COMBINATION OF MULTIPLICATION AND DIVISION OF RATIONAL EXPRESSION
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## LEARNING CENTER VIDEOSMathmatics

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These videos are available for student viewing in the Learning Center. Although many students are assigned to watch these tapes by their instructors, any student may watch them for personal improvement.

### BASIC MATHEMATICS -

Operation on the Whole Numbers
Standard Notation.
Subtraction.
Rounding and Estimating; Order
Multiplication.
Division.
Solving Equations.
Applications and Problem Solving.
Exponential Notation and Order of Operations.

Fractional Notation: Multiplication and Division.
Factorizations.
Divisibility.
Fractions.
Multiplication and Applications.
Simplifying.
Multiplying, Simplifying, and Applications.
Division and Applications.
Fractional Notation and Mixed Numerals
Least Common Multiples.
Subtraction, Order, and Applications.
Mixed Numerals.
Addition and Subtraction Using Mixed Numerals; Applications.
Multiplication and Division Using Mixed Numerals: Applications.
Order of Operations; Estimation.

Decimal Notation
Decimal Notation, Order, and Rounding.
Addition and Subtraction with Decimal Notation.
Multiplication with Decimal Notation
Division with Decimal Notation.
Converting from Fractional to Decimal Notation.
Estimating.
Application and Problem Solving.

Ratio and Proportion
Introduction to Ratios.
Rates and Unit Prices.
Proportions.
Applicat6ions of Proportions.
Similar Triangles.

Percent Notation
Percent Notation and Fractional Notation.
Solving Percent Problems using Equations.
Solving Percent Problems using Proportions.
Applications of Percent.
Consumer Applications: Sales Tax, Commission, and Discount.
Consumer Applications: Interest.

Data Analysis, Graphs, and Statistics
Averages, Medians, and Modes.
Tables and Pictographs
Bar Graphs and Line Graphs
Circle Graphs
Data Analysis and Predictions

Geometry and Measures: Length and Area
Linear Measures: American Units.
Linear Measures: The Metric System.
Perimeter
Area
Areas of Parallelograms, Triangles, and Trapezoids
Circles
Square Roots and the Pythagorean Theorem

More Geometry and Measures
Volume and Capacity
Volume of Cylinders, Spheres, and Cones.
Weight, Mass, and Time.
Temperature
Converting Units of Area
Angles and Triangles

The Real-Number System
Subtraction of Real Numbers
Multiplication of Real Numbers
Division and Order of Operations

Algebra: Solving Equations and Problems
Introduction to Algebra
Solving Equations: The Multiplication Principle
Using the Principles Together
Solving Application Problems

### BEGINNING ALGEBRA -

Real Numbers and Their Basic Properties
Real Numbers and their Graphs
Fractions
Exponents and Order of Operations
Multiplying and Dividing Real Numbers
Algebraic Expressions
Properties of Real Numbers

Equations and Inequalities
Introduction to Equations
Solving More Equations
Simplifying Expressions to Solve Equations
Literal Equations
Applications of Equations
More Applications of Equations
Solving Inequalities

Polynomials
Natural-Number Exponents
Zero and Negative Integral Exponents
Scientific Notation
Polynomials
Multiplying Polynomials
Dividing Polynomials by Monomials
Dividing Polynomials by Polynomials

Factoring Polynomials
Factoring Out of the Greatest Common Factor
Factoring by Grouping
Factoring the Difference of Two Squares
Factoring Trinomials with Lead Coefficients of 1
Factoring General Trinomials
Factoring the Sum and Difference of Two Cubes
Summary of Factoring Techniques
Problem Solving

Rational Expressions
The Basic Properties of Fractions
Multiplying Fractions
Dividing Fractions
Adding and Subtracting Fractions with Like Denominators
Adding and Subtracting Fractions with Unlike Denominators
Complex Fractions
Solving Equations that Contain Fractions
Applications of Equations that contain Fractions
Ratio and Proportion

Graphing Linear Equations and Inequalities
Graphing Linear Equations
The Slope of a Line
Writing Equations of Lines
Graphs of Other Equations
Graphing Inequalities
Relations and Functions
Variation

Solving Systems of Equations and Inequalities
Solving Systems of Equations by Graphing
Solving Systems of Equations by Substitution
Solving Systems of Equations by Addition
Applications of Systems of Equations
Solving Systems of Linear Inequalities
Solving Systems of Three Equations in Three
Variables

Rational Exponents
The Distance Formula

Solving Equations of the Form x2=c
Completing the Square
Complex Numbers

### INTERMEDIATE ALGEBRA -

The Real Number System
Sets and the Real Number System
Equality and Properties of Real Numbers
Inequalities and Graphs of Real Numbers
Arithmetic of Real Numbers

Exponents and Polynomials
Exponents
Scientific Notation
Multiplying Polynomials
Dividing Polynomials
Synthetic Division (Optional)

Equations and Inequalities
Linear Equations and Their Solutions
Applications
More Applications of Equations
Formulas and Literal Equations
Absolute Value Equations
Linear Inequalities
Inequalities with Absolute Values

Factoring Polynomials
The Greatest Common Factor
The Difference of Two Squares; the Sum and Difference of Two
Cubes
Factoring Trinomials
Summary of Factoring Techniques
Solving Equations by Factoring

Rational Expressions
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Complex Fractions
Equations Containing Rational Expressions

Graphs, Equations of Lines, and Variation
The Rectangular Coordinate System
Slope of a Non-vertical Line
Equations of Lines
Graphs of Other Equations
Graphs of Linear Inequalities in Two Variables
Introduction to Functions
Proportion and Variation

Rational Exponents

Completing the Square and the Quadratic Formula
Complex Numbers

Systems of Equations and Inequalities
Solution by Graphing
Solution of Three Equations in Three Variables
Determinants
Matrices
Systems of Inequalities

More Functions and Conic Sections
Polynomials and Other Functions
Algebra and Composition of Functions
Inverses of Functions
The Circle and the Parabola
The Ellipse and the Hyperbola
Solving Simaltaneous Second-Degree Equations

Exponential and Logarithmic Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Applications of Logarithms
Exponential and Logarithmic Equations

Miscellaneous Topics
The Binomial Theorem
The nth Term of a Binomial Expansion
Arithmetic Sequences
Geometric Sequences
Infinite Geometric Sequences
Permutations and Combinations

### COLLEGE ALGEBRA -

Prerequisites
Real Numbers
Polynomials and Special Products
Factoring
Fractional Expressions
Errors and the Algebra of Calculus
Graphical Representation of Data

Equations and Inequalities
Graphs and Graphing Utilities
Linear Equations
Modeling with Linear Equations
Complex Numbers
Other Types of Equation
Linear Inequalities
Other Types of Inequalities

Functions and Their Graphs
Lines in the Plane and Slope
Functions
Analyzing Graphs of Functions
Translations and Combinations
Inverse Functions

Zeros of Polynomial Functions
Polynomial Functions of Higher Degree
Polynomial and Synthetic Division
Real Zeros of Polynomial Functions
The Fundamental Theorem of Algebra
Mathematical Modeling

Rational Functions and Conics
Rational Functions and Asymptotes
Graphs and Rational Functions
Partial Fractions
Conics
Translations of Conics

Exponential and Logarithmic Functions
Exponential Functions and their Graphs
Logarithmic Functions and their Graphs
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential and Logarithmic Models

Systems of Equations and Inequalities
Solving Systems of Equations
Two-Variable Linear Systems
Multivariable Linear Systems
Systems of Inequalities
Linear Programming

Matrices and Determinants
Matrices and Systems of Equations
Operations with Matrices
The Inverse of a Square Matrix
The Determinant of a Square Matrix
Applications of Matrices and Determinants

Sequences and Probability
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences
Mathematical Induction
The Binomial Theorem
Counting Principles
Probability

### TRIGONOMETRY

Introduction to Trigonometric Functions
Trigonometric Functions of General Angles
Evaluating Trigonometric Functions
Graphing Trigonometric Functions
Trigonometric Identities
Inverse Trigonometric Functions
Trigonometric Equations
Right Triangle Applications
Law of Sines
Law of Cosines
Polar Coordinates
Trigonometric Form, Demoivre s Theorem & Nth Roots
of Complex Numbers

### PRECALCULUS

Prerequisites
Real Numbers
Polynomials and Factoring
Fractional Expressions
Solving Equations
Solving Inequalities
Errors and the Algebra of Calculus
Graphical Representation of Data

Functions and Their Graphs
Graphs & Graphing Utilities
Lines in the Plane and Slope
Functions
Analyzing Graphs of Functions
Translations and Combinations
Inverse Functions
Mathematical Modeling

Polynomial and Rational Functions
Polynomial Functions of Higher Degree
Polynomial and Synthetic Division
Real Zeros of Polynomial Functions
Complex Numbers
The Fundamental Theorem of Algebra
Rational Functions
Partial Fractions

Exponential and Logarithmic Functions
Exponential Functions and their Graphs
Logarithmic Functions and their Graphs
Properties of Logarithms
Exponential and Logarithmic Functions
Exponential and Logarithmic Models

Trigonometry
Trigonometric Functions: The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions
Graphs of Other Trigonometric Functions
Inverse Trigonometric Functions
Applications and Models

Analytic Trigonometry
Using Fundamental Identities
Verifying Trigonometric Identities
Solving Trigonometric Equations
Sum and Difference Formulas
Multiple-Angle and Product-to-Sum Formulas

Law of Sines
Law of Cosines
Vectors in the Plane
Victors and Dot Products
DeMoivre s Theorem

Systems of Equations and Inequalities
Solving Systems of Equations
Two-Variable Linear Systems
Multivariable Linear Systems
Systems of Inequalities
Linear Programming

Matrices and Determinants
Matrices and Systems of Equations
Operations with Matrices
The Inverse of a Square Matrix
The Determinant of a Square Matrix
Application of Matrices and Determinants

Sequences and Probability
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences
Mathematical Induction
The Binomial Theorem
Counting Principles
Probability

Topics in Analytic Geometry
Lines
Introduction to Conics: Parabolas
Ellipses
Hyperbolas
Rotation of Conics
Parametric Equations
Polar Coordinates
Graphs of Polar Equations
Polar Equations of Conics

### CALCULUS - Limits and their Properties

Definitions and Properties of Limits
Techniques for evaluating limits
Continuity and one-sided limits
Infinite limits

Differentiation
Derivatives and tangent lines
Velocity and other rates of change
Differentiation rules for sums, products, quotients, powers, and
Trigonometric functions
The chain rule
Differentiation
Related rules

Applications of Differentiation
Extremes on an interval
Rolle s Theorem and the Mean
Value Theorem
Increasing and decreasing functions and the first Derivative Test
Concavity and the Second Derivative Test
Limits at infinity
A summary of curve sketching
Optimization problems
Differentials

Integration
Antiderivatives and indefinite integration
Area
Riemann sums, and
The definite integral
Fundamental theorem of integral calculus
Integration by substitution

Transcendental Functions
The natural logarithm function
Inverse functions
Exponential functions
Applications
Inverse trigonometric functions
Differentiation, Integration, and
Completing the square
Hyperbolic functions

Applications of Integration
Area; Volumes; arc length
Surfaces of revolution
Work

Integration Techniques
Basic integration formulas
Integration by parts
Trigonometric integrals
Trigonometric substitution

More Integration TechniquesL Hopital s Rule
Partial fractions
Integrations by tables
Indeterminate forms and
L Hopital s rule
Improper integrals

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