-PRE-ALGEBRA 1
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-PRE-ALGEBRA 1
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301
Chapter 1: Sets
Theory
Page 11
1.1 Basic Concepts of Sets
Theory
Page 12
Defining a Set
Theory
Page 12
Representing Sets
Theory
Page 13
Number of Elements of a Set
Theory
Page 14
Comparing Sets
Theory
Page 15
Types of Sets
Theory
Page 16
Subsets
Theory
Page 18
Exercises 1.1
Problem
Page 21
1.2 Operations on Sets
Theory
Page 23
Union of Sets
Theory
Page 23
Intersection of Sets
Theory
Page 25
Complement of a Set
Theory
Page 28
Difference of Two Sets
Theory
Page 29
Survey Problems
Problem
Page 31
Exercises 1.2
Problem
Page 34
Chapter 1 Map
Other
Page 35
Chapter 1 Review Exercises
Problem
Page 38
Chapter 1 Review Test
Test
Page 41
Chapter 2: Numeration Systems
Theory
Page 43
2.1 Numeration Systems
Theory
Page 44
Ancient Numeration Systems
Theory
Page 44
Introduction
Theory
Page 44
The Egyptian Numeration System
Theory
Page 44
The Babylonian Numeration System
Theory
Page 45
The Roman Numeration System
Theory
Page 46
The Mayan Numeration System
Theory
Page 47
The Hindu-Arabic Numeration System
Theory
Page 48
The Decimal Place Value System
Theory
Page 49
Exponential Notation
Theory
Page 50
Expanded Notation in the Decimal System
Theory
Page 52
Powers of Ten
Theory
Page 52
Expanded Notation
Theory
Page 52
Exercises 2.1
Problem
Page 54
2.2 Arithmetic in Other Bases
Theory
Page 55
The Base 5 Counting System
Theory
Page 55
Converting Base 5 Numbers to Base 10
Theory
Page 55
Converting Base 10 Numbers to Base 5
Theory
Page 56
The Binary (Base 2) Counting System
Theory
Page 57
Converting Base 2 Numbers to Base 10
Theory
Page 57
Converting Base 10 Numbers to Base 2
Theory
Page 58
Chapter 2 Map
Other
Page 61
Chapter 2 Review Exercises
Problem
Page 64
Chapter 2 Review Test
Test
Page 66
Chapter 3: Natural Numbers
Theory
Page 67
3.1 Natural Numbers
Theory
Page 68
The Concept of Natural Numbers
Theory
Page 68
Natural Numbers
Theory
Page 68
Whole Numbers
Theory
Page 68
The Order of Natural Numbers
Theory
Page 69
Betweenness in N
Theory
Page 70
Addition of Natural Numbers
Theory
Page 71
Concept of Addition
Theory
Page 71
Addition on a Number Line
Theory
Page 72
Properties of Addition in N
Theory
Page 73
Subtraction of Natural Numbers
Theory
Page 74
Concept of Subtraction
Theory
Page 74
Subtraction on a Number Line
Theory
Page 75
Properties of Subtraction in N
Theory
Page 76
Multiplication of Natural Numbers
Theory
Page 77
Concept of Multiplication
Theory
Page 77
Multiplication on a Number Line
Theory
Page 78
Multiplying Powers of Ten
Theory
Page 78
Properties of Multiplication in N
Theory
Page 79
Division of Natural Numbers
Theory
Page 81
Concept of Division
Theory
Page 81
Division with Remainder
Theory
Page 81
Zero in Division
Theory
Page 82
Properties of Division in N
Theory
Page 82
Mixed Operations
Theory
Page 83
Order of Operations
Theory
Page 83
The Sum of Consecutive Natural Numbers
Theory
Page 84
Written Problems
Problem
Page 86
Chapter 3 Map
Other
Page 87
Chapter 3 Review Exercises
Problem
Page 89
Chapter 3 Review Test
Test
Page 90
Chapter 4: Divisibility, Greatest Common Factor and Least Common Multiple
Theory
Page 91
4.1 Division of Natural Numbers
Theory
Page 92
Rules of Divisibility
Theory
Page 92
The Division Algorithm
Theory
Page 92
Divisibility Rules
Theory
Page 93
Factors and Divisors of Natural Numbers
Theory
Page 99
Exercises 4.1
Problem
Page 100
4.2 Factorization of Natural Numbers
Theory
Page 101
Prime Numbers and Composite Numbers
Theory
Page 101
Prime Numbers
Theory
Page 101
Composite Numbers
Theory
Page 101
Prime Factorization of Natural Numbers
Theory
Page 103
Prime Factors
Theory
Page 103
Prime Factorization
Theory
Page 104
Number of Factors of a Natural Number
Theory
Page 106
4.3 Greatest Common Factor and Least Common Multiple
Theory
Page 108
Greatest Common Factor (GCF)
Theory
Page 108
Common Factors
Theory
Page 108
Greatest Common Factor (GCF)
Theory
Page 109
Relatively Prime Numbers
Theory
Page 110
Written Problems
Problem
Page 111
Least Common Multiple (LCM)
Theory
Page 113
Common Multiple
Theory
Page 113
Least Common Multiple
Theory
Page 113
Written Problems
Problem
Page 114
Properties of the Greatest Common Factor and the Least Common Multiple
Theory
Page 115
Chapter 4 Map
Other
Page 117
Chapter 4 Review Exercises
Problem
Page 119
Chapter 4 Review Test
Test
Page 120
Chapter 5: Integers
Theory
Page 121
5.1 Integers
Theory
Page 122
Understanding Integers
Theory
Page 122
Integers on the Number Line
Theory
Page 124
The Order of Integers
Theory
Page 125
Exercises 5.1
Problem
Page 126
5.2 Addition of Integers
Theory
Page 127
Addition in Z
Theory
Page 127
Properties of Addition in Z
Theory
Page 129
Closure Property
Theory
Page 129
Commutative Property
Theory
Page 129
Associative Property
Theory
Page 129
Identity Element
Theory
Page 130
Inverse Element
Theory
Page 130
Exercises 5.2
Problem
Page 131
5.3 Subtraction of Integers
Theory
Page 133
Subtraction in Z
Theory
Page 133
Properties of Subtraction in Z
Theory
Page 134
Closure Property
Theory
Page 134
Commutative Property
Theory
Page 134
Associative Property
Theory
Page 135
Identity Element
Theory
Page 135
Exercises 5.3
Problem
Page 135
5.4 Multiplication of Integers
Theory
Page 136
Multiplication in Z
Theory
Page 136
Properties of Multiplication in Z
Theory
Page 138
Closure Property
Theory
Page 138
Commutative Property
Theory
Page 138
Associative Property
Theory
Page 138
Identity Element
Theory
Page 139
Null Element
Theory
Page 139
The Distributive Property of Multiplication Over Addition
Theory
Page 139
The Distributive Property of Multiplication Over Subtraction
Theory
Page 139
Powers of Integers
Theory
Page 140
Understanding Powers of Integers
Theory
Page 140
Square of an Integer
Theory
Page 140
Cube of an Integer
Theory
Page 140
Even and Odd Powers of a Negative Integer
Theory
Page 141
Powers of Ten
Theory
Page 142
Exercises 5.4
Problem
Page 143
5.5 Division of Integers, and Mixed Operations
Theory
Page 144
Division in Z
Theory
Page 144
Understanding Division in Z
Theory
Page 144
Dividing Integers by 1 and −1
Theory
Page 144
Dividing Integers by Powers of Ten
Theory
Page 144
Properties of Division in Z
Theory
Page 146
Closure Property
Theory
Page 146
Commutative Property
Theory
Page 146
Associative Property
Theory
Page 146
Identity Element
Theory
Page 146
Null Element
Theory
Page 146
Distributive Property
Theory
Page 146
Mixed Operations in Z
Theory
Page 146
Exercises 5.5
Problem
Page 148
Chapter 5 Map
Other
Page 149
Chapter 5 Review Exercises
Problem
Page 151
Chapter 5 Review Test
Test
Page 152
Chapter 6: Rational Numbers
Theory
Page 153
6.1 Fractions
Theory
Page 154
Concept of Fraction
Theory
Page 154
Understanding Fractions
Theory
Page 154
Terms of a Fraction
Theory
Page 155
Types of Fraction
Theory
Page 156
Proper Fractions
Theory
Page 156
Improper Fractions
Theory
Page 156
Mixed Numbers
Theory
Page 157
Writing an Improper Fraction as a Mixed Number
Theory
Page 157
Writing a Mixed Number as an Improper Fraction
Theory
Page 158
Representing Fractions on a Number Line
Theory
Page 159
Equivalent Fractions
Theory
Page 160
Equivalent Fractions
Theory
Page 160
Enlarging a Fraction
Theory
Page 161
Simplifying and Reducing a Fraction
Theory
Page 162
Written Problems
Problem
Page 163
Exercises 6.1
Problem
Page 164
6.2 Rational Numbers
Theory
Page 166
Rational Numbers: The Set Q
Theory
Page 166
Understanding Rational Numbers
Theory
Page 166
The Set of Positive Rational Numbers
Theory
Page 166
The Set of Negative Rational Numbers
Theory
Page 166
The Set of Rational Numbers
Theory
Page 167
Showing Rational Numbers on the Number Line
Theory
Page 168
Comparing and Ordering Rational Numbers
Theory
Page 170
Comparing and Ordering Positive Rational Numbers
Theory
Page 170
Comparing and Ordering Negative Rational Numbers
Theory
Page 174
Density Property of Rational Numbers
Theory
Page 175
Exercises 6.2
Problem
Page 178
6.3 Addition of Rational Numbers
Theory
Page 179
Addition in Q
Theory
Page 179
Adding Rational Numbers with Common Denominators
Theory
Page 179
Adding Rational Numbers with Different Denominators
Theory
Page 180
Properties of Addition in Q
Theory
Page 183
Exercises 6.3
Problem
Page 184
6.4 Subtraction of Rational Numbers
Theory
Page 185
Subtraction in Q
Theory
Page 185
Subtracting Rational Numbers with Common Denominators
Theory
Page 185
Subtracting Rational Numbers with Different Denominators
Theory
Page 186
Properties of Subtraction in Q
Theory
Page 187
Exercises 6.4
Problem
Page 188
6.5 Multiplication of Rational Numbers
Theory
Page 189
Multiplication in Q
Theory
Page 189
Multiplying Two Rational Numbers
Theory
Page 189
Multiplying a Rational Number by an Integer
Theory
Page 190
Multiplying Mixed Numbers
Theory
Page 190
Properties of Multiplication in Q
Theory
Page 191
Powers of Rational Numbers
Theory
Page 193
Understanding Powers of Rational Numbers
Theory
Page 193
Even and Odd Powers of Negative Rational Numbers
Theory
Page 194
Exercises 6.5
Problem
Page 196
6.6 Division of Rational Numbers
Theory
Page 197
Division in Q
Theory
Page 197
Properties of Division in Q
Theory
Page 200
Exercises 6.6
Problem
Page 201
6.7 Mixed Operations
Theory
Page 202
Mixed Operations in Q
Theory
Page 202
Operations on Complex Fractions
Theory
Page 203
Exercises 6.7
Problem
Page 210
Chapter 6 Map
Other
Page 211
Chapter 6 Review Exercises
Problem
Page 214
Chapter 6 Review Test
Test
Page 217
Chapter 7: Decimal Numbers
Theory
Page 219
7.1 Decimals
Theory
Page 220
The Concept of Decimal Number
Theory
Page 220
Understanding Decimals and Decimal Fractions
Theory
Page 220
Decimal Notation
Theory
Page 221
Representing Decimals on the Number Line
Theory
Page 226
Comparing and Ordering Decimals
Theory
Page 226
Relationship Between Fractions and Decimal Numbers
Theory
Page 228
Terminating Decimals
Theory
Page 228
Repeating Decimals
Theory
Page 228
Rounding Decimals
Theory
Page 231
Exercises 7.1
Problem
Page 233
7.2 Addition and Subtraction of Decimals
Theory
Page 235
Addition of Decimals
Theory
Page 235
Subtraction of Decimals
Theory
Page 238
Exercises 7.2
Problem
Page 239
7.3 Multiplication and Division of Decimals
Theory
Page 240
Multiplication of Decimals
Theory
Page 240
Multiplying Decimals
Theory
Page 240
Multiplying a Decimal by a Power of 10
Theory
Page 242
Division of Decimals
Theory
Page 243
Dividing a Decimal by a Whole Number
Theory
Page 243
Dividing a Decimal by a Decimal Number
Theory
Page 244
Dividing a Decimal by a Power of 10
Theory
Page 247
Mixed Operations
Theory
Page 248
Written Problems
Problem
Page 249
Exercises 7.3
Problem
Page 250
7.4 Very Large and Very Small Numbers
Theory
Page 252
Scientific Notation
Theory
Page 252
Understanding Scientific Notation
Theory
Page 252
Converting from Standard Notation to Scientific Notation
Theory
Page 254
Converting From Scientific Notation to Standard Notation
Theory
Page 255
Operations in Scientific Notation
Theory
Page 256
Addition and Subtraction in Scientific Notation
Theory
Page 256
Multiplication and Division in Scientific Notation
Theory
Page 257
Exercises 7.4
Problem
Page 259
Chapter 7 Map
Other
Page 260
Chapter 7 Review Exercises
Problem
Page 263
Chapter 7 Review Test
Test
Page 265
Chapter 8: Real Numbers
Theory
Page 267
8.1 Real Numbers
Theory
Page 268
The Set of Real Numbers
Theory
Page 268
Understanding Real Numbers
Theory
Page 268
Properties of Real Numbers
Theory
Page 270
Absolute Value
Theory
Page 271
Properties of the Absolute Value
Theory
Page 272
Exercises 8.1
Problem
Page 274
8.2 Exponents
Theory
Page 275
Powers of Real Numbers
Theory
Page 275
Properties of Exponents
Theory
Page 276
Exponential Equations
Theory
Page 282
Exercises 8.2
Problem
Page 285
8.3 Square Roots
Theory
Page 287
Understanding Square Roots
Theory
Page 287
Properties of Square Roots
Theory
Page 288
Working with Pure and Mixed Radicals
Theory
Page 290
Multiplying Square Roots
Theory
Page 295
Rationalizing Denominators
Theory
Page 297
Exercises 8.3
Problem
Page 300
8.4 Rational Exponents
Theory
Page 302
Rational Exponents
Theory
Page 302
nth Roots
Theory
Page 302
Rational Exponents
Theory
Page 303
Properties of Radicals
Theory
Page 304
Radical Equations
Theory
Page 306
Exercises 8.4
Problem
Page 309
Chapter 8 Map
Other
Page 310
Chapter 8 Review Exercises
Problem
Page 313
Chapter 8 Review Test 1
Test
Page 315
Chapter 8 Review Test 2
Test
Page 317
Answers to Practice Problems
Answer
Page 319
Answers to Exercises
Answer
Page 328
Answers to Review Exercises
Answer
Page 335
Answers to Review Tests
Answer
Page 337
Symbols
Other
Page 338
Glossary
Other
Page 339
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