CliffsNotes Basic Math & Pre-Algebra Quick Review, 2nd Edition

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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

  • ISBN-13: 9780470880401
  • Publisher: Houghton Mifflin Harcourt
  • Publication date: 5/3/2011
  • Edition number: 2
  • Pages: 192
  • Sales rank: 382,120
  • Product dimensions: 5.12 (w) x 8.12 (h) x 0.44 (d)

Meet the Author

JERRY BOBROW, Ph.D. was a national authority in the field of test preparation. His test-prep company, Bobrow Test Preparation Services, administered test preparation programs at over 25 California institutions.

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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

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