Prealgebra Textbook

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