Foundations of Mathematics for Virginia

1.1 Exponents and Prime Numbers

• Examples
• Example 1: Writing Exponents
• Example 2: Translating Expressions with Exponents
• Example 3: Prime Numbers
• Example 4: Composite Numbers
• Example 5: Prime Factorization
• Example 6: Prime Factorization

1.2 Introduction to Fractions and Mixed Numbers

• Examples
• Example 1: Understanding Fractions
• Example 2: Proper Fractions
• Example 3: Improper Fractions
• Example 4: The Number 0 in Fractions
• Example 5: Reducing Fractions to Lowest Terms
• Example 6: Reducing Fractions to Lowest Terms
• Example 8: Changing a Mixed Number to an Improper Fraction
• Example 10: Changing an Improper Fraction to a Mixed Number

1.3 Ratios and Rates

• Examples
• Example 1: Comparing Two Quantities as a Ratio
• Example 2: Comparing Two Quantities as a Ratio
• Example 3: Application of Writing a Unit Rate
• Example 4: Application of Writing a Unit Rate
• Example 5: Application of Writing a Unit Rate
• Example 6: Comparing Unit Prices
• Example 7: Price per Unit

1.4 Multiplication and Division with Fractions and Mixed Numbers

• Examples
• Example 1: Multiplication with Fractions
• Example 2: Multiplication with Fractions
• Example 3: Multiplication with Mixed Numbers
• Example 4: Multiplication with Fractions and Mixed Numbers
• Example 5: Multiplying and Reducing with Fractions
• Example 6: Multiplying and Reducing with Fractions
• Example 8: Multiplying and Reducing with Mixed Numbers
• Example 9: Multiplying and Reducing with Fractions
• Example 10: Multiplying and Reducing with Fractions
• Example 11: Application of Multiplying and Reducing with Fractions
• Example 12: Reciprocals
• Example 13: Reciprocals
• Example 14: Dividing with Fractions
• Example 15: Dividing and Reducing Fractions
• Example 16: Dividing and Reducing with Fractions and Mixed Numbers
• Example 18: Multiplying and Dividing with Fractions and Mixed Numbers
• Example 19: Multiplying and Dividing with Fractions and Mixed Numbers

1.5 Least Common Multiple

• Examples
• Example 1: Finding the Least Common Multiple (LCM)
• Example 2: Finding the Least Common Multiple (LCM)
• Example 4: Finding the Least Common Multiple (LCM)
• Example 5: Finding the Least Common Multiple (LCM)
• Example 6: Understanding Least Common Multiple (LCM)
• Example 7: Understanding Least Common Multiple (LCM)
• Example 8: Application: Finding the LCM
• Example 9: Finding Equivalent Fractions
• Example 10: Finding Equivalent Fractions

1.6 Addition and Subtraction with Fractions

• Examples
• Example 1: Adding Fractions with the Same Denominator
• Example 2: Adding Fractions with the Same Denominator
• Example 3: Adding Fractions with the Same Denominator
• Example 4: Adding Fractions with Different Denominators
• Example 5: Adding Fractions with Different Denominators
• Example 6: Adding Three Fractions with Different Denominators
• Example 7: Application of Adding Fractions with Different Denominators
• Example 8: Application of Adding Fractions with Different Denominators
• Example 9: Subtracting Fractions with the Same Denominator
• Example 10: Subtracting Fractions with the Same Denominator
• Example 11: Subtracting Fractions with Different Denominators
• Example 12: Subtracting Fractions with Different Denominators
• Example 14: Application of Subtracting Fractions with Different Denominators

1.7 Addition and Subtraction with Mixed Numbers

• Examples
• Example 1: Adding Mixed Numbers
• Example 2: Adding Mixed Numbers
• Example 3: Adding Mixed Numbers
• Example 4: Subtracting Mixed Numbers
• Example 5: Subtracting Mixed Numbers
• Example 6: Subtracting Mixed Numbers with Borrowing
• Example 7: Subtracting Mixed Numbers with Borrowing
• Example 8: Subtracting Mixed Numbers with Borrowing

1.8 Order of Operations with Fractions and Mixed Numbers

• Examples
• Example 1: Comparing Fractions
• Example 2: Comparing Fractions
• Example 3: Comparing Fractions
• Example 4: Order of Operations with Fractions
• Example 5: Order of Operations with Fractions
• Example 6: Order of Operations with Fractions
• Example 8: Order of Operations with Mixed Numbers
• Example 9: Order of Operations with Mixed Numbers
• Example 10: Order of Operations with Mixed Numbers
• Example 11: Average of Mixed Numbers

2.1 Introduction to Decimal Numbers

• Examples
• Example 1: Reading and Writing Decimal Numbers
• Example 2: Reading and Writing Decimal Numbers
• Example 3: Reading and Writing Decimal Numbers
• Example 4: Reading and Writing Decimal Numbers
• Example 5: Comparing Decimal Numbers
• Example 6: Comparing Decimal Numbers
• Example 7: Comparing Decimal Numbers
• Example 8: Rounding Decimal Numbers
• Example 9: Rounding Decimal Numbers

2.2 Addition and Subtraction with Decimal Numbers

• Examples
• Example 1: Adding Decimal Numbers
• Example 2: Adding Decimal Numbers
• Example 3: Adding Decimal Numbers
• Example 4: Adding Decimal Numbers
• Example 5: Subtracting Decimal Numbers
• Example 6: Subtracting Decimal Numbers
• Example 7: Estimating a Sum

2.3 Multiplication with Decimal Numbers

• Examples
• Example 1: Multiplication with Decimal Numbers
• Example 2: Multiplication with Decimal Numbers
• Example 3: Multiplication with Decimal Numbers
• Example 5: Multiplication of a Decimal Number by a Power of 10
• Example 6: Estimating a Product
• Example 7: Buying a Car

2.4 Division with Decimal Numbers

• Examples
• Example 1: Division with Decimal Numbers
• Example 3: Division with Decimal Numbers
• Example 4: Division with Decimal Numbers
• Example 5: Division by Powers of 10
• Example 6: Division with Decimal Numbers
• Example 7: Order of Operations with Decimal Numbers
• Example 8: Order of Operations with Decimal Numbers
• Example 9: Gas Mileage
• Example 10: Bicycle Speed
• Example 11: Gasoline Prices

2.5 Decimal Numbers and Fractions

• Examples
• Example 1: Changing Decimal Numbers to Fractions
• Example 2: Changing Decimal Numbers to Fractions
• Example 3: Changing Decimal Numbers to Fractions
• Example 4: Changing Decimal Numbers to Fractions
• Example 5: Changing Decimal Numbers to Fractions
• Example 6: Changing Decimal Numbers to Fractions
• Example 7: Changing Fractions to Decimal Numbers
• Example 8: Changing Fractions to Decimal Numbers
• Example 9: Changing Fractions to Decimal Numbers
• Example 10: Changing Fractions to Decimal Numbers
• Example 11: Operating with Both Fractions and Decimal Numbers
• Example 12: Operating with Both Fractions and Decimal Numbers

2.6 Decimal Numbers and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ to Percents
• Example 2: Changing Decimal Numbers to Percents
• Example 3: Changing Percents to Decimal Numbers

2.7 Fractions and Percents

• Examples
• Example 1: Changing Fractions to Percents
• Example 2: Changing Mixed Numbers to Percents
• Example 3: Changing Fractions to Percents
• Example 4: Changing Fractions to Percents
• Example 5: Changing Percents to Fractions
• Example 6: Changing Percents to Fractions

2.8 Solving Proportions

• Examples
• Example 1: Verifying the Proportion
• Example 3: Solving Proportions
• Example 4: Solving Proportions
• Example 5: Solving Proportions
• Example 7: Problems with Proportions
• Example 8: Problems with Proportions

2.9 U.S. Measurements

• Examples
• Example 1: Basic Conversions
• Example 2: Using Multiplication/Division to Convert Measures
• Example 3: Using Unit Fractions to Convert Measures
• Example 4: Using Unit Fractions to Convert Measures in Two Steps
• Example 5: Converting Measures with a Remainder
• Example 6: Adding and Subtracting Measures

2.10 The Metric System

• Examples
• Example 1: Converting Metric Units of Length
• Example 2: Converting Metric Units of Length
• Example 3: Converting Metric Units of Length
• Example 4: Converting Metric Units of Length
• Example 5: Equivalent Measures of Mass
• Example 6: Equivalent Measures of Mass
• Example 7: Equivalent Measures of Volume
• Example 8: Equivalent Measures of Volume
• Example 9: Equivalent Measures of Liquid Volume
• Example 10: Equivalent Measures of Liquid Volume
• Example 11: Operation with Metric Units

2.11 U.S. to Metric Conversions

• Examples
• Example 1: Equivalent Measures of Temperature
• Example 2: Converting Measures of Temperature
• Example 3: Converting Measures of Temperature
• Example 4: Converting Measures of Length
• Example 5: Converting Measures of Length
• Example 6: Converting Measures of Length
• Example 7: Converting Measures of Length
• Example 8: Converting Measures of Area
• Example 9: Converting Measures of Area
• Example 10: Converting Measures of Area
• Example 11: Converting Measures of Area
• Example 12: Converting Measures of Liquid Volume
• Example 13: Converting Measures of Liquid Volume
• Example 14: Converting Measures of Liquid Volume
• Example 15: Converting Measures of Volume
• Example 16: Converting Measures of Mass
• Example 17: Converting Measures of Mass

2.12 Reading Graphs

• Examples
• Example 1: Reading a Bar Graph
• Example 2: Reading a Circle Graph
• Example 3: Reading a Circle Graph
• Example 4: Reading a Line Graph
• Example 5: Reading a Histogram

3.1a The Real Number Line and Inequalities

• Examples
• Example 1: Opposites
• Example 2: Number Line
• Example 3: Identifying Types of Numbers
• Example 4: Inequalities
• Example 5: Graphing Sets of Numbers

3.1b Introduction to Absolute Value

• Examples
• Example 1: Absolute Value
• Example 2: Absolute Value
• Example 3: Absolute Value

3.2 Introduction to Exponents

• Examples
• Example 1: Understanding the Terms Base and Exponent
• Example 2: Reading Equations Containing Exponential Expressions
• Example 3: Writing and Evaluating Exponential Expressions
• Example 5: Order of Operations
• Example 6: Order of Operations
• Example 7: Order of Operations
• Example 8: Order of Operations
• Example 9: Order of Operations

3.3 Square Roots

• Examples
• Example 1: Finding Square Roots
• Example 2: Evaluating Expressions Containing Square Roots

3.4 Addition with Real Numbers

• Examples
• Example 1: Addition with Like Signs
• Example 2: Addition with Unlike Signs
• Example 3: Adding More Than Two Real Numbers
• Example 4: Addition in a Vertical Format
• Example 5: Addition in a Vertical Format
• Example 6: Determining Possible Solutions

3.5 Subtraction with Real Numbers

• Examples
• Example 1: Additive Inverse
• Example 2: Subtraction
• Example 3: Subtraction
• Example 4: Change in Value
• Example 5: Net Change
• Example 6: Evaluating Possible Solutions

3.6 Multiplication and Division with Real Numbers

• Examples
• Example 1: Products of Positive and Negative Real Numbers
• Example 2: Products of Negative Real Numbers
• Example 3: Multiplication by $0$
• Example 4: Division with Real Numbers
• Example 5: Division with Fractions and Decimals
• Example 6: Average

3.7 Order of Operations with Real Numbers

• Examples
• Example 1: Order of Operations with Integers
• Example 3: Negative Numbers and Exponents
• Example 4: Order of Operations with Fractions

3.8 Introduction to Scientific Notation

• Examples
• Example 1: Decimals in Scientific Notation
• Example 2: Scientific Notation to Decimal Form

3.9 Properties of Real Numbers

• Examples
• Example 1: Properties of Addition and Multiplication
• Example 2: Properties of Addition and Multiplication

3.10 Simplifying and Evaluating Algebraic Expressions

• Examples
• Example 1: Like Terms
• Example 2: Combining Like Terms
• Example 4: Simplifying and Evaluating Algebraic Expressions

3.11a Solving Linear Equations: x + b = c

• Examples
• Example 1: Solving x + b = c
• Example 2: Solving x + b = c
• Example 3: Solving x + b = c
• Example 4: Solving x + b = c
• Example 5: Simplifying and Solving Equations
• Example 7: Application

3.11b Solving Linear Equations: ax = c

• Examples
• Example 1: Solving ax = c
• Example 2: Solving ax = c
• Example 3: Solving ax = c

3.12 Solving Percent Problems Using the Equation: R * B = A

• Examples
• Example 1: Finding the Amount
• Example 2: Finding the Base
• Example 3: Finding the Percent
• Example 4: Finding the Amount
• Example 5: Finding the Base

3.13 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease

• Examples
• Example 1: Solving Discount Problems
• Example 2: Solving Discount Problems
• Example 3: Solving Sales Tax Problems
• Example 4: Solving Commission Problems
• Example 5: Finding the Percent Increase
• Example 6: Finding the Percent Decrease

3.14 Applications: Simple Interest

• Examples
• Example 1: Calculating Simple Interest
• Example 3: Calculating Principal using Simple Interest
• Example 4: Calculating Time using Simple Interest

3.15 Perimeter

• Examples
• Example 1: Finding the Perimeter of a Square
• Example 2: Finding the Perimeter of a Triangle
• Example 3: Finding the Perimeter of a Rectangle
• Example 4: Finding the Perimeter of a Polygon
• Example 5: Finding the Cost of a Fencing Project
• Example 6: Finding the Perimeter of a Polygon

3.16 Area

• Examples
• Example 1: Finding the Area of a Triangle
• Example 2: Finding the Area of a Trapezoid
• Example 3: Finding the Area of a Composite Figure
• Example 4: Finding the Area of a Rectangle
• Example 5: Finding the Area of a Polygon
• Example 6: Finding the Perimeter and Area

3.17 Circles

• Examples
• Example 1: Finding the Circumference and Area of a Circle
• Example 2: Finding the Circumference and Area of a Circle
• Example 3: Finding the Perimeter of a Semicircle
• Example 4: Finding the Area of a Washer
• Example 5: Finding the Perimeter and Area

3.18 Volume

• Examples
• Example 1: Finding the Volume of a Rectangular Solid
• Example 2: Finding the Volume of a Sphere
• Example 3: Finding the Volume of a Cylinder
• Example 4: Finding the Volume of a Solid
• Example 5: Finding the Volume of a Cube
• Example 6: Finding the Surface Area of a Rectangular Solid
• Example 7: Finding the Surface Area of a Right Circular Cylinder

4.1a Solving Linear Equations: x + b = c

• Examples
• Example 1: Solving x + b = c
• Example 2: Solving x + b = c
• Example 3: Solving x + b = c
• Example 4: Solving x + b = c
• Example 5: Simplifying and Solving Equations
• Example 7: Application

4.1b Solving Linear Equations: ax = c

• Examples
• Example 1: Solving ax = c
• Example 2: Solving ax = c
• Example 3: Solving ax = c

4.2 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations of the Form ax + b = c
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Decimals
• Example 6: Solving Linear Equations with Fractional Coefficients
• Example 7: Solving Linear Equations with Fractional Coefficients

4.3 Solving Linear Equations: ax + b = cx + d

• Examples
• Example 1: Solving Equations of the Form ax + b = cx + d
• Example 2: Solving Equations of the Form ax + b = cx + d
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations with Fractional Coefficients
• Example 5: Solving Equations with Parentheses
• Example 6: Solving Equations with Parentheses
• Example 8: Solutions of Equations
• Example 9: Solutions of Equations
• Example 10: Solutions of Equations

4.4 Working with Formulas

• Examples
• Example 1: Evaluating Formulas
• Example 2: Evaluating Formulas
• Example 3: Evaluating Formulas
• Example 4: Evaluating Formulas
• Example 5: Solving for Different Variables
• Example 6: Solving for Different Variables
• Example 7: Solving for Different Variables
• Example 8: Solving for Different Variables

4.5 Translating English Phrases and Algebraic Expressions

• Examples
• Example 1: Translating English Phrases into Algebraic Expressions
• Example 2: Translating Algebraic Expressions to English Phrases
• Example 3: Translating English Phrases to Algebraic Expressions

4.6 Applications: Number Problems and Consecutive Integers

• Examples
• Example 1: Number Problems
• Example 2: Number Problems
• Example 3: Number Problems
• Example 4: Consecutive Integers
• Example 5: Consecutive Integers
• Example 6: Living Expenses
• Example 7: School Supplies

4.7 Applications: Distance-Rate-Time, Interest, Average

• Examples
• Example 1: Distance-Rate-Time
• Example 2: Distance-Rate-Time
• Example 3: Interest
• Example 4: Average (or Mean)
• Example 5: Cost

4.8 Solving Absolute Value Equations

• Examples
• Example 1: Solving Absolute Value Equations

4.9 Linear Inequalities

• Examples
• Example 1: Graphing Intervals
• Example 2: Graphing Intervals
• Example 3: Graphing Intervals
• Example 4: Graphing Intervals
• Example 5: Sets of Real Numbers Illustrating Union
• Example 6: Sets of Real Numbers Illustrating Intersection
• Example 7: Solving Linear Inequalities
• Example 8: Solving Linear Inequalities
• Example 9: Solving Linear Inequalities
• Example 11: Solving Compound Inequalities
• Example 12: Solving Compound Inequalities
• Example 13: Solving Compound Inequalities
• Example 14: Application with an Inequality
• Example 15: Application with an Inequality

5.1 The Cartesian Coordinate System

• Examples
• Example 1: Graphing Ordered Pairs
• Example 2: Determining Ordered Pairs
• Example 3: Reading Points on a Graph

5.2 Graphing Linear Equations in Two Variables

• Examples
• Example 1: Graphing a Linear Equation in Two Variables
• Example 2: x- and y-Intercepts
• Example 4: Horizontal Line
• Example 5: Vertical Line

5.3a Slope

• Examples
• Example 1: Finding the Slope of a Line
• Example 2: Finding the Slope of a Line
• Example 3: Finding the Slope of a Line
• Example 4: Slopes of Horizontal and Vertical Lines

5.3b Slope-Intercept Form

• Examples
• Example 1: Using the Form y = mx + b
• Example 2: Using the Form y = mx + b
• Example 3: Using the Form y = mx + b

5.4a Point-Slope Form

• Examples
• Example 1: Graphing a Line Given a Point and the Slope
• Example 2: Finding Equations of Lines Using the Slope and a Point
• Example 3: Using Two Points to Find the Equation of a Line

5.4b Parallel and Perpendicular Lines

• Examples
• Example 1: Finding the Equations of Parallel Lines
• Example 2: Finding the Equations of Perpendicular Lines

5.5 Graphing Linear Inequalities in Two Variables

• Examples
• Example 1: Graphing Linear Inequalities

5.6 Introduction to Functions and Function Notation

• Examples
• Example 1: Evaluation with Function Notation
• Example 2: Evaluation with Function Notation
• Example 3: Using a Graph to Find Values of g(x)
• Example 4: Using a Graph to Find Values of x

5.7 Systems of Linear Equations: Solutions by Graphing

• Examples
• Example 1: Solution of a System
• Example 2: Not a Solution of a System
• Example 3: A System with One Solution
• Example 4: A System with No Solution
• Example 5: A System with Infinitely Many Solutions
• Example 6: A System that Requires Estimation

5.8 Systems of Linear Equations: Solutions by Substitution

• Examples
• Example 1: A System with One Solution
• Example 2: A System with No Solution
• Example 3: A System with Infinitely Many Solutions
• Example 4: A System with Decimals

5.9 Systems of Linear Equations: Solutions by Addition

• Examples
• Example 1: A System with One Solution
• Example 2: A System with Infinitely Many Solutions
• Example 3: A System with Decimals

5.10 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs

• Examples
• Example 1: Distance-Rate-Time (Rates Unknown)
• Example 2: Distance-Rate-Time (Times Unknown)
• Example 3: Number Problem
• Example 4: Counting Coins
• Example 5: Calculating Age
• Example 6: Amounts and Costs

5.11 Applications: Interest and Mixture

• Examples
• Example 1: Interest
• Example 2: Interest
• Example 3: Mixture
• Example 4: Mixture

6.1a Exponents

• Examples
• Example 1: Product Rule for Exponents
• Example 2: Product Rule for Exponents
• Example 3: The Exponent 0
• Example 4: Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients

6.1b Negative Exponents

• Examples
• Example 1: Negative Exponents
• Example 2: Combining Rules for Exponents

6.2a Power Rules for Exponents

• Examples
• Example 1: Power Rule for Exponents
• Example 2: Rule for Power of a Product
• Example 3: Rule for Power of a Quotient
• Example 4: Using Combinations of Rules for Exponents
• Example 5: Two Approaches with Fractional Expressions and Negative Exponents
• Example 6: A More Complex Example

6.2b Scientific Notation

• Examples
• Example 1: Decimals in Scientific Notation
• Example 2: Scientific Notation and Properties of Exponents

6.3 Introduction to Polynomials

• Examples
• Example 1: Simplifying Polynomials
• Example 3: Evaluating Polynomials

6.4 Addition and Subtraction with Polynomials

• Examples
• Example 1: Adding Polynomials
• Example 3: Subtracting Polynomials
• Example 5: Simplifying Algebraic Expressions

6.5 Multiplication with Polynomials

• Examples
• Example 1: Multiplication with Polynomials

6.6a The FOIL Method

• Examples
• Example 1: FOIL Method

6.6b Special Products of Binomials

• Examples
• Example 1: Difference of Two Squares
• Example 3: Squares of Binomials

6.7 Division by a Monomial

• Examples
• Example 1: Dividing by a Monomial

6.8a Greatest Common Factor of Two or More Terms

• Examples
• Example 1: Finding the GCF

6.8b Greatest Common Factor of a Polynomial

• Examples
• Example 1: Factoring Out the GCF of a Polynomial
• Example 2: Factoring Out the GCF of a Polynomial

6.8c Factoring Expressions by Grouping

• Examples
• Example 1: Factoring Out a Common Binomial Factor
• Example 2: Factoring by Grouping

6.9 Factoring Trinomials with Leading Coefficient 1

• Examples
• Example 1: Factoring Trinomials with Leading Coefficient 1
• Example 3: Finding a Common Monomial Factor

6.10a Factoring Trinomials by the ac-Method

• Examples
• Example 1: Using the ac-Method

6.10b Factoring Trinomials by Trial and Error

• Examples
• Example 1: Using the Trial-and-Error Method
• Example 2: Factoring Completely

6.11a Special Factorizations - Squares

• Examples
• Example 1: Factoring the Difference of Two Squares
• Example 2: Using the Sum of Two Squares
• Example 3: Factoring Perfect Square Trinomials

6.11b Special Factorizations - Cubes

• Examples
• Example 1: Factoring Sums and Differences of Two Cubes

6.12 Additional Factoring Practice

6.13 Solving Quadratic Equations by Factoring

• Examples
• Example 1: Solving Factored Quadratic Equations
• Example 2: Solving Quadratic Equations by Factoring
• Example 4: Solving Higher Degree Equations

6.14 Applications of Quadratic Equations

• Examples
• Example 1: Applications of Quadratic Equations
• Example 2: Consecutive Integers
• Example 3: The Pythagorean Theorem

7.1a Introduction to Rational Expressions

• Examples
• Example 1: Finding Restrictions on the Variable
• Example 2: Evaluating Rational Expressions
• Example 3: Reducing Rational Expressions

7.1b Multiplication and Division with Rational Expressions

• Examples
• Example 3: Multiplication with Rational Expressions
• Example 5: Division with Rational Expressions

7.2 Addition and Subtraction with Rational Expressions

• Examples
• Example 1: Adding Rational Expressions with a Common Denominator
• Example 2: Finding the LCD of Two Rational Expressions
• Example 3: Building Rational Expressions to Higher Terms
• Example 4: Adding Rational Expressions with Different Denominators
• Example 6: Subtracting Rational Expressions with a Common Denominator
• Example 7: Subtracting Rational Expressions with Different Denominators

7.3 Complex Fractions

• Examples
• Example 1: First Method for Simplifying Complex Fractions
• Example 2: First Method for Simplifying Complex Fractions
• Example 3: Second Method for Simplifying Complex Fractions
• Example 4: Simplifying Complex Algebraic Expressions

7.4a Division by a Monomial

• Examples
• Example 1: Dividing by a Monomial

7.4b The Division Algorithm

• Examples
• Example 1: The Division Algorithm
• Example 2: Long Division (Remainder 0)
• Example 3: Long Division (Terms Missing)

7.5 Solving Equations with Rational Expressions

• Examples
• Example 1: Solving Equations with Rational Expressions
• Example 3: Solving a Formula for a Specified Variable

7.6 Applications: Rational Expressions

• Examples
• Example 1: Fractions
• Example 2: Work Problems
• Example 3: Distance-Rate-Time

8.1 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

8.2 Rational Exponents

• Examples
• Example 1: Evaluating Principal n^th Roots
• Example 2: Conversion Between Exponential Notation and Radical Notation
• Example 3: Simplifying Expressions with Rational Exponents
• Example 4: Simplifying Radical Notation by Changing to Exponential Notation

8.3 Simplifying Radicals

• Examples
• Example 1: Simplifying Numerical Expressions with Square Roots
• Example 2: Simplifying Square Roots with Variables
• Example 3: Simplifying Square Roots
• Example 4: Simplifying Expressions with Cube Roots

8.4a Addition and Subtraction with Radicals

• Examples
• Example 1: Addition and Subtraction with Radicals

8.4b Multiplication with Radicals

• Examples
• Example 1: Multiplication with Radicals

8.5 Rationalizing Denominators

• Examples
• Example 1: Rationalizing Denominators
• Example 2: Rationalizing a Denominator with a Sum or Difference Involving a Square Root

8.6 Equations with Radicals

• Examples
• Example 1: Equations with One Radical
• Example 3: Equations with Two Radicals
• Example 4: Equations containing a Cube Root

8.7 Complex Numbers

• Examples
• Example 1: Square Roots of Negative Numbers
• Example 2: Real and Imaginary Parts
• Example 3: Addition and Subtraction with Complex Numbers
• Example 4: Multiplication with Complex Numbers

8.8a Applications: The Pythagorean Theorem

• Examples
• Example 1: Right Triangles
• Example 2: Finding the Length of the Hypotenuse
• Example 3: Finding the Length of a Leg
• Example 4: Finding the Length of a Guy Wire

8.8b Applications: Distance Formula and Midpoint Formula

• Examples
• Example 1: The Distance Formula
• Example 2: Pythagorean Theorem
• Example 3: Midpoint Formula

9.1 Functions and Function Notation

• Examples
• Example 1: Finding the Domain and Range
• Example 2: Reading the Domain and Range from the Graph of a Relation
• Example 3: Functions
• Example 4: Vertical Line Test
• Example 5: Domain
• Example 6: Finding the Domain of a Radical Function
• Example 7: Function Evaluation
• Example 8: Nonlinear Function Evaluation
• Example 9: Evaluating Radical Functions

9.2a Solving Quadratic Equations: The Square Root Method

• Examples
• Example 2: Using the Square Root Property to Solve Quadratic Equations

9.2b Solving Quadratic Equations: Completing the Square

• Examples
• Example 1: Completing the Square
• Example 2: Solving Quadratic Equations by Completing the Square

9.3 The Quadratic Formula

• Examples
• Example 1: The Quadratic Formula
• Example 2: Cubic Equations
• Example 3: Finding the Discriminant
• Example 4

9.4 Applications: Quadratic Equations

• Examples
• Example 1: The Pythagorean Theorem
• Example 2: Projectiles
• Example 3: Geometry
• Example 4: Cost per Person
• Example 5: Work

9.5 Graphs of Quadratic Functions

• Examples
• Example 1: Quadratic Functions (Vertical Shift)
• Example 2: Quadratic Functions (Vertical Shift)
• Example 3: Graph a Quadratic Function with Horizontal and Vertical Shifts

9.6 Quadratic Functions: Completing the Square and Applications

• Examples
• Example 1: Completing the Square
• Example 2: Graphing Quadratic Functions by Completing the Square
• Example 3: Graphing Quadratic Functions using the Vertex Formula
• Example 4: Graphing Quadratic Functions using the Vertex Formula
• Example 5: Minimum and Maximum Values