with a brief discussion related to a concept developed in the coming material and includes questions students will solve later in the chapter to solidify their knowledge and understanding. viii Preface Pathways to College Mathematics: Content Highlights © All Rights Reser ved.Objectives The objectives provide students with a clear and concise list of the main concepts and methods taught in each section, enabling students to focus their time and effort on the most important topics. Objectives have corresponding labels located in the section text where the topic is introduced for ease of reference. Objectives A. Multiply fractions. B. Reduce fractions to lowest terms. C. Multiply and reduce fractions to lowest terms. A First objective Examples Examples are denoted with titled headers indicating the problem-solving skill being presented. Each section contains carefully explained examples with appropriate tables, diagrams, and graphs. Examples are presented in an easy-to-understand, step-by-step fashion and annotated with notes for additional clarification. Example 1 Multiplying Fractions Multiply: 6 7 8 5 68 75 48 35 13 35 ⋅= ⋅ ⋅ = or 1 Solution 6 7 8 5 68 75 48 35 13 35 ⋅= ⋅ ⋅ = or 1 Now work margin exercise 1. Completion Examples Completion examples encourage students to practice the methods taught in the lesson by providing a partial solution to an example and guiding the student to fill in the missing parts. Answers for completion examples are located at the end of the instruction for that lesson. Example 1 Prime Factorizations Find the prime factorization of 60. Solution 60 =6· 10 = 2 · 3 · 2 · 5 = Now work margin exercise 1. Completion Example Answers 1. 6 · 10 = 2 · 3 · 2 · 5 = 22 · 3 · 5 23 5 2 ⋅⋅ Margin Exercises Each example has a corresponding margin exercise to test students’ understanding of what was taught in the example. Answers for the margin exercises are located at the end of the instruction for that lesson. 1. Solve: 3x + 4 = 7 Margin Exercise Answers 1. x = 1 Notes Note boxes in the margin point out important infor- mation that will help deepen students’ understanding of the topics. Often these are helpful hints about subtle details in the definitions that many students do not notice upon first glance. Note Greek mathematician Euclid is often referred to as the ‘Father of Geometry’ for his revolutionary ideas and influential textbook called Elements that he wrote around the year 300 BC. ix Pathways to College Mathematics: Content Highlights Preface © All Rights Reser ved.Next >