Prealgebra and Introductory Algebra
1.1 Introduction to Whole Numbers
1.2 Addition and Subtraction with Whole Numbers
1.3 Multiplication and Division with Whole Numbers
- Examples
- Example 1: Properties of Multiplication
- Example 3: Properties of Multiplication
- Example 4: Multiplication with Whole Numbers
- Example 5: Multiplication with Whole Numbers
- Example 6: Finding Area
- Example 7: Division with Whole Numbers
- Example 8: Factors
- Example 9: Plumbing
- Example 10: Estimating a Product
- Example 11: Estimating a Quotient
- Example 15: Finding the Quotient and Remainder
- Example 16: Acres of Land
- Bonus Videos
- Bonus 1: Multiplication and Division with Whole Numbers
1.4 Problem Solving with Whole Numbers
1.5 Solving Equations with Whole Numbers (x + b = c and ax = c)
1.6 Exponents and Order of Operations
1.7 Introduction to Polynomials I
1.8 Introduction to Integers
- Examples
- Example 1: Opposites
- Example 2: Graphing Integers
- Example 3: Graphing Integers
- Example 4: Correcting False Statements
- Example 5: Absolute Value
- Example 6: Absolute Value
- Example 7: Absolute Value
- Example 8: Absolute Value
- Example 9: Absolute Value
- Example 10: Finding the Possible Integer Values
- Bonus Videos
- Bonus 1: Introduction to Integers
1.9 Addition with Integers
1.10 Subtraction with Integers
1.11 Multiplication and Division with Integers, Order of Operations
- Examples
- Example 1: Multiplication with Integers
- Example 2: Multiplication with Integers
- Example 3: Multiplication with Integers
- Example 4: Division with Integers
- Example 5: Division Involving 0
- Example 6: Order of Operations with Integers
- Example 7: Order of Operations with Integers
- Bonus Videos
- Bonus 1: Multiplication and Division with Integers, Order of Operations
1.12 Applications: Change in Value and Mean
1.13 Introduction to Like Terms and Polynomials
1.14 Solving Equations with Integers (x + b = c and ax = c)
2.1 Tests for Divisibility
2.2 Prime Numbers
2.3 Prime Factorization
2.4 Least Common Multiple (LCM)
- Examples
- Example 1: Finding the Least Common Multiple
- Example 2: Finding the Least Common Multiple
- Example 5: Finding the LCM of Algebraic Terms
- Example 6: Finding the LCM of Algebraic Terms
- Example 8: Weather Satellites
- Example 9: Finding All Divisors and the Greatest Common Divisor
- Example 10: Finding the GCD
- Example 11: Finding the GCD
- Example 12: Finding the GCD
- Example 13: Relatively Prime Numbers
- Example 14: Relatively Prime Numbers
- Bonus Videos
- Bonus 1: Least Common Multiple (LCM)
- Bonus 2: Least Common Multiple (LCM)
2.5 Reducing and Multiplication with Fractions
- Examples
- Example 1: Understanding Fractions
- Example 2: Placement of Negative Signs in Fractions
- Example 3: Multiplying Rational Numbers
- Example 4: Multiplying Rational Numbers
- Example 5: Multiplying Rational Numbers
- Example 6: The Commutative Property of Multiplication
- Example 7: The Associative Property of Multiplication
- Example 8: Raising Fractions to Higher Terms
- Example 9: Raising Fractions to Higher Terms
- Example 10: Reducing Fractions to Lowest Terms
- Example 11: Reducing Fractions to Lowest Terms
- Example 12: Reducing Fractions to Lowest Terms
- Example 14: Multiplying and Reducing Fractions
- Example 15: Multiplying and Reducing Fractions
- Example 16: Multiplying and Reducing Fractions
- Example 18: The Division Method
- Example 19: The Division Method
- Example 20: Buying Computer Disks
- Bonus Videos
- Bonus 1: Reducing and Multiplication with Fractions
2.6 Division with Fractions
- Examples
- Example 1: Finding the Reciprocal of a Fraction
- Example 2: Finding the Reciprocal of an Algebraic Expression
- Example 3: Dividing Fractions
- Example 4: Dividing Fractions
- Example 5: Dividing and Reducing Fractions
- Example 6: Dividing and Reducing Fractions
- Example 8: Dividing the Product by the Known Number
- Example 9: Dividing the Product by the Known Number
- Example 10: Application
- Bonus Videos
- Bonus 1: Division with Fractions
2.7 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Two Fractions with the Same Denominator
- Example 2: Adding Three Fractions with the Same Denominator
- Example 3: Adding Two Fractions with Different Denominators
- Example 4: Adding Two Fractions with Different Denominators
- Example 5: Adding Three Fractions with Different Denominators
- Example 6: Subtracting Two Fractions with the Same Denominator
- Example 7: Subtracting Two Fractions with the Same Denominator
- Example 8: Subtracting Two Fractions with Different Denominators
- Example 9: Subtracting Two Fractions with Different Denominators
- Example 11: Adding Fractions Containing Variables
- Example 12: Adding Fractions Containing Variables
- Example 13: Subtracting Fractions Containing Variables
- Example 14: Subtracting Fractions Containing Variables
- Example 16: Keith's Budget
- Bonus Videos
- Bonus 1: Addition and Subtraction with Fractions
2.8 Introduction to Mixed Numbers
- Examples
- Example 1: Changing Mixed Numbers to Improper Fractions
- Example 2: Changing Mixed Numbers to Improper Fractions
- Example 3: The Shortcut Method
- Example 4: The Shortcut Method
- Example 6: Changing Improper Fractions to Mixed Numbers
- Example 7: Changing Improper Fractions to Mixed Numbers
- Example 8: Reducing Improper Fractions and Changing to Mixed Number
- Bonus Videos
- Bonus 1: Introduction to Mixed Numbers
2.9 Multiplication and Division with Mixed Numbers
- Examples
- Example 1: Multiplying Mixed Numbers
- Example 2: Multiplying and Reducing Mixed Numbers
- Example 3: Multiplying and Reducing Mixed Numbers
- Example 6: Fractional Parts of Mixed Numbers
- Example 7: Fractional Parts of Mixed Numbers
- Example 8: Area of a Rectangle
- Example 9: Area of a Triangle
- Example 10: Volume of a Rectangular Solid
- Example 11: Dividing Mixed Numbers
- Example 13: Dividing the Product by the Known Number
- Bonus Videos
- Bonus 1: Multiplication and Division with Mixed Numbers
2.10 Addition and Subtraction with Mixed Numbers
- Examples
- Example 1: Adding Mixed Numbers with the Same Denominator
- Example 2: Adding Mixed Numbers with Different Denominators
- Example 3: Adding Mixed Numbers with Different Denominators
- Example 4: Adding Mixed Numbers and Whole Numbers
- Example 5: Subtracting Mixed Numbers with the Same Denominator
- Example 6: Subtracting Mixed Numbers with Different Denominators
- Example 7: Subtracting Mixed Numbers by Borrowing
- Example 8: Subtracting Mixed Numbers from Whole Numbers
- Example 9: Subtracting Mixed Numbers by Borrowing
- Example 11: Finding the Algebraic Sum of Mixed Numbers
- Example 12: Finding the Algebraic Sum of Mixed Numbers
- Example 13: Adding Mixed Numbers Using Improper Fractions
- Example 14: Adding Mixed Numbers Using Improper Fractions
- Example 15: Subtracting Mixed Numbers Using Improper Fractions
- Bonus Videos
- Bonus 1: Addition and Subtraction with Mixed Numbers
2.11 Complex Fractions and Order of Operations
2.12 Solving Equations with Fractions (ax + b = c)
- Examples
- Example 1: Solving Equations Using the Addition Principle
- Example 2: Solving Equations Using the Multiplication Principle
- Example 3: Solving Equations
- Example 4: Solving Equations
- Example 5: Solving Equations with Fractional Coefficients
- Example 6: Solving Equations with Fractional Coefficients
- Example 7: Solving Equations with Fractional Coefficients
- Bonus Videos
- Bonus 1: Solving Equations with Fractions (ax + b = c)
2.13a Ratios and Price per Unit
2.13b Proportions
2.13c Finding the Unknown Term in a Proportion
- Examples
- Example 13: Finding the Unknown Term in a Proportion
- Example 14: Finding the Unknown Term in a Proportion
- Example 15: Finding the Unknown Term in a Proportion
- Example 17: Finding the Unknown Term in a Proportion
- Bonus Videos
- Bonus 1: Finding the Unknown Term in a Proportion
- Bonus 2: Finding the Unknown Term in a Proportion
3.1 Reading, Writing, and Rounding 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: Reading and Writing Decimal Numbers
- Example 6: Rounding Decimal Numbers
- Example 7: Rounding Decimal Numbers
- Bonus Videos
- Bonus 1: Reading, Writing, and Rounding Decimal Numbers
3.2 Addition and Subtraction with Decimal Numbers
- Examples
- Example 1: Adding Decimal Numbers
- Example 2: Combining Like Terms
- Example 3: Subtracting Decimal Numbers
- Example 4: Subtracting Decimal Numbers
- Example 5: Subtracting Signed Decimal Numbers
- Example 6: Solving Equations Involving Decimal Numbers
- Example 7: Estimating the Sum of Decimal Numbers
- Bonus Videos
- Bonus 1: Addition and Subtraction with Decimal Numbers
3.3 Multiplication and Division with Decimal Numbers
- Examples
- Example 1: Multiplying Positive Decimal Numbers
- Example 2: Multiplying Signed Decimal Numbers
- Example 3: Multiplying by Powers of 10
- Example 4: Dividing Decimal Numbers
- Example 5: Dividing Decimal Numbers
- Example 6: Dividing Decimal Numbers
- Example 7: Dividing Decimal Numbers
- Example 8: Dividing by Powers of 10
- Example 9: Estimating Products of Decimal Numbers
- Example 10: Estimating Quotients of Decimal Numbers
- Example 11: Buying a Car
- Example 12: Fuel Efficiency
- Example 13: Jogging
- Example 14: Price of Gasoline
- Bonus Videos
- Bonus 1: Multiplication and Division with Decimal Numbers
3.4 Measures of Center
3.5 Decimals, Fractions, and Scientific Notation
- Examples
- Example 1: Changing a Decimal Number to a Fraction
- Example 2: Changing a Fraction to a Decimal Number
- Example 3: Changing a Fraction to a Decimal Number
- Example 4: Changing a Fraction to a Decimal Number
- Example 5: Changing a Fraction to a Decimal Number
- Example 6: Operating with Both Decimal Numbers and Fractions
- Example 7: Operating with Both Decimal Numbers and Fractions
- Example 8: Operating with Both Decimal Numbers and Fractions
- Example 9: Operating with Both Decimal Numbers and Fractions
- Example 10: Absolute Value
- Example 11: Decimal Numbers in Scientific Notation
- Bonus Videos
- Bonus 1: Decimals, Fractions, and Scientific Notation
- Bonus 2: Decimals, Fractions, and Scientific Notation
3.6 Basics of Percent
- Examples
- Example 1: Calculating a Fraction to a Percentage
- Example 2: Percent of profit
- Example 4: Changing a Decimal Number to a Percentage
- Example 5: Changing a Percentage to a Decimal Number
- Example 6: Changing a Fraction to a Percentage
- Example 7: Changing a Fraction to a Percentage
- Example 9: Changing a Fraction to a Percentage
- Example 10: College Graduates
- Example 11: Changing a Percentage to a Fraction
- Bonus Videos
- Bonus 1: Basics of Percent
3.7 Applications of Percent
3.8 Simple and Compound Interest
- Examples
- Example 1: Calculating Simple Interest
- Example 2: Calculating Simple Interest
- Example 3: Calculating Simple Interest
- Example 5: Calculating Compound Interest
- Example 6: Calculating Compound Interest
- Example 7: Calculating Total Interest Earned
- Example 9: Calculating Inflation
- Example 10: Calculating Depreciation
- Bonus Videos
- Bonus 1: Simple and Compound Interest
3.9 Square Roots
4.1a Metric System: Length and Area
- 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 Metric Measures of Area
- Example 6: Converting Metric Measures of Area
- Example 7: Converting Metric Measures of Area
- Example 8: Converting Metric Measurements of Land Area
- Bonus Videos
- Bonus 1: Metric System: Length and Area
- Bonus 2: Metric System: Length and Area
- Bonus 3: Metric System: Length and Area
4.1b Metric System: Weight and Volume
- Examples
- Example 1: Equivalent Measures of Mass
- Example 2: Equivalent Measures of Mass
- Example 3: Converting Metric Measures of Volume
- Example 4: Converting Metric Measures of Volume
- Example 5: Equivalent Measures of Volume
- Example 6: Equivalent Measures of Volume
- Example 7: Equivalent Measures of Liquid Volume
- Example 8: Equivalent Measures of Liquid Volume
- Example 9: The Prefixes Mega-, Giga-, and Tera-
- Bonus Videos
- Bonus 1: Metric System: Weight and Volume
- Bonus 2: Metric System: Weight and Volume
4.2 U.S. Customary Measurements and Metric Equivalents
- 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 6: 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
4.3 Introduction to Geometry
4.4 Formulas for Perimeter
4.5 Formulas for Area
4.6 Formulas for Volume
4.7 Similarity
4.8 The Pythagorean Theorem
4.9 Reading Graphs
5.1a Variables and Algebraic Expressions
- Examples
- Example 1: Like Terms
- Bonus Videos
- Bonus 1: Variables and Algebraic Expressions
5.1b Simplifying Expressions
5.1c Evaluating Algebraic Expressions
5.2 Translating English Phrases and Algebraic Expressions
5.3a Solving Linear Equations Using Addition and Subtraction
5.3b Solving Linear Equations Using Multiplication and Division
5.4 Solving Linear Equations: ax + b = c
5.5 Solving Linear Equations: ax + b = cx + d
- Examples
- Example 1: Solving Equations with Variables on Both Sides
- Example 2: Solving Linear Equations Involving Decimals
- Example 3: Solving Linear Equations with Fractional Coefficients
- Example 4: Solving Equations with Parentheses
- Example 5: Solutions of Equations
- Bonus Videos
- Bonus 1: Solving Linear Equations: ax + b = cx + d
- Bonus 2: Solving Linear Equations: ax + b = cx + d
5.6 Introduction to Problem Solving
5.7 Applications with Percent
5.8 Working with Formulas
5.9 Applications: Distance-Rate-Time, Interest, Mean
6.1 The Cartesian Coordinate System
6.2 Graphing Linear Equations in Two Variables: ax + by = c
6.3 The Slope - Intercept Form: y = mx + b
6.4a Finding the Equation of a Line
- Examples
- Example 1: Using Two Points to Find the Equation of a Line
- Example 2: Graphing a Line Given a Point and the Slope
- Example 3: Finding Equations of Lines Using the Slope and a Point
- Example 4: Finding Equations of Lines Using a Graph
- Bonus Videos
- Bonus 1: Finding the Equation of a Line
- Bonus 2: Finding the Equation of a Line
- Bonus 3: Finding the Equation of a Line
- Bonus 4: Finding the Equation of a Line
6.4b Graphing Linear Equations in Point - Slope Form
6.5a Solving Linear Inequalities
- Examples
- Example 1: Graphing Intervals
- Example 2: Sets of Real Numbers Illustrating Union
- Example 3: Sets of Real Numbers Illustrating Intersection
- Example 4: Solving Linear Inequalities
- Example 5: Solving Compound Inequalities
- Example 6: Application with an Inequality
- Example 7: Application with an Inequality
- Bonus Videos
- Bonus 1: Solving Linear Inequalities
- Bonus 2: Solving Linear Inequalities
6.5b Graphing Linear Inequalities
- Examples
- Example 1: Graphing Linear Inequalities
- Bonus Videos
- Bonus 1: Graphing Linear Inequalities
6.6 Introduction to 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: Function Evaluation
- Example 7: Nonlinear Function Evaluation
- Example 8: Function Evaluation from a Graph
- Bonus Videos
- Bonus 1: Introduction to Functions and Function Notation
- Bonus 2: Introduction to Functions and Function Notation
7.1a Simplifying Integer Exponents I
- 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
- Example 6: Negative Exponents
- Example 7: Combining Rules for Exponents
- Bonus Videos
- Bonus 1: Simplifying Integer Exponents I
7.1b Simplifying Integer Exponents II
- Examples
- Example 9: Power Rule for Exponents
- Example 10: Rule for Power of a Product
- Example 11: Rule for Power of a Quotient
- Example 12: Using Combinations of Rules for Exponents
- Example 13: Two Approaches with Fractional Expressions and Negative Exponents
- Example 14: A More Complex Example
- Bonus Videos
- Bonus 1: Simplifying Integer Exponents II
7.2 Introduction to Polynomials II
7.3 Addition and Subtraction with Polynomials
7.4 Multiplication with Polynomials
7.5a The FOIL Method
- Examples
- Example 1: FOIL Method
- Bonus Videos
- Bonus 1: The FOIL Method
7.5b Special Products
7.6a Division by a Monomial
- Examples
- Example 1: Dividing by a Monomial
- Bonus Videos
- Bonus 1: Division by a Monomial
7.6b Greatest Common Factor of Two or More Terms
- Examples
- Example 2: Finding the GCF
- Bonus Videos
- Bonus 1: Greatest Common Factor of Two or More Terms
7.6c Greatest Common Factor of a Polynomial
7.6d Factoring Expressions by Grouping
7.7 Factoring Trinomials: x^2 + bx + c
7.8a Factoring Trinomials by Trial and Error
7.8b Factoring Trinomials by Grouping
7.9a Special Factorizations - Squares
7.9b Special Factorizations - Cubes
7.10 Solving Quadratic Equations by Factoring
7.11 Applications of Quadratic Equations
8.1 Systems of Equations: Solutions by Graphing
- Examples
- Example 1: Solution of a System
- Example 2: Not a Solution of a System
- Example 3: Solving a System of Linear Equations by Graphing
- Example 4: A System with No Solution
- Example 5: A System with Infinitely Many Solutions
- Example 6: A System that Requires Estimation
- Bonus Videos
- Bonus 1: Systems of Equations: Solutions by Graphing
8.2 Systems of Equations: Solutions by Substitution
8.3 Systems of Equations: Solutions by Addition
8.4 Applications: Distance - Rate - Time, Number Problems, Amounts and Costs
8.5 Applications: Interest and Mixture
8.6 Systems of Linear Equations: Three Variables
8.7 Matrices and Gaussian Elimination
8.8 Systems of Linear Inequalities
9.1 Evaluating Radicals
9.2 Simplifying Radicals
9.3 Rational Exponents
- Examples
- Example 1: Evaluating Principal 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
- Bonus Videos
- Bonus 1: Rational Exponents
- Bonus 2: Rational Exponents
9.4a Addition and Subtraction with Radicals
9.4b Multiplication with Radicals
- Examples
- Example 2: Multiplication with Radicals
- Bonus Videos
- Bonus 1: Multiplication with Radicals
9.4c Rationalizing Denominators
9.5 Solving Radical Equations
9.6 Functions with Radicals
10.1 Algebra of Functions
10.2 Composite and Inverse Functions
10.3 Exponential Functions
10.4 Logarithmic Functions
- Examples
- Example 1: Writing an Exponential Expression as a Logarithmic Expression
- Example 2: Writing a Logarithmic Expression as an Exponential Expression
- Example 3: Evaluating Logarithms
- Example 4: Evaluating Logarithms
- Example 5: Evaluating Logarithms
- Example 6: Using the Exponential Form to Solve Logarithmic Equations
- Bonus Videos
- Bonus 1: Logarithmic Functions
10.5 Properties of Logarithms
- Examples
- Example 1: Using Basic Properties of Logarithms
- Example 2: Using the Product Rule for Logarithms
- Example 3: Using the Quotient Rule for Logarithms
- Example 4: Using the Power Rule
- Example 5: Expanding Logarithms
- Example 6: Using the Properties of Logarithms to Write a Single Logarithmic Expression
- Bonus Videos
- Bonus 1: Properties of Logarithms
10.6 Common Logarithms and Natural Logarithms
10.7 Exponential and Logarithmic Equations
11.1a Defining Rational Expressions
11.1b Multiplication and Division with Rational Expressions
11.2 Addition and Subtraction with Rational Expressions
- Examples
- Example 1: Adding Rational Expressions with a Common Denominator
- Example 2: Adding Rational Expressions with Different Denominators
- Example 4: Subtracting Rational Expressions with a Common Denominator
- Example 5: Subtracting Rational Expressions with Different Denominators
- Bonus Videos
- Bonus 1: Addition and Subtraction with Rational Expressions
- Bonus 2: Addition and Subtraction with Rational Expressions
- Bonus 3: Addition and Subtraction with Rational Expressions