Introductory Algebra
R.1 Review of Exponents and Order of Operations
R.2 Review of Prime Numbers, Factoring, and LCM
- 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
- Example 7: Least Common Multiple (LCM)
- Example 8: Least Common Multiple (LCM)
- Example 9: LCM with Variables
- Bonus Videos
- Bonus 1: Review of Prime Numbers, Factoring, and LCM
- Bonus 2: Review of Prime Numbers, Factoring, and LCM
R.3 Review of Fractions (Multiplication and Division)
R.4 Review of Fractions (Addition and Subtraction)
R.5 Review of Decimals and Percents
- Bonus Videos
- Bonus 1: Review of Decimals and Percents
2.1a Variables and Algebraic Expressions
2.1b Simplifying Expressions
2.1c Simplifying Expressions with Parentheses
2.1d Evaluating Algebraic Expressions
2.2a Reduction of Fractions
2.2b Multiplication and Division with Fractions
- Examples
- Example 4: Dividing Fractions with Negative Numbers
- Example 5: Dividing Fractions with Variables
- Example 6: Multiplication and Division of Fractions
- Example 7: Multiplication and Division of Fractions
- Bonus Videos
- Bonus 1: Multiplication and Division with Fractions
- Bonus 2: Multiplication and Division with Fractions
- Bonus 3: Multiplication and Division with Fractions
2.3 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with Like Denominators
- Example 2: LCM with Numbers
- Example 3: LCM with Variables
- Example 4: Adding Fractions with Unlike Denominators
- Example 5: Subtracting Fractions
- Bonus Videos
- Bonus 1: Addition and Subtraction with Fractions
- Bonus 2: Addition and Subtraction with Fractions
2.4 Decimals and Fractions
- Examples
- Example 1: Multiplication with Decimals
- Example 2: Division with Decimals
- Example 3: Fraction to Decimal Form, Terminating Decimal
- Example 4: Fraction to Decimal Form, Infinite Repeating Decimal
- Example 5: Decimal to Fraction Form
- Example 6: Calculating Average Speed
- Example 8: Converting Fractions to Infinite Repeating Decimals
- Bonus Videos
- Bonus 1: Decimals and Fractions
2.5 Order of Operations with Negative Numbers and Fractions
2.6 Translating Phrases into Algebraic Expressions
3.1a Solving Linear Equations Using Addition and Subtraction
3.1b Applications of Linear Equations: Addition and Subtraction
3.1c Solving Linear Equations Using Multiplication and Division
3.1d Applications of Linear Equations: Multiplication and Division
3.2 Solving Linear Equations
3.3 More Linear Equations: ax + b = dx + c
3.4 Solving Linear Inequalities
3.5a Solving Formulas
3.5b Working with Formulas
- Examples
- Example 1: Evaluating Formulas
- Bonus Videos
- Bonus 1: Working with Formulas
3.6 Applications: Number Problems and Consecutive Integers
3.7 Percents and Applications
3.8 Formulas in Geometry
4.1 Introduction to the Cartesian Coordinate System
4.2 Graphing Linear Equations by Plotting Points
- Examples
- Example 1: Graph by Plotting Points
- Example 2: Graph Using the y- and x-intercepts
- Example 3: Lines that Contain the Origin
- Example 4: Horizontal and Vertical lines
- Bonus Videos
- Bonus 1: Graphing Linear Equations by Plotting Points
- Bonus 2: Graphing Linear Equations by Plotting Points
- Bonus 3: Graphing Linear Equations by Plotting Points
- Bonus 4: Graphing Linear Equations by Plotting Points
4.3 The Slope-Intercept Form: y = mx + b
- Examples
- Example 1: Finding the Slope of a Line
- Example 2: Slopes of Vertical and Horizontal Lines
- Example 3: Using the Form y = mx + b
- Example 4: Finding the Equation of a Line
- Example 5: Graphing Horizontal and Vertical Lines
- Bonus Videos
- Bonus 1: The Slope-Intercept Form: y = mx + b
- Bonus 2: The Slope-Intercept Form: y = mx + b
4.4 Finding the Equation of a Line
- Examples
- Example 1: Graph a Line Given a Point and a Slope
- Example 2: Using the Point-Slope Form
- Example 3: Using the Two Points to Find the Equation of Line
- Example 4: Finding the Equations of Parallel Lines
- Example 5: Finding the Equations of Perpendicular Lines
- 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
- Bonus 5: Finding the Equation of a Line
- Bonus 6: Finding the Equation of a Line
4.5 Introduction to Functions and Function Notation
- Examples
- Example 1: Finding the Domain and Range
- Example 2: Determining Functions
- Example 3: Vertical Line Test
- Example 4: Function Evaluation
- Example 5: Nonlinear Function Evaluation
- Example 6: Nonlinear Function Evaluation
- Example 7: Nonlinear Function Evaluation
- Bonus Videos
- Bonus 1: Introduction to Functions and Function Notation
4.6 Graphing Linear Inequalities
- Examples
- Example 1: Graphing Linear Inequalities
- Bonus Videos
- Bonus 1: Graphing Linear Inequalities
5.1 Solving Systems of Linear Equations by Graphing
5.2 Solving Systems of Linear Equations by Substitution
5.3 Solving Systems of Linear Equations by Addition
5.4 Applications: Distance - Rate - Time, Number Problems, Amounts and Costs
5.5 Applications: Interest and Mixture
5.6 Systems of Linear Inequalities
6.1 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
- Bonus 2: Simplifying Integer Exponents I
6.2a Simplifying Integer Exponents II
- 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
- Bonus Videos
- Bonus 1: Simplifying Integer Exponents II
6.2b Scientific Notation
6.3a Identifying Polynomials
6.3b Evaluating Polynomials
6.4 Adding and Subtracting Polynomials
6.5a Multiplying a Polynomial by a Monomial
- Bonus Videos
- Bonus 1: Multiplying a Polynomial by a Monomial
6.5b Multiplying Two Polynomials
6.6a The FOIL Method
- Examples
- Example 1: FOIL Method
- Bonus Videos
- Bonus 1: The FOIL Method
- Bonus 2: The FOIL Method
6.6b Special Products
6.7a Division by a Monomial
6.7b The Division Algorithm
7.1a Greatest Common Factor of Two or More Terms
7.1b Greatest Common Factor of a Polynomial
7.1c Factoring Expressions by Grouping
7.2 Factoring Trinomials: Leading Coefficient 1
7.3a Factoring Trinomials by Grouping
7.3b Factoring Trinomials by Trial and Error
7.4 Special Factorizations - Squares
7.5 Solving Quadratic Equations by Factoring
7.6 Applications of Quadratic Equations
8.1a Defining Rational Expressions
8.1b Reducing Rational Expressions
8.2 Multiplication and Division of Rational Expressions
8.3 Addition and Subtraction of Rational Expressions
- Examples
- Example 1: Adding Rational Expressions
- Example 2: Using the LCM to Add Rational Expressions
- Example 3: Subtraction
- Example 4: Using the LCM to Subtract Rational Expressions
- Example 5: Simplifying Using −1 as a Factor
- Bonus Videos
- Bonus 1: Addition and Subtraction of Rational Expressions
- Bonus 2: Addition and Subtraction of Rational Expressions
- Bonus 3: Addition and Subtraction of Rational Expressions
- Bonus 4: Addition and Subtraction of Rational Expressions
8.4 Complex Algebraic Fractions
8.5 Solving Equations Involving Rational Expressions
- Examples
- Example 1: Proportions
- Example 2: Proportion Word Problems
- Example 3: Solving Equations Involving Rational Expressions
- Bonus Videos
- Bonus 1: Solving Equations Involving Rational Expressions
- Bonus 2: Solving Equations Involving Rational Expressions
- Bonus 3: Solving Equations Involving Rational Expressions