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CliffsNotes Basic Math & PreAlgebra Quick Review, 2nd Edition
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Overview
Inside the Book:
 Preliminaries
 Whole numbers
 Decimals
 Fractions
 Percents
 Integers and rationals
 Powers, exponents, and roots
 Powers of ten and scientific notation
 Measurements
 Graphs
 Probability and statistics
 Number series
 Variables, algebraic expressions, and simple equations
 Word problems
 Review questions
 Resource center
 Glossary
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Product Details
ISBN13:  9780470880401 

Publisher:  Houghton Mifflin Harcourt 
Publication date:  05/03/2011 
Pages:  192 
Sales rank:  392,732 
Product dimensions:  5.12(w) x 8.12(h) x 0.44(d) 
Age Range:  15 Years 
About the Author
JERRY BOBROW, Ph.D. was a national authority in the field of test preparation. His testprep company, Bobrow Test Preparation Services, administered test preparation programs at over 25 California institutions.
Read an Excerpt
JERRY BOBROW, Ph.D. was a national authority in the field of test preparation. His testprep company, Bobrow Test Preparation Services, administered test preparation programs at over 25 California institutions.
First Chapter
JERRY BOBROW, Ph.D. was a national authority in the field of test preparation. His testprep company, Bobrow Test Preparation Services, administered test preparation programs at over 25 California institutions.
Table of Contents
Introduction 1
Chapter 1: Preliminaries 3
Groups of Numbers 3
Ways to Show Multiplication and Division 4
Multiplying and Dividing Using Zero 5
Common Math Symbols 5
Properties of Basic Mathematical Operations 6
Some properties (axioms) of addition 6
Some properties (axioms) of multiplication7
A property of two operations 8
Grouping Symbols and Order of Operations 9
Order of Operations 10
Chapter 2: Whole Numbers 12
Place Value 12
Expanded notation 13
Rounding off 14
Estimating Sums, Diff erences, Products, and Quotients 14
Estimating sums 14
Estimating differences 14
Estimating products 15
Estimating quotients 16
Divisibility Rules 16
Factors, Primes, Composites, and Factor Trees 17
Factors 18
Prime numbers 18
Composite numbers 18
Factor trees 19
Chapter 3: Decimals 21
Using the Place Value Grid 22
Expanded notation 22
Writing decimals 23
Comparing decimals 23
Rounding decimals 24
Decimal Computation 24
Adding and subtracting decimals 25
Multiplying decimals 26
Dividing decimals 26
Estimating Sums, Differences, Products, and Quotients 27
Estimating sums 27
Estimating differences 28
Estimating products 28
Estimating quotients 29
Repeating Decimals 30
Chapter 4: Fractions 31
Proper and Improper Fractions 32
Mixed Numbers 32
Changing improper fractions 32
Changing mixed numbers 32
Renaming Fractions33
Equivalent fractions 33
Simplifying fractions 33
Enlarging denominators 34
Factors 34
Common factors 35
Greatest common factor 35
Multiples 36
Common multiples 36
Least common multiple 36
Adding and Subtracting Fractions 37
Adding fractions 37
Subtracting fractions 38
Adding and Subtracting Mixed Numbers 39
Adding mixed numbers 39
Subtracting mixed numbers 40
Multiplying Fractions and Mixed Numbers41
Multiplying fractions 42
Multiplying mixed numbers 43
Dividing Fractions and Mixed Numbers 43
Dividing fractions 43
Dividing complex fractions 44
Dividing mixed numbers 45
Simplifying Fractions and Complex Fractions 45
Changing Fractions to Decimals 48
Changing Terminating Decimals to Fractions 49
Changing Infi nite Repeating Decimals to Fractions 50
Chapter 5: Percents 53
Changing Percents, Decimals, and Fractions 53
Changing decimals to percents 53
Changing percents to decimals 54
Changing fractions to percents 54
Changing percents to fractions 55
Important Equivalents 56
Applications of Percents 57
Finding percent of a number 57
Finding what percent one number is of another 58
Finding a number when a percent of it is known 60
Percent—proportion method 61
Finding percent increase or percent decrease 64
Chapter 6: Integers and Rationals 66
Integers 66
Number lines 66
Addition of integers 67
Subtraction of integers 68
Minus preceding a parenthesis 69
Multiplying and dividing integers 70
Absolute value 70
Rationals (Signed Numbers Including Fractions) 71
Negative fractions 71
Adding positive and negative fractions 71
Adding positive and negative mixed numbers 72
Subtracting positive and negative fractions 72
Subtracting positive and negative mixed numbers 73
Multiplying positive and negative fractions 74
Canceling 74
Multiplying positive and negative mixed numbers 75
Dividing positive and negative fractions 75
Dividing positive and negative mixed numbers 76
Chapter 7: Powers, Exponents, and Roots 78
Powers and Exponents 78
Exponents 78
Negative exponents 79
Squares and cubes 79
Operations with powers and exponents80
Square Roots and Cube Roots 81
Square roots 81
Cube roots 82
Approximating square roots 82
Simplifying square roots 84
Chapter 8: Powers of Ten and Scientific Notation 87
Powers of Ten 87
Multiplying powers of ten 88
Dividing powers of ten 88
Scientifi c Notation 89
Multiplication in scientific notation 90
Division in scientific notation 91
Chapter 9: Measurements 93
U.S. Customary System 93
Metric System 94
Converting Units of Measure 95
Precision 97
Significant Digits 99
Calculating Measurements of Basic Figures 100
Perimeter of some polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Area of polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Circumference and area of a circle 107
Chapter 10: Graphs 110
Bar Graphs 110
Line Graphs114
Circle Graphs or Pie Charts 115
Coordinate Graphs 117
Chapter 11: Probability and Statistics 123
Probability 123
Arrangements 126
Permutations 126
Statistics 128
Mean 129
Median 130
Mode 131
Chapter 12: Number Series 133
Arithmetic Progressions 133
Geometric Progressions 134
Chapter 13: Variables, Algebraic Expressions, and Simple Equations 135
Variables and Algebraic Expressions 135
Variables 135
Algebraic expressions 136
Evaluating expressions 136
Solving Simple Equations 137
Addition and subtraction equations 138
Multiplication and division equations 139
Combinations of operations 142
Chapter 14: Word Problems150
Solving Process 150
Key Words 151
Add 151
Subtract 151
Multiply 152
Divide 152
Review Questions 168
Resource Center 176
Glossary 178
Index 181
Reading Group Guide
Introduction 1
Chapter 1: Preliminaries 3
Groups of Numbers 3
Ways to Show Multiplication and Division 4
Multiplying and Dividing Using Zero 5
Common Math Symbols 5
Properties of Basic Mathematical Operations 6
Some properties (axioms) of addition 6
Some properties (axioms) of multiplication7
A property of two operations 8
Grouping Symbols and Order of Operations 9
Order of Operations 10
Chapter 2: Whole Numbers 12
Place Value 12
Expanded notation 13
Rounding off 14
Estimating Sums, Diff erences, Products, and Quotients 14
Estimating sums 14
Estimating differences 14
Estimating products 15
Estimating quotients 16
Divisibility Rules 16
Factors, Primes, Composites, and Factor Trees 17
Factors 18
Prime numbers 18
Composite numbers 18
Factor trees 19
Chapter 3: Decimals 21
Using the Place Value Grid 22
Expanded notation 22
Writing decimals 23
Comparing decimals 23
Rounding decimals 24
Decimal Computation 24
Adding and subtracting decimals 25
Multiplying decimals 26
Dividing decimals 26
Estimating Sums, Differences, Products, and Quotients 27
Estimating sums 27
Estimating differences 28
Estimating products 28
Estimating quotients 29
Repeating Decimals 30
Chapter 4: Fractions 31
Proper and Improper Fractions 32
Mixed Numbers 32
Changing improper fractions 32
Changing mixed numbers 32
Renaming Fractions33
Equivalent fractions 33
Simplifying fractions 33
Enlarging denominators 34
Factors 34
Common factors 35
Greatest common factor 35
Multiples 36
Common multiples 36
Least common multiple 36
Adding and Subtracting Fractions 37
Adding fractions 37
Subtracting fractions 38
Adding and Subtracting Mixed Numbers 39
Adding mixed numbers 39
Subtracting mixed numbers 40
Multiplying Fractions and Mixed Numbers41
Multiplying fractions 42
Multiplying mixed numbers 43
Dividing Fractions and Mixed Numbers 43
Dividing fractions 43
Dividing complex fractions 44
Dividing mixed numbers 45
Simplifying Fractions and Complex Fractions 45
Changing Fractions to Decimals 48
Changing Terminating Decimals to Fractions 49
Changing Infi nite Repeating Decimals to Fractions 50
Chapter 5: Percents 53
Changing Percents, Decimals, and Fractions 53
Changing decimals to percents 53
Changing percents to decimals 54
Changing fractions to percents 54
Changing percents to fractions 55
Important Equivalents 56
Applications of Percents 57
Finding percent of a number 57
Finding what percent one number is of another 58
Finding a number when a percent of it is known 60
Percent—proportion method 61
Finding percent increase or percent decrease 64
Chapter 6: Integers and Rationals 66
Integers 66
Number lines 66
Addition of integers 67
Subtraction of integers 68
Minus preceding a parenthesis 69
Multiplying and dividing integers 70
Absolute value 70
Rationals (Signed Numbers Including Fractions) 71
Negative fractions 71
Adding positive and negative fractions 71
Adding positive and negative mixed numbers 72
Subtracting positive and negative fractions 72
Subtracting positive and negative mixed numbers 73
Multiplying positive and negative fractions 74
Canceling 74
Multiplying positive and negative mixed numbers 75
Dividing positive and negative fractions 75
Dividing positive and negative mixed numbers 76
Chapter 7: Powers, Exponents, and Roots 78
Powers and Exponents 78
Exponents 78
Negative exponents 79
Squares and cubes 79
Operations with powers and exponents80
Square Roots and Cube Roots 81
Square roots 81
Cube roots 82
Approximating square roots 82
Simplifying square roots 84
Chapter 8: Powers of Ten and Scientific Notation 87
Powers of Ten 87
Multiplying powers of ten 88
Dividing powers of ten 88
Scientifi c Notation 89
Multiplication in scientific notation 90
Division in scientific notation 91
Chapter 9: Measurements 93
U.S. Customary System 93
Metric System 94
Converting Units of Measure 95
Precision 97
Significant Digits 99
Calculating Measurements of Basic Figures 100
Perimeter of some polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Area of polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Circumference and area of a circle 107
Chapter 10: Graphs 110
Bar Graphs 110
Line Graphs114
Circle Graphs or Pie Charts 115
Coordinate Graphs 117
Chapter 11: Probability and Statistics 123
Probability 123
Arrangements 126
Permutations 126
Statistics 128
Mean 129
Median 130
Mode 131
Chapter 12: Number Series 133
Arithmetic Progressions 133
Geometric Progressions 134
Chapter 13: Variables, Algebraic Expressions, and Simple Equations 135
Variables and Algebraic Expressions 135
Variables 135
Algebraic expressions 136
Evaluating expressions 136
Solving Simple Equations 137
Addition and subtraction equations 138
Multiplication and division equations 139
Combinations of operations 142
Chapter 14: Word Problems150
Solving Process 150
Key Words 151
Add 151
Subtract 151
Multiply 152
Divide 152
Review Questions 168
Resource Center 176
Glossary 178
Index 181
Interviews
Introduction 1
Chapter 1: Preliminaries 3
Groups of Numbers 3
Ways to Show Multiplication and Division 4
Multiplying and Dividing Using Zero 5
Common Math Symbols 5
Properties of Basic Mathematical Operations 6
Some properties (axioms) of addition 6
Some properties (axioms) of multiplication7
A property of two operations 8
Grouping Symbols and Order of Operations 9
Order of Operations 10
Chapter 2: Whole Numbers 12
Place Value 12
Expanded notation 13
Rounding off 14
Estimating Sums, Diff erences, Products, and Quotients 14
Estimating sums 14
Estimating differences 14
Estimating products 15
Estimating quotients 16
Divisibility Rules 16
Factors, Primes, Composites, and Factor Trees 17
Factors 18
Prime numbers 18
Composite numbers 18
Factor trees 19
Chapter 3: Decimals 21
Using the Place Value Grid 22
Expanded notation 22
Writing decimals 23
Comparing decimals 23
Rounding decimals 24
Decimal Computation 24
Adding and subtracting decimals 25
Multiplying decimals 26
Dividing decimals 26
Estimating Sums, Differences, Products, and Quotients 27
Estimating sums 27
Estimating differences 28
Estimating products 28
Estimating quotients 29
Repeating Decimals 30
Chapter 4: Fractions 31
Proper and Improper Fractions 32
Mixed Numbers 32
Changing improper fractions 32
Changing mixed numbers 32
Renaming Fractions33
Equivalent fractions 33
Simplifying fractions 33
Enlarging denominators 34
Factors 34
Common factors 35
Greatest common factor 35
Multiples 36
Common multiples 36
Least common multiple 36
Adding and Subtracting Fractions 37
Adding fractions 37
Subtracting fractions 38
Adding and Subtracting Mixed Numbers 39
Adding mixed numbers 39
Subtracting mixed numbers 40
Multiplying Fractions and Mixed Numbers41
Multiplying fractions 42
Multiplying mixed numbers 43
Dividing Fractions and Mixed Numbers 43
Dividing fractions 43
Dividing complex fractions 44
Dividing mixed numbers 45
Simplifying Fractions and Complex Fractions 45
Changing Fractions to Decimals 48
Changing Terminating Decimals to Fractions 49
Changing Infi nite Repeating Decimals to Fractions 50
Chapter 5: Percents 53
Changing Percents, Decimals, and Fractions 53
Changing decimals to percents 53
Changing percents to decimals 54
Changing fractions to percents 54
Changing percents to fractions 55
Important Equivalents 56
Applications of Percents 57
Finding percent of a number 57
Finding what percent one number is of another 58
Finding a number when a percent of it is known 60
Percent—proportion method 61
Finding percent increase or percent decrease 64
Chapter 6: Integers and Rationals 66
Integers 66
Number lines 66
Addition of integers 67
Subtraction of integers 68
Minus preceding a parenthesis 69
Multiplying and dividing integers 70
Absolute value 70
Rationals (Signed Numbers Including Fractions) 71
Negative fractions 71
Adding positive and negative fractions 71
Adding positive and negative mixed numbers 72
Subtracting positive and negative fractions 72
Subtracting positive and negative mixed numbers 73
Multiplying positive and negative fractions 74
Canceling 74
Multiplying positive and negative mixed numbers 75
Dividing positive and negative fractions 75
Dividing positive and negative mixed numbers 76
Chapter 7: Powers, Exponents, and Roots 78
Powers and Exponents 78
Exponents 78
Negative exponents 79
Squares and cubes 79
Operations with powers and exponents80
Square Roots and Cube Roots 81
Square roots 81
Cube roots 82
Approximating square roots 82
Simplifying square roots 84
Chapter 8: Powers of Ten and Scientific Notation 87
Powers of Ten 87
Multiplying powers of ten 88
Dividing powers of ten 88
Scientifi c Notation 89
Multiplication in scientific notation 90
Division in scientific notation 91
Chapter 9: Measurements 93
U.S. Customary System 93
Metric System 94
Converting Units of Measure 95
Precision 97
Significant Digits 99
Calculating Measurements of Basic Figures 100
Perimeter of some polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Area of polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Circumference and area of a circle 107
Chapter 10: Graphs 110
Bar Graphs 110
Line Graphs114
Circle Graphs or Pie Charts 115
Coordinate Graphs 117
Chapter 11: Probability and Statistics 123
Probability 123
Arrangements 126
Permutations 126
Statistics 128
Mean 129
Median 130
Mode 131
Chapter 12: Number Series 133
Arithmetic Progressions 133
Geometric Progressions 134
Chapter 13: Variables, Algebraic Expressions, and Simple Equations 135
Variables and Algebraic Expressions 135
Variables 135
Algebraic expressions 136
Evaluating expressions 136
Solving Simple Equations 137
Addition and subtraction equations 138
Multiplication and division equations 139
Combinations of operations 142
Chapter 14: Word Problems150
Solving Process 150
Key Words 151
Add 151
Subtract 151
Multiply 152
Divide 152
Review Questions 168
Resource Center 176
Glossary 178
Index 181
Recipe
Introduction 1
Chapter 1: Preliminaries 3
Groups of Numbers 3
Ways to Show Multiplication and Division 4
Multiplying and Dividing Using Zero 5
Common Math Symbols 5
Properties of Basic Mathematical Operations 6
Some properties (axioms) of addition 6
Some properties (axioms) of multiplication7
A property of two operations 8
Grouping Symbols and Order of Operations 9
Order of Operations 10
Chapter 2: Whole Numbers 12
Place Value 12
Expanded notation 13
Rounding off 14
Estimating Sums, Diff erences, Products, and Quotients 14
Estimating sums 14
Estimating differences 14
Estimating products 15
Estimating quotients 16
Divisibility Rules 16
Factors, Primes, Composites, and Factor Trees 17
Factors 18
Prime numbers 18
Composite numbers 18
Factor trees 19
Chapter 3: Decimals 21
Using the Place Value Grid 22
Expanded notation 22
Writing decimals 23
Comparing decimals 23
Rounding decimals 24
Decimal Computation 24
Adding and subtracting decimals 25
Multiplying decimals 26
Dividing decimals 26
Estimating Sums, Differences, Products, and Quotients 27
Estimating sums 27
Estimating differences 28
Estimating products 28
Estimating quotients 29
Repeating Decimals 30
Chapter 4: Fractions 31
Proper and Improper Fractions 32
Mixed Numbers 32
Changing improper fractions 32
Changing mixed numbers 32
Renaming Fractions33
Equivalent fractions 33
Simplifying fractions 33
Enlarging denominators 34
Factors 34
Common factors 35
Greatest common factor 35
Multiples 36
Common multiples 36
Least common multiple 36
Adding and Subtracting Fractions 37
Adding fractions 37
Subtracting fractions 38
Adding and Subtracting Mixed Numbers 39
Adding mixed numbers 39
Subtracting mixed numbers 40
Multiplying Fractions and Mixed Numbers41
Multiplying fractions 42
Multiplying mixed numbers 43
Dividing Fractions and Mixed Numbers 43
Dividing fractions 43
Dividing complex fractions 44
Dividing mixed numbers 45
Simplifying Fractions and Complex Fractions 45
Changing Fractions to Decimals 48
Changing Terminating Decimals to Fractions 49
Changing Infi nite Repeating Decimals to Fractions 50
Chapter 5: Percents 53
Changing Percents, Decimals, and Fractions 53
Changing decimals to percents 53
Changing percents to decimals 54
Changing fractions to percents 54
Changing percents to fractions 55
Important Equivalents 56
Applications of Percents 57
Finding percent of a number 57
Finding what percent one number is of another 58
Finding a number when a percent of it is known 60
Percent—proportion method 61
Finding percent increase or percent decrease 64
Chapter 6: Integers and Rationals 66
Integers 66
Number lines 66
Addition of integers 67
Subtraction of integers 68
Minus preceding a parenthesis 69
Multiplying and dividing integers 70
Absolute value 70
Rationals (Signed Numbers Including Fractions) 71
Negative fractions 71
Adding positive and negative fractions 71
Adding positive and negative mixed numbers 72
Subtracting positive and negative fractions 72
Subtracting positive and negative mixed numbers 73
Multiplying positive and negative fractions 74
Canceling 74
Multiplying positive and negative mixed numbers 75
Dividing positive and negative fractions 75
Dividing positive and negative mixed numbers 76
Chapter 7: Powers, Exponents, and Roots 78
Powers and Exponents 78
Exponents 78
Negative exponents 79
Squares and cubes 79
Operations with powers and exponents80
Square Roots and Cube Roots 81
Square roots 81
Cube roots 82
Approximating square roots 82
Simplifying square roots 84
Chapter 8: Powers of Ten and Scientific Notation 87
Powers of Ten 87
Multiplying powers of ten 88
Dividing powers of ten 88
Scientifi c Notation 89
Multiplication in scientific notation 90
Division in scientific notation 91
Chapter 9: Measurements 93
U.S. Customary System 93
Metric System 94
Converting Units of Measure 95
Precision 97
Significant Digits 99
Calculating Measurements of Basic Figures 100
Perimeter of some polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Area of polygons—squares, rectangles, parallelograms, trapezoids, and triangles 101
Circumference and area of a circle 107
Chapter 10: Graphs 110
Bar Graphs 110
Line Graphs114
Circle Graphs or Pie Charts 115
Coordinate Graphs 117
Chapter 11: Probability and Statistics 123
Probability 123
Arrangements 126
Permutations 126
Statistics 128
Mean 129
Median 130
Mode 131
Chapter 12: Number Series 133
Arithmetic Progressions 133
Geometric Progressions 134
Chapter 13: Variables, Algebraic Expressions, and Simple Equations 135
Variables and Algebraic Expressions 135
Variables 135
Algebraic expressions 136
Evaluating expressions 136
Solving Simple Equations 137
Addition and subtraction equations 138
Multiplication and division equations 139
Combinations of operations 142
Chapter 14: Word Problems150
Solving Process 150
Key Words 151
Add 151
Subtract 151
Multiply 152
Divide 152
Review Questions 168
Resource Center 176
Glossary 178
Index 181