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
