Prealgebra Textbook

Description

1 The Whole Numbers 1.1 An Introduction to the Whole Numbers Graphing numbers on the number line Ordering the whole numbers Expanded notation Rounding whole numbers Tables and graphs Exercises Answers 1.2 Adding and Subtracting Whole Numbers The Commutative Property of Addition Grouping Symbols The Associative Property of Addition The Additive Identity Adding Larger Whole Numbers Subtraction of Whole Numbers Subtracting Larger Whole Numbers Order of Operations Applications — Geometry Application — Alternative Fuels Exercises Answers 1.3 Multiplication and Division of Whole Numbers The Multiplicative Identity Multiplication by Zero The Associative Property of Multiplication Multiplying Larger Whole Numbers Division of Whole Numbers Division is not Commutative Division is not Associative Division by Zero is Undefined Dividing Larger Whole Numbers Application — Counting Rectangular Arrays Application — Area Exercises Answers 1.4 Prime Factorization Divisibility Divisibility Tests Prime Numbers Factor Trees Exponents Application Exercises Answers 1.5 Order of Operations Fraction Bars The Distributive Property Exercises Answers 1.6 Solving Equations by Addition and Subtraction Equivalent Equations Operations that Produce Equivalent Equations Wrap and Unwrap Word Problems Exercises Answers 1.7 Solving Equations by Multiplication and Division Word Problems Exercises Answers 2 The Integers 2.1 An Introduction to the Integers The Integers Ordering the Integers Opposites of Opposites Positive and Negative Absolute Value Applications Exercises Answers 2.2 Adding Integers Vectors on the Number Line Magnitude and Absolute Value Adding Integers with Like Signs Adding Integers with Unlike Signs Properties of Addition of Integers Grouping for Efficiency Exercises Answers 2.3 Subtracting Integers Order of Operations Change as a Difference Exercises Answers 2.4 Multiplication and Division of Integers The Product of a Positive Integer and a Negative Integer The Distributive Property The Multiplicative Property of Zero Multiplying by Minus One The Product of Two Negative Integers Memory Device Division of Integers Exercises Answers 2.5 Order of Operations with Integers Evaluating Fractions Absolute Value Exercises Answers 2.6 Solving Equations Involving Integers Adding or Subtracting the Same Amount Multiplying or Dividing by the Same Amount Combining Operations Applications Exercises Answers 3 The Fundamentals of Algebra 3.1 Mathematical Expressions Translating Words into Mathematical Expressions Combinations Exercises Answers 3.2 Evaluating Algebraic Expressions Exercises Answers 3.3 Simplifying Algebraic Expressions Speeding Things Up The Distributive Property Moving a Bit Quicker Extending the Distributive Property Distributing a Negative Exercises Answers 3.4 Combining Like Terms Like Terms Combining Like Terms Speeding Things Up a Bit Simplify Applications Exercises Answers 3.5 Solving Equations Involving Integers II Variables on Both Sides Exercises Answers 3.6 Applications Consecutive Integers Consecutive Odd Integers Tables Exercises Answers 4 Fractions 4.1 Equivalent Fractions The Greatest Common Divisor Reducing a Fraction to Lowest Terms Reducing Fractions with Variables A Word on Mathematical Notation. Equivalent Fractions in Higher Terms Negative Fractions Exercises Answers 4.2 Multiplying Fractions Multiplication Rule Multiply and Reduce Multiply and Cancel or Cancel and Multiply Parallelograms Triangles Exercises Answers 4.3 Dividing Fractions Reciprocals Division Exercises Answers 4.4 Adding and Subtracting Fractions Adding Fractions with Different Denominators Least Common Multiple Least Common Multiple Using Prime Factorization Comparing Fractions Exercises Answers 4.5 Multiplying and Dividing Mixed Fractions Changing Mixed Fractions to Improper Fractions Changing Improper Fractions to Mixed Fractions Multiplying and Dividing Mixed Fractions Exercises Answers 4.6 Adding and Subtracting Mixed Fractions Adding Mixed Fractions Working in Vertical Format Subtracting Mixed Fractions Working in Vertical Format Borrowing in Vertical Format Exercises Answers 4.7 Order of Operations with Fractions Order of Operations Complex Fractions Application — Trapezoid Exercises Answers 4.8 Solving Equations with Fractions Undoing Subtraction Undoing Addition Undoing Multiplication Clearing Fractions from the Equation Applications Exercises Answers 5 Decimals 5.1 Introduction to Decimals Decimal Notation Pronouncing Decimal Numbers Decimals to Fractions Rounding Comparing Decimals Exercises Answers 5.2 Adding and Subtracting Decimals Adding Decimals Subtracting Decimals Adding and Subtracting Signed Decimal Numbers Exercises Answers 5.3 Multiplying Decimals Multiplying Signed Decimal Numbers Order of Operations Powers of Ten Multiplying Decimal Numbers by Powers of Ten The Circle Exercises Answers 5.4 Dividing Decimals Decimal Divisors Dividing Signed Decimal Numbers Rounding Dividing by Powers of Ten Order of Operations Exercises Answers 5.5 Fractions and Decimals Terminating Decimals Repeating Decimals Expressions Containing Both Decimals and Fractions Exercises Answers 5.6 Equations With Decimals Combining Operations Combining Like Terms Using the Distributive Property Rounding Solutions Applications Exercises Answers 5.7 Introduction to Square Roots Square Roots Radical Notation Order of Operations Fractions and Decimals Estimating Square Roots Exercises Answers 5.8 The Pythagorean Theorem Exercises Answers 6 Ratio and Proportion 6.1 Introduction to Ratios and Rates Rates Unit Rates Exercises Answers 6.2 Introduction to Proportion Solving Proportions Applications Exercises Answers 6.3 Unit Conversion: American System Units of Length Units of Weight Units of Volume Units of Time Converting Units of Speed Exercises Answers 6.4 Unit Conversion: Metric System Units of Length Units of Mass Units of Volume Exercises Answers 6.5 American Units to Metric Units and Vice-Versa Converting Units of Length Converting Units of Weight and Mass Converting Units of Volume Converting Units of Speed Exercises Answers 7 Percent 7.1 Percent, Decimals, Fractions Changing a Percent to a Fraction Changing a Percent to a Decimal Changing a Decimal to a Percent Changing a Fraction to a Percent Exercises Answers 7.2 Solving Basic Percent Problems Find a Given Percent of a Given Number Find a Percent Given Two Numbers Find a Number that is a Given Percent of Another Number Exercises Answers 7.3 General Applications of Percent Exercises Answers 7.4 Percent Increase or Decrease Percent Increase Percent Decrease Discount Exercises Answers 7.5 Interest Extending the Simple Interest Formula Exercises Answers 7.6 Pie Charts Pie Charts Exercises Answers 8 Graphing 8.1 The Cartesian Coordinate System Allowing for Negative Numbers Exercises Answers 8.2 Graphing Linear Equations The Graph of an Equation Linear Equations Exercises Answers Index