Algebra FOUNDATIONS Crisonino – Slavin ALF_1e_Book.indb 12/3/2021 11:28:11 AMEditor: Lisa Hinton Project Manager: Emily Christian Assistant Editors: Allison Conger, Marvin Glover, Barbara Miller Creative Services Manager: Trudy Tronco Designer: Joel Travis Cover Design: Lizbeth Mendoza 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. Library of Congress Control Number 2020924807 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 978-1-64277-445-0 AIE ISBN: 978-1-64277-444-3 ALF_1e_Book.indb 22/3/2021 11:28:11 AMTable of Contents Preface Algebra Foundations Content Highlights ................................................................................................ix Strategies for Academic Success ............................................................................................................xiii CHAPTER 1 Addition and Subtraction of Whole Numbers 1.1 Place Value ..................................................................................................................................... 2 1.2 Rounding ........................................................................................................................................ 6 1.3 Adding and Subtracting Whole Numbers ...................................................................................10 1.4 Applications ....................................................................................................................................17 Chapter 1 Review .........................................................................................................................20 Chapter 1 Test 1 ...........................................................................................................................23 Chapter 1 Test 2 ...........................................................................................................................25 CHAPTER 2 Multiplication and Division of Whole Numbers 2.1 Multiplying Whole Numbers .........................................................................................................30 2.2 Exponents .......................................................................................................................................36 2.3 Squares and Roots of Whole Numbers .......................................................................................39 2.4 Dividing Whole Numbers ..............................................................................................................45 2.5 Arithmetic Properties ....................................................................................................................56 2.6 Order of Operations Applied to Whole Numbers ......................................................................61 2.7 Applications ....................................................................................................................................65 Chapter 2 Review .........................................................................................................................72 Chapter 2 Test 1 ...........................................................................................................................74 Chapter 2 Test 2 ...........................................................................................................................76 CHAPTER 3 Fractions and Mixed Numbers 3.1 Picturing Fractions, Mixed Numbers, and Improper Fractions ................................................81 3.2 Prime Factorization and Reducing Fractions ..............................................................................89 3.3 Multiplying and Dividing Fractions and Mixed Numbers ..........................................................98 3.4 Adding and Subtracting Fractions and Mixed Numbers ........................................................110 3.5 Complex Fractions and the Order of Operations Applied to Fractions and Mixed Numbers ..................................................................................................124 3.6 Applications .................................................................................................................................134 Chapter 3 Review ......................................................................................................................140 Chapter 3 Test 1 ........................................................................................................................145 Chapter 3 Test 2 ........................................................................................................................148 ALF_1e_Book.indb 32/3/2021 11:28:12 AMCHAPTER 4 Decimals 4.1 Place Value ..................................................................................................................................154 4.2 Rounding Decimals .....................................................................................................................161 4.3 Adding and Subtracting Decimals .............................................................................................165 4.4 Multiplying Decimals ..................................................................................................................169 4.5 Dividing Decimals .......................................................................................................................178 4.6 Square Roots of Decimals ..........................................................................................................185 4.7 Order of Operations Applied to Decimals ...............................................................................188 4.8 Applications .................................................................................................................................191 Chapter 4 Review ......................................................................................................................197 Chapter 4 Test 1 ........................................................................................................................199 Chapter 4 Test 2 ........................................................................................................................200 CHAPTER 5 Conversions, Ratios, and Proportions 5.1 Fraction and Decimal Conversions ...........................................................................................204 5.2 Rate and Ratio .............................................................................................................................215 5.3 Length, Distance, and Weight ....................................................................................................221 5.4 Unit Pricing ..................................................................................................................................226 5.5 Dimensional Analysis .................................................................................................................230 5.6 Solving Equations by Division ....................................................................................................236 5.7 Proportions .................................................................................................................................240 Chapter 5 Review ......................................................................................................................249 Chapter 5 Test 1 ........................................................................................................................252 Chapter 5 Test 2 ........................................................................................................................253 CHAPTER 6 Percents 6.1 What Are Percents? ....................................................................................................................256 6.2 Basic Percent Problems .............................................................................................................271 6.3 Solving Percent Word Problems ...............................................................................................279 6.4 Applications .................................................................................................................................286 Chapter 6 Review ......................................................................................................................294 Chapter 6 Test 1 ........................................................................................................................296 Chapter 6 Test 2 ........................................................................................................................297 ivTable of Contents ALF_1e_Book.indb 42/3/2021 11:28:12 AMCHAPTER 7 Introduction to Geometry 7.1 Perimeter and Area ....................................................................................................................300 7.2 Circles ...........................................................................................................................................312 7.3 Volume .........................................................................................................................................318 7.4 Applications .................................................................................................................................322 Chapter 7 Review ......................................................................................................................327 Chapter 7 Test 1 ........................................................................................................................329 Chapter 7 Test 2 ........................................................................................................................331 CHAPTER 8 Signed Numbers 8.1 Basic Notation .............................................................................................................................334 8.2 Adding and Subtracting Signed Numbers ................................................................................340 8.3 Multiplying and Dividing Signed Numbers ..............................................................................353 8.4 Order of Operations Applied to Signed Numbers ..................................................................363 8.5 Applications .................................................................................................................................374 8.6 The Real Number System ..........................................................................................................379 Chapter 8 Review ......................................................................................................................383 Chapter 8 Test 1 ........................................................................................................................385 Chapter 8 Test 2 ........................................................................................................................387 CHAPTER 9 Exponents and Algebraic Expressions 9.1 Basic Rules of Exponents Applied to Multiplication ................................................................390 9.2 Algebraic Substitution ................................................................................................................399 9.3 Combining Like Terms and the Distributive Property ............................................................408 9.4 Translating Words into Mathematical Symbols ......................................................................418 Chapter 9 Review ......................................................................................................................430 Chapter 9 Test 1 ........................................................................................................................433 Chapter 9 Test 2 ........................................................................................................................434 CHAPTER 10 Linear Equations and Inequalities 10.1 Solving Linear Equations in One Variable ................................................................................438 10.2 Notations and Graphs of Inequalities ......................................................................................448 10.3 Solving Linear Inequalities in One Variable .............................................................................453 10.4 Applications .................................................................................................................................462 Chapter 10 Review ....................................................................................................................474 Chapter 10 Test 1 ......................................................................................................................477 Chapter 10 Test 2 ......................................................................................................................478 vTable of Contents ALF_1e_Book.indb 52/3/2021 11:28:12 AMCHAPTER 11 Fractional Expressions 11.1 Reducing Fractional Expressions ..............................................................................................482 11.2 Multiplying and Dividing Fractional Expressions ....................................................................487 11.3 Adding and Subtracting Algebraic Fractions ............................................................................494 11.4 Solving Fractional Equations and Inequalities .........................................................................502 11.5 Ratios and Proportions ..............................................................................................................511 Chapter 11 Review ....................................................................................................................519 Chapter 11 Test 1 ......................................................................................................................522 Chapter 11 Test 2 ......................................................................................................................523 CHAPTER 12 Negative Exponents and Polynomials 12.1 More Basic Rules of Exponents .................................................................................................526 12.2 Zero and Negative Exponents ...................................................................................................533 12.3 Scientific Notation.......................................................................................................................546 12.4 Introduction to Polynomials, Multiplying Polynomials, and Special Product Rules .........................................................................................................553 Chapter 12 Review ....................................................................................................................564 Chapter 12 Test 1 ......................................................................................................................567 Chapter 12 Test 2 ......................................................................................................................568 CHAPTER 13 Factoring, Solving Equations by Factoring, and Division of Polynomials 13.1 The Greatest Common Factor and Factoring by Grouping ....................................................572 13.2 The Difference of Two Squares and the Sum and Difference of Two Cubes .......................581 13.3 Factoring Trinomials: Leading Coefficient is One ....................................................................590 13.4 Factoring Trinomials: Leading Coefficient is NOT One ...........................................................597 13.5 Solving Equations by Factoring .................................................................................................606 13.6 Dividing Polynomials ..................................................................................................................614 Chapter 13 Review ....................................................................................................................620 Chapter 13 Test 1 ......................................................................................................................622 Chapter 13 Test 2 ......................................................................................................................624 viTable of Contents ALF_1e_Book.indb 62/3/2021 11:28:12 AMCHAPTER 14 Rational Expressions 14.1 Reducing Rational Expressions .................................................................................................628 14.2 Multiplying and Dividing Rational Expressions .......................................................................633 14.3 Adding and Subtracting Rational Expressions and Solving Rational Equations and Inequalities .........................................................................................638 14.4 Absolute Value Equations and Inequalities .............................................................................650 14.5 Simplifying Complex Fractions ..................................................................................................663 14.6 Solving Literal Equations ............................................................................................................669 14.7 Applications .................................................................................................................................676 Chapter 14 Review ....................................................................................................................685 Chapter 14 Test 1 ......................................................................................................................689 Chapter 14 Test 2 ......................................................................................................................692 CHAPTER 15 Graphing, Writing, and Interpreting Linear Equations 15.1 The Cartesian Coordinate System and Graphing Linear Equations ......................................696 15.2 Finding and Interpreting the Slope of a Linear Equation .......................................................729 15.3 Writing the Equation of a Line ...................................................................................................745 Chapter 15 Review ....................................................................................................................758 Chapter 15 Test 1 ......................................................................................................................766 Chapter 15 Test 2 ......................................................................................................................769 CHAPTER 16 Solving Systems of Linear Equations 16.1 Solving Systems of Linear Equations Using the Graphing Method .......................................774 16.2 Solving Systems of Linear Equations by the Elimination and Substitution Methods ..........779 16.3 Applications .................................................................................................................................791 Chapter 16 Review ....................................................................................................................803 Chapter 16 Test 1 ......................................................................................................................807 Chapter 16 Test 2 ......................................................................................................................809 CHAPTER 17 Simplifying Radical Expressions and Solving Radical Equations 17.1 The Basics ....................................................................................................................................812 17.2 Adding and Subtracting Radical Expressions ..........................................................................821 17.3 Multiplying Radical Expressions and Rationalizing Denominators .......................................825 17.4 Solving Radical Equations ..........................................................................................................839 Chapter 17 Review ....................................................................................................................848 Chapter 17 Test 1 ......................................................................................................................852 Chapter 17 Test 2 ......................................................................................................................853 viiTable of Contents ALF_1e_Book.indb 72/3/2021 11:28:12 AMCHAPTER 18 Quadratic Equations 18.1 Solving Quadratic Equations Using the Factoring Method ....................................................856 18.2 Solving Quadratic Equations Using the Square Root Method ...............................................863 18.3 Solving Quadratic Equations Using the Completing the Square Method.............................869 18.4 Solving Quadratic Equations Using the Quadratic Formula ..................................................878 18.5 Graphing Quadratic Equations and Applications of Quadratic Equations ...........................889 18.6 Complex Numbers and Complex Solutions to Quadratic Equations ....................................913 Chapter 18 Review ....................................................................................................................920 Chapter 18 Test 1 ......................................................................................................................924 Chapter 18 Test 2 ......................................................................................................................926 Answer Key ..........................................................................................................................................AK-1 Index ...........................................................................................................................................................I-1 viiiTable of Contents ALF_1e_Book.indb 82/3/2021 11:28:12 AMAlgebra Foundations Î Practice Problems Throughout each lesson, we’ve included Practice Problems for students to quickly assess what has just been taught. Each Practice Problem section includes solutions so students can have immediate feedback. Î Workbook Each lesson concludes with a selection of exercises designed to allow the student to practice skills and master concepts. Î Challenge Problems Challenge problems are included at the end of many of the workbook sections for instructors to assign if exercises with a higher degree of difficulty are desired. Î Chapter Reviews Chapter Reviews are presented at the end of each chapter and have an additional selection of exercises. designed to prepare students for the upcoming Chapter Tests. Î Chapter Tests Every chapter concludes with two tests. The tests are of different lengths and difficulty levels. ixPreface ALF_1e_Book.indb 92/3/2021 11:28:14 AMNext >