Beginning Algebra
MATH 100B
,2
Preface
This math book has been created by the BYU-Idaho Math Study Center for the
college student who needs an introduction to Algebra. This book is the product of many
years of implementation of an extremely successful Beginning Algebra program and
includes perspectives and tips from experienced instructors and tutors.
Videos of instruction and solutions can be found at the following url:
https://youtu.be/YKgyvSq42j8
We hope that it will be helpful to you as you take Algebra this semester.
The BYU-Idaho Math Study Center
July 2023 Edition
, 3
Contents
Preface......................................................................................................................................................... 2
Section R-1 Factoring and Least Common Multiple .................................................................................. 7
Factoring ................................................................................................................................................. 7
Least Common Multiple ......................................................................................................................... 8
Section R-1 Exercises ........................................................................................................................... 10
Section R-2 Fractions and Decimals ......................................................................................................... 12
Arithmetic of Fractions ......................................................................................................................... 12
Arithmetic of Decimals ......................................................................................................................... 15
Turn a Fraction into a Decimal ............................................................................................................. 16
Section R-2 Exercises ........................................................................................................................... 17
Section R-3 Rounding, Percents, Exponents, Roots, and Order of Operations ........................................ 19
Rounding ............................................................................................................................................... 19
Percents ................................................................................................................................................. 20
Section R-3 Exercises ........................................................................................................................... 23
Section R-4 Variables and Formulas ........................................................................................................ 26
Variables ............................................................................................................................................... 26
Formulas ............................................................................................................................................... 28
Section R-4 Exercises ........................................................................................................................... 35
Chapter R Review Exercises ................................................................................................................. 38
Section 1-1 Negatives, Addition, Subtraction, Inequalities ...................................................................... 41
Number Line ......................................................................................................................................... 41
Inequalities ............................................................................................................................................ 41
Absolute Value...................................................................................................................................... 42
Adding/Subtracting Negatives .............................................................................................................. 43
Section 1-1 Exercises ............................................................................................................................ 46
Perform the indicated operation. ........................................................................................................... 46
Section 1-2 Negatives in Multiplication and Division .............................................................................. 49
Common Mistakes ................................................................................................................................ 50
Section 1-2 Exercises ............................................................................................................................ 51
Section 1-3 Laws of Simplifying .............................................................................................................. 53
Laws of Simplifying ............................................................................................................................. 53
Factoring ............................................................................................................................................... 54
Simplifying with Variables ................................................................................................................... 55
, 4
Section 1-3 Exercises ............................................................................................................................ 57
Chapter 1 Review Exercises ................................................................................................................. 60
Section 2-1 The 3-Step Process to Solving: .............................................................................................. 63
Basics .................................................................................................................................................... 63
The Balance Rule .................................................................................................................................. 64
3-Step Process to solving: The Addition Principle ............................................................................... 65
3-Step Process to solving: The Multiplication Principle ...................................................................... 67
SOLVING: Using Both Addition and Multiplication Principles Together .......................................... 68
Section 2-1 Exercises ............................................................................................................................ 69
Section 2-2 Applications and Formulas .................................................................................................... 72
D.U.P.E. Process for word problems with translation & formulas ....................................................... 72
Section 2-2 Exercises ............................................................................................................................ 77
Section 2-3 3-Step Process to Solving ...................................................................................................... 80
Combine “like terms” and get all x’s on one side ................................................................................. 80
Distributing across ( )............................................................................................................................ 81
Special Cases ........................................................................................................................................ 82
Section 2-3 Exercises ............................................................................................................................ 83
Section 2-4 Applications: Substitution and Percents ................................................................................ 86
D.U.P.E. Process for word problems with substitution ........................................................................ 86
Simple Percent Problems ...................................................................................................................... 89
Forward Percent Problems .................................................................................................................... 90
Backward Percent Problems ................................................................................................................. 91
Reverse Averages.................................................................................................................................. 92
Section 2-4 Exercises ............................................................................................................................ 93
Section 2-5 The 3-Step Process to Solving ............................................................................................... 96
Section 2-5 Exercises ............................................................................................................................ 99
Section 2-6 Inequalities........................................................................................................................... 102
Section 2-6 Exercises .......................................................................................................................... 105
Section 2-7 Word Problems: Inequalities ............................................................................................... 108
Section 2-7 Exercises .......................................................................................................................... 111
Chapter 2 Review Exercises ............................................................................................................... 114
Section 3-1 Coordinates and Graphing Lines ......................................................................................... 117
Graphs ................................................................................................................................................. 117
Finding Points ..................................................................................................................................... 118
MATH 100B
,2
Preface
This math book has been created by the BYU-Idaho Math Study Center for the
college student who needs an introduction to Algebra. This book is the product of many
years of implementation of an extremely successful Beginning Algebra program and
includes perspectives and tips from experienced instructors and tutors.
Videos of instruction and solutions can be found at the following url:
https://youtu.be/YKgyvSq42j8
We hope that it will be helpful to you as you take Algebra this semester.
The BYU-Idaho Math Study Center
July 2023 Edition
, 3
Contents
Preface......................................................................................................................................................... 2
Section R-1 Factoring and Least Common Multiple .................................................................................. 7
Factoring ................................................................................................................................................. 7
Least Common Multiple ......................................................................................................................... 8
Section R-1 Exercises ........................................................................................................................... 10
Section R-2 Fractions and Decimals ......................................................................................................... 12
Arithmetic of Fractions ......................................................................................................................... 12
Arithmetic of Decimals ......................................................................................................................... 15
Turn a Fraction into a Decimal ............................................................................................................. 16
Section R-2 Exercises ........................................................................................................................... 17
Section R-3 Rounding, Percents, Exponents, Roots, and Order of Operations ........................................ 19
Rounding ............................................................................................................................................... 19
Percents ................................................................................................................................................. 20
Section R-3 Exercises ........................................................................................................................... 23
Section R-4 Variables and Formulas ........................................................................................................ 26
Variables ............................................................................................................................................... 26
Formulas ............................................................................................................................................... 28
Section R-4 Exercises ........................................................................................................................... 35
Chapter R Review Exercises ................................................................................................................. 38
Section 1-1 Negatives, Addition, Subtraction, Inequalities ...................................................................... 41
Number Line ......................................................................................................................................... 41
Inequalities ............................................................................................................................................ 41
Absolute Value...................................................................................................................................... 42
Adding/Subtracting Negatives .............................................................................................................. 43
Section 1-1 Exercises ............................................................................................................................ 46
Perform the indicated operation. ........................................................................................................... 46
Section 1-2 Negatives in Multiplication and Division .............................................................................. 49
Common Mistakes ................................................................................................................................ 50
Section 1-2 Exercises ............................................................................................................................ 51
Section 1-3 Laws of Simplifying .............................................................................................................. 53
Laws of Simplifying ............................................................................................................................. 53
Factoring ............................................................................................................................................... 54
Simplifying with Variables ................................................................................................................... 55
, 4
Section 1-3 Exercises ............................................................................................................................ 57
Chapter 1 Review Exercises ................................................................................................................. 60
Section 2-1 The 3-Step Process to Solving: .............................................................................................. 63
Basics .................................................................................................................................................... 63
The Balance Rule .................................................................................................................................. 64
3-Step Process to solving: The Addition Principle ............................................................................... 65
3-Step Process to solving: The Multiplication Principle ...................................................................... 67
SOLVING: Using Both Addition and Multiplication Principles Together .......................................... 68
Section 2-1 Exercises ............................................................................................................................ 69
Section 2-2 Applications and Formulas .................................................................................................... 72
D.U.P.E. Process for word problems with translation & formulas ....................................................... 72
Section 2-2 Exercises ............................................................................................................................ 77
Section 2-3 3-Step Process to Solving ...................................................................................................... 80
Combine “like terms” and get all x’s on one side ................................................................................. 80
Distributing across ( )............................................................................................................................ 81
Special Cases ........................................................................................................................................ 82
Section 2-3 Exercises ............................................................................................................................ 83
Section 2-4 Applications: Substitution and Percents ................................................................................ 86
D.U.P.E. Process for word problems with substitution ........................................................................ 86
Simple Percent Problems ...................................................................................................................... 89
Forward Percent Problems .................................................................................................................... 90
Backward Percent Problems ................................................................................................................. 91
Reverse Averages.................................................................................................................................. 92
Section 2-4 Exercises ............................................................................................................................ 93
Section 2-5 The 3-Step Process to Solving ............................................................................................... 96
Section 2-5 Exercises ............................................................................................................................ 99
Section 2-6 Inequalities........................................................................................................................... 102
Section 2-6 Exercises .......................................................................................................................... 105
Section 2-7 Word Problems: Inequalities ............................................................................................... 108
Section 2-7 Exercises .......................................................................................................................... 111
Chapter 2 Review Exercises ............................................................................................................... 114
Section 3-1 Coordinates and Graphing Lines ......................................................................................... 117
Graphs ................................................................................................................................................. 117
Finding Points ..................................................................................................................................... 118
