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Professor Fraser

Multiplication and Division Techniques

Slide Duration:Table of Contents

I. Basic Concepts

Variables and Expressions

24m 5s

- Intro0:00
- Definitions0:20
- Variable0:27
- Algebraic Expression2:21
- Arithmetic Operations2:27
- Lecture Example 17:16
- Lecture Example 28:27
- Additional Example 3-1
- Additional Example 4-2

Order of Operations

22m 16s

- Intro0:00
- Why We Need It0:15
- Example: Order of Operations1:25
- Procedure To Evaluate3:22
- Lecture Example 16:45
- Lecture Example 210:55
- Additional Example 3-1
- Additional Example 4-2

The Distributive Property

16m 27s

- Intro0:00
- The Distributive Property0:20
- Extension to Several Numbers2:05
- Lecture Example 12:50
- Lecture Example 25:15
- Additional Example 3-1
- Additional Example 4-2

The Real Number System

22m 35s

- Intro0:00
- The Real Number System0:21
- Natural Numbers0:22
- Whole Numbers0:37
- Integers1:06
- Rational Numbers1:35
- Example: Decimals2:07
- The Real Number System, Cont.5:00
- Square Roots5:10
- Principle Square Root6:04
- Irrational Numbers6:35
- The Real Number System, Cont.9:11
- Picture Representation9:25
- Lecture Example 111:54
- Lecture Example 214:10
- Additional Example 3-1
- Additional Example 4-2

Functions and Graphs

27m 49s

- Intro0:00
- Functions0:30
- Definition0:30
- Example: Square Roots1:18
- Example: Gas Prices3:20
- Graphs4:03
- Definition4:03
- Example: Square Roots4:48
- Domain and Range9:30
- Definition9:30
- Example: Square Roots10:01
- Lecture Example 111:22
- Lecture Example 213:58
- Additional Example 3-1
- Additional Example 4-2

II. Solving Linear Equations

From Sentences to Equations

22m 13s

- Intro0:00
- Strategy1:40
- Using Variables1:55
- Translating Phrases2:18
- Equality3:00
- Lecture Example 13:52
- Lecture Example 28:36
- Additional Example 3-1
- Additional Example 4-2

Addition and Subtraction Techniques

14m 39s

- Intro0:00
- Techniques0:22
- Adding the Same Number0:28
- Example0:47
- Subtracting the Same Number1:50
- Example1:54
- Strategy2:36
- Isolate the Variable2:46
- Lecture Example 13:48
- Lecture Example 25:41
- Additional Example 3-1
- Additional Example 4-2

Multiplication and Division Techniques

19m 19s

- Intro0:00
- Techniques0:16
- Multiplied by the Same Number0:18
- Example0:26
- Divided by the Same Number1:23
- Non-zero Exception1:28
- Dividing by Zero2:17
- Example3:01
- Strategy3:51
- Isolate the Variable3:55
- Lecture Example 14:55
- Lecture Example 26:40
- Additional Example 3-1
- Additional Example 4-2

Techniques for Multi-Step Equations

19m 13s

- Intro0:00
- What are Multi-step Equations?0:08
- Strategy0:30
- Opposite Operations0:50
- Last Operation1:18
- Lecture Example 11:54
- Lecture Example 24:16
- Additional Example 3-1
- Additional Example 4-2

When the Variable is on Both Sides of the Equation

24m 16s

- Intro0:00
- Solving More Complicated Equations0:17
- Distributive Property and Grouping Symbols0:36
- Combining0:51
- Moving Variables to One Side1:06
- Posibble Outcomes1:50
- Exactly One Solution2:02
- No Solution2:35
- Example2:51
- Identities-True for All Real Numbers4:26
- Example4:45
- Lecture Example 16:17
- Lecture Example 29:39
- Additional Example 3-1
- Additional Example 4-2

Ratios and Proportions

22m 39s

- Intro0:00
- Definitions0:16
- Ratio0:21
- Proportion0:56
- Example1:13
- Cross Products3:00
- Example: Original Proportion3:12
- Example 25:24
- Rates6:55
- Example: Gas7:22
- Example 2: Apples7:43
- Example 3: Speed8:16
- Example 4: Cookies8:46
- Lecture Example 19:17
- Lecture Example 211:53
- Additional Example 3-1
- Additional Example 4-2

Applications of Percents

20m 38s

- Intro0:00
- Definitions0:22
- Percent of Change0:23
- Percent of Increase0:42
- Percent of Decrease0:55
- Examples of Percent of Change1:14
- Sales Tax1:21
- Discount1:57
- Lecture Example 12:51
- Lecture Example 24:46
- Additional Example 3-1
- Additional Example 4-2

More Than One Variable

22m 34s

- Intro0:00
- More Than One Variable0:21
- Strategy1:02
- Typical Application1:33
- Example: Circumference1:48
- Example: Perimeter2:21
- Lecture Example 12:53
- Lecture Example 25:43
- Additional Example 3-1
- Additional Example 4-2

III. Functions

Relations

24m 39s

- Intro0:00
- Definition0:17
- List, Table, Graph0:42
- Example: List0:56
- Example: Table2:00
- Example: Graph2:47
- Domain and Range4:10
- Inverse of a Relation5:01
- Example5:21
- Lecture Example 17:26
- Lecture Example 210:39
- Additional Example 3-1
- Additional Example 4-2

Functions

19m 3s

- Intro0:00
- Definition0:21
- Function0:24
- Example: Relation0:50
- Vertical Line Test1:48
- Example: Pass2:02
- Example 2: Fail3:32
- Example 3: Fail4:18
- Function Notation5:33
- Proper Notation5:43
- Example6:29
- Domain and Range7:32
- Lecture Example 18:06
- Lecture Example 29:39
- Additional Example 3-1
- Additional Example 4-2

Linear Functions

20m 3s

- Intro0:00
- Definition0:12
- Linear Equation0:15
- Example: A and B not zero0:27
- Example: B is zero0:58
- Example: A is zero1:13
- Graph and Intercepts1:43
- Straight Line1:52
- x-intercepts, y-intercepts2:19
- Example: Intercepts2:27
- Graphing Linear Equations4:19
- Example4:40
- Linear Functions7:23
- Example8:00
- Lecture Example 110:11
- Lecture Example 212:42
- Additional Example 3-1
- Additional Example 4-2

IV. Linear Functions and their Graphs

Slope and Rate of Change

23m 58s

- Intro0:00
- Rate of Change0:27
- Independent Variable0:37
- Dependent Variable0:51
- Slope2:02
- Example2:19
- Steepness of the Line4:56
- Possible Slopes5:58
- Positive6:13
- Negative6:34
- Zero6:50
- Undefined7:11
- Lecture Example 18:03
- Lecture Example 210:34
- Additional Example 3-1
- Additional Example 4-2

Direct Variation

13m 18s

- Intro0:00
- Definitions0:13
- Direct Variation0:14
- Constant of Variation0:26
- Graph1:02
- Example: Positive and Negative k1:18
- Applications1:49
- Lecture Example 12:16
- Lecture Example 24:39
- Additional Example 3-1
- Additional Example 4-2

Slope Intercept Form of an Equation

17m 11s

- Intro0:00
- Slope Intercept Form0:16
- Example0:37
- Lecture Example 12:24
- Lecture Example 25:43
- Additional Example 3-1
- Additional Example 4-2

Point Slope Form of an Equation

10m 32s

- Intro0:00
- Point Slope Form0:11
- Example0:50
- Lecture Example 12:03
- Lecture Example 23:03
- Additional Example 3-1
- Additional Example 4-2

Parallel and Perpendicular Lines

18m 15s

- Intro0:00
- Parallel Lines0:12
- Example: Non-vertical Lines0:32
- Perpendicular lines1:57
- Example: Slope Product is -12:15
- Negative Reciprocal3:08
- Lecture Example 13:58
- Lecture Example 27:12
- Additional Example 3-1
- Additional Example 4-2

V. Systems of Equations

Graphing Systems of Equations

20m 1s

- Intro0:00
- System of Equations0:09
- Definition0:15
- Solution0:59
- Solving by Graphing1:27
- Example2:33
- Number of Solutions3:37
- Independent3:58
- Dependent4:03
- Inconsistent4:08
- Example: 1 Solution4:15
- Example: No Solution4:34
- Example: Infinite Solution4:51
- Lecture Example 15:39
- Lecture Example 28:51
- Additional Example 3-1
- Additional Example 4-2

Solving by Substitution

24m 12s

- Intro0:00
- Substitution0:17
- Example0:51
- Number of Solutions1:43
- Infinite Solutions2:14
- No Solutions2:50
- Lecture Example 13:40
- Lecture Example 26:56
- Additional Example 3-1
- Additional Example 4-2

Solving by Addition and Subtraction

12m 18s

- Intro0:00
- Fundamental Principle0:18
- Adding or Subtracting0:50
- Lecture Example 11:23
- Lecture Example 24:03
- Additional Example 3-1
- Additional Example 4-2

Solving by Multiplication

19m 11s

- Intro0:00
- Fundamental Principle0:24
- Multiplication0:28
- Lecture Example 11:40
- Lecture Example 26:36
- Additional Example 3-1
- Additional Example 4-2

Applications: Systems of Equations

18m 24s

- Intro0:00
- Solving Systems of Equations0:08
- Graphing0:32
- Addition0:50
- Subtraction1:04
- Multiplication1:13
- Substitution1:30
- Lecture Example 13:20
- Lecture Example 24:27
- Additional Example 3-1
- Additional Example 4-2

VI. Inequalities

Inequalities: Addition and Subtraction Techniques

10m 8s

- Intro0:00
- Fundamental Principle0:11
- Solutions of Inequalities0:55
- Inequality1:02
- Set Builder Notation1:13
- Example1:15
- Graph on a Number Line2:13
- Lecture Example 13:29
- Lecture Example 25:14
- Additional Example 3-1
- Additional Example 4-2

Inequalities: Multiplication and Division Techniques

10m 59s

- Intro0:00
- Fundamental Principle0:11
- Example: Positive Number0:51
- Fundamental Principle1:35
- Example: Negative Number1:50
- Lecture Example 14:05
- Lecture Example 25:12
- Additional Example 3-1
- Additional Example 4-2

Techniques for Multi-Step Inequalities

16m 21s

- Intro0:00
- Similarity to Multi-step Equations0:15
- Inequalities Containing Grouping Symbols1:03
- Special Cases1:26
- Solution: All Real Numbers1:40
- Solution: Empty Set2:16
- Lecture Example 12:54
- Lecture Example 24:37
- Additional Example 3-1
- Additional Example 4-2

Compound Inequalities

23m

- Intro0:00
- Inequalities Combined by 'And'0:12
- Three Ways to Write Solution Set1:41
- Set Notation2:01
- Inequalities2:12
- Graph2:29
- Examples2:31
- Inequalities Combined by 'Or'4:45
- Example5:59
- Lecture Example 17:40
- Lecture Example 210:55
- Additional Example 3-1
- Additional Example 4-2

Equations with Absolute Values

23m 13s

- Intro0:00
- Absolute Value0:15
- Example: Distance1:00
- Absolute Value Function2:34
- Example3:05
- Lecture Example 14:57
- Lecture Example 28:28
- Additional Example 3-1
- Additional Example 4-2

Inequalities with Absolute Values

17m 34s

- Intro0:00
- Inequalities of the Form |x|< n0:22
- Inequalities of the Form |x|> n3:30
- Lecture Example 15:33
- Lecture Example 28:50
- Additional Example 3-1
- Additional Example 4-2

Graphing Inequalities with Two Variables

30m 50s

- Intro0:00
- Graph0:22
- Half-Plane0:28
- Boundary1:37
- Technique for Graphing3:14
- Example4:01
- Dashed Line5:13
- Solid Line6:30
- Technique for Graphing, cont.8:58
- Example9:09
- Lecture Example 112:19
- Lecture Example 215:48
- Additional Example 3-1
- Additional Example 4-2

Graphing Systems of Inequalities

27m 38s

- Intro0:00
- System of Inequalities0:26
- Example0:43
- Solving a System of Inequalities1:17
- Example1:41
- Lecture Example 12:58
- Lecture Example 27:22
- Additional Example 3-1
- Additional Example 4-2

VII. Polynomials

Multiplying Monomials

19m 55s

- Intro0:00
- What is a Monomial?0:43
- Constant1:11
- Power1:48
- Exponent and Base2:39
- Properties of Exponents3:02
- Simplified Form5:52
- Each Base Appears Exactly Once6:02
- No Powers of Powers6:18
- All Fractions Simplified6:33
- Lecture Example 16:43
- Lecture Example 28:12
- Additional Example 3-1
- Additional Example 4-2

Dividing Monomials

23m 9s

- Intro0:00
- Properties of Exponents0:26
- Example1:07
- Properties of Exponents, cont2:18
- Example3:18
- Properties of Exponents, cont4:55
- Example5:32
- Properties of Exponents, cont8:49
- Lecture Example 111:43
- Lecture Example 213:13
- Additional Example 3-1
- Additional Example 4-2

Polynomials

16m 35s

- Intro0:00
- What is a Polynomial0:45
- Monomial0:47
- Example: Trinomial1:46
- Trinomial2:10
- Example: Binomial2:21
- Binomial2:30
- Degree of a Polynomial4:28
- Example4:40
- Ordering Polynomials6:45
- Example7:27
- Lecture Example 19:27
- Lecture Example 210:31
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Polynomials

22m

- Intro0:00
- Adding Polynomials0:36
- Like Polynomials0:48
- Example1:04
- Subtracting Polynomials3:55
- Example4:01
- Lecture Example 15:30
- Lecture Example 28:04
- Additional Example 3-1
- Additional Example 4-2

Multiplying Polynomials by Monomials

24m 8s

- Intro0:00
- Distributive Property0:22
- Basic Principle0:42
- Example1:04
- Solving Equations3:25
- Lecture Example 14:26
- Lecture Example 27:51
- Additional Example 3-1
- Additional Example 4-2

Multiplying Polynomials

26m 37s

- Intro0:00
- Distributive Property0:23
- Example0:34
- Example1:55
- Foil Method5:17
- Lecture Example 17:44
- Lecture Example 210:15
- Additional Example 3-1
- Additional Example 4-2

Special Products

19m 40s

- Intro0:00
- Square of a Sum0:12
- Perfect Square Trinomial1:43
- Example2:13
- FOIL Technique3:09
- Square of a Difference3:38
- Example5:27
- Difference of Two Squares6:12
- Example7:43
- Lecture Example 18:51
- Lecture Example 211:06
- Additional Example 3-1
- Additional Example 4-2

VIII. Factoring

Factoring Monomials

27m 25s

- Intro0:00
- Prime and Composite Numbers1:01
- Prime Number1:23
- Composite Number3:03
- Factored Forms4:07
- Prime Factored Form4:19
- Factored Form5:40
- Greatest Common Factor (GCF)7:41
- Example8:00
- GCF of Monomials10:07
- Example10:18
- Lecture Example 112:52
- Lecture Example 217:08
- Additional Example 3-1
- Additional Example 4-2

Factoring Using Greatest Common Factor (GCF)

26m 3s

- Intro0:00
- Distributive Property0:19
- Factor Out an Expression1:21
- Example2:52
- Factoring by Grouping4:40
- Example6:00
- Zero Product Property8:24
- Example9:03
- Lecture Example 111:19
- Lecture Example 214:19
- Additional Example 3-1
- Additional Example 4-2

Factoring Trinomials with Leading Coefficient 1

27m 37s

- Intro0:00
- Factoring Trinomials0:23
- Example2:06
- Rules for Signs6:27
- Both Positive6:41
- Both Negative7:00
- Opposite Signs7:33
- Solving Equations8:26
- Example8:59
- Lecture Example 111:14
- Lecture Example 214:01
- Additional Example 3-1
- Additional Example 4-2

Factoring General Trinomials

34m 11s

- Intro0:00
- Factoring Trinomials0:40
- Example: List1:38
- Grouping5:46
- Example5:55
- Rules for Signs9:04
- Example9:22
- Greatest Common Factor (GCF)10:29
- Prime Polynomials11:03
- Example11:32
- Solving Equations12:32
- Lecture Example 113:11
- Lecture Example 218:37
- Additional Example 3-1
- Additional Example 4-2

Factoring the Difference of Two Squares

20m 22s

- Intro0:00
- Difference of Two Squares0:40
- Example1:56
- Factoring Using Several Techniques3:33
- Solving Equations4:11
- Lecture Example 14:55
- Lecture Example 26:05
- Additional Example 3-1
- Additional Example 4-2

Factoring Perfect Squares

18m 7s

- Intro0:00
- Perfect Squares0:10
- Perfect Square Trinomials1:17
- Solving Equations2:53
- Square Root Property2:58
- Example3:06
- Lecture Example 14:23
- Lecture Example 26:56
- Additional Example 3-1
- Additional Example 4-2

IX. Quadratic Functions

Graphing Quadratic Functions

28m 5s

- Intro0:00
- Parabolas0:09
- Parabolas That Open Upward3:58
- Minimum4:26
- Parabolas That Open Downward4:54
- Maximum5:09
- Vertex7:28
- Example8:01
- Axis of Symmetry11:03
- Lecture Example 113:27
- Lecture Example 217:17
- Additional Example 3-1
- Additional Example 4-2

Solving Equations by Graphing

28m 18s

- Intro0:00
- Solving a Quadratic Equation0:22
- Example0:50
- Two Distinct Solutions/Roots5:08
- One Double Root5:58
- No Real Roots7:14
- Estimating Solutions8:00
- Example8:16
- Example8:31
- Lecture Example 19:43
- Lecture Example 214:10
- Additional Example 3-1
- Additional Example 4-2

Solving Equations by Completing the Square

25m 7s

- Intro0:00
- Perfect Square Trinomials0:22
- Example1:12
- Completing the Square3:17
- Example3:25
- Solving Equations6:12
- Example6:27
- Leading Coefficient is 18:25
- Lecture Example 110:23
- Lecture Example 214:17
- Additional Example 3-1
- Additional Example 4-2

Solving Equations Using the Quadratic Formula

24m 15s

- Intro0:00
- Quadratic Formula1:26
- Example2:23
- Discriminant4:28
- Two Distinct Real Roots5:07
- One Double Real Root5:23
- No Real Root5:42
- Why Does It Work?6:05
- Lecture Example 17:53
- Lecture Example 211:50
- Additional Example 3-1
- Additional Example 4-2

X. Radical Expressions and Equations

Simplifying Radical Expressions

32m 40s

- Intro0:00
- Radical Expressions0:14
- Radicand0:28
- Example0:32
- Simplest Form1:07
- Example1:35
- Product Property2:34
- Verifications2:47
- Square Roots of Variables with Even Powers4:27
- Quotient Rule6:45
- Example6:55
- Rationalizing Denominators7:32
- Example7:41
- Conjugates10:44
- Examples10:59
- Simplest Radical Form14:44
- Example15:39
- Lecture Example 117:34
- Lecture Example 219:38
- Additional Example 3-1
- Additional Example 4-2

Operations with Radical Expressions

19m 59s

- Intro0:00
- Adding and Subtracting Radical Expressions0:12
- Example0:19
- Multiplying Radical Expressions1:53
- Example2:07
- Lecture Example 15:29
- Lecture Example 26:36
- Additional Example 3-1
- Additional Example 4-2

Solving Radical Equations

26m 50s

- Intro0:00
- Radical Equations0:22
- Example0:33
- Solving a Radical Equation2:04
- Example2:16
- Extraneous Solutions3:14
- Example4:31
- Lecture Example 17:33
- Lecture Example 29:45
- Additional Example 3-1
- Additional Example 4-2

Pythagorean Theorem

19m 8s

- Intro0:00
- Right Triangles0:51
- Right Angle1:03
- Vertex1:11
- Symbol1:16
- Hypotenuse and Legs1:42
- Pythagorean Theorem2:27
- Example2:47
- Example3:12
- Pythagorean Triples4:03
- Converse of the Pythagorean Theorem6:39
- Example7:41
- Lecture Example 18:57
- Lecture Example 210:05
- Additional Example 3-1
- Additional Example 4-2

Distance Formula

18m 27s

- Intro0:00
- Distance Formula0:17
- Missing Coordinates1:46
- Example1:55
- Lecture Example 14:10
- Lecture Example 25:57
- Additional Example 3-1
- Additional Example 4-2

XI. Rational Expressions and Equations

Inverse Variation

14m 43s

- Intro0:00
- Inverse Variation0:23
- Constant of Variation0:37
- Graphing Inverse Variation1:08
- Example: Hyperbola1:15
- Product Rule3:54
- Lecture Example 15:31
- Lecture Example 27:43
- Additional Example 3-1
- Additional Example 4-2

Rational Expressions

32m 43s

- Intro0:00
- Rational Expression0:55
- Example1:03
- Excluded Values1:29
- Examples1:40
- Simplifying Rational Expressions5:36
- Greatest Common Factor (GCF)5:46
- Example5:55
- Example7:42
- Simplifying and Excluded Values9:34
- Lecture Example 19:50
- Lecture Example 213:55
- Additional Example 3-1
- Additional Example 4-2

Multiplying Rational Expressions

27m 22s

- Intro0:00
- Procedure0:16
- Example0:33
- Cancel Before Multiplication3:44
- Example3:55
- Rational Expressions Containing Polynomials6:19
- Example6:26
- Lecture Example 111:09
- Lecture Example 215:39
- Additional Example 3-1
- Additional Example 4-2

Dividing Rational Expressions

28m 30s

- Intro0:00
- Procedure0:21
- Example0:59
- Cancel Before Multiplication4:31
- Example4:39
- Rational Expressions Containing Polynomials8:01
- Example8:08
- Lecture Example 110:43
- Lecture Example 213:46
- Additional Example 3-1
- Additional Example 4-2

Dividing Polynomials

29m 44s

- Intro0:00
- Dividing a Polynomial by a Monomial1:07
- Example1:14
- Dividing a Polynomial by a Binomial3:30
- Example3:51
- Long Division5:20
- Example6:25
- Missing Terms11:11
- Example12:25
- Lecture Example 114:54
- Lecture Example 216:35
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Rational Expressions with Like Denominators

16m 50s

- Intro0:00
- Adding with Like Denominators0:14
- Example0:41
- Subtraction with Like Denominators2:23
- Example2:30
- Denominators That Are Additive Inverses2:55
- Example3:03
- Lecture Example 16:41
- Lecture Example 27:09
- Additional Example 3-1
- Additional Example 4-2

Adding and Subtracting Rational Expressions with Unlike Denominators

36m

- Intro0:00
- Least Common Multiple (LCM) of Polynomials0:34
- Example0:45
- Example1:55
- Adding and Subtracting4:08
- Example4:45
- Lecture Example 18:13
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2

Complex Fractions

18m 43s

- Intro0:00
- Mixed Expression0:08
- Example0:30
- Complex Fraction2:45
- Example2:57
- Example3:11
- Example3:22
- Simplifying Complex Fractions3:58
- Why Does It Work?4:22
- Lecture Example 14:48
- Lecture Example 28:44
- Additional Example 3-1
- Additional Example 4-2

Rational Equations

39m 10s

- Intro0:00
- Definition0:08
- Examples0:17
- Solving Rational Expressions3:02
- Example3:09
- Work Problems6:31
- Example6:48
- Extraneous Solutions13:12
- Example14:13
- Lecture Example 117:21
- Lecture Example 219:59
- Additional Example 3-1
- Additional Example 4-2

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1 answer

Last reply by: Jorge Sardinas

Sat Apr 28, 2012 5:47 PM

Post by Jorge Sardinas on April 28, 2012

On example 3 you' re suppose to divide not multiply you did it all wrong you made a careless mistake.

0 answers

Post by Ronnie Niven on April 20, 2012

Very good and well explained.

0 answers

Post by Caroline Rodgers on September 20, 2009

In the section "Strategy," it is awkward to use what appears to be a zero to represent an unknown number, since isolating variables depends upon using a "nonzero quantity."