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Dr. Carleen Eaton

From Sentences to Equations

Slide Duration:Table of Contents

I. Basic Concepts

Variables and Expressions

11m 22s

- Intro0:00
- History of Algebra0:12
- Origin of Word0:21
- Real World Problems0:35
- Definitions0:58
- Variable1:03
- Algebraic Expression1:37
- Operations2:02
- Example 1: Words into Expressions3:02
- Example 2: Words into Expressions5:20
- Example 3: Words into Expressions6:45
- Example 4: Words into Expressions9:46

Order of Operations

15m 59s

- Intro0:00
- Example0:17
- Definition0:57
- Procedure to Evaluate an Arithmetic Expression1:08
- Grouping Symbols (Parentheses, Brackets, Braces)1:19
- Powers1:42
- Multiply/Divide Left to Right1:57
- Add/Subtract Left to Right2:21
- Example: Fraction Bar2:49
- Example 1: Evaluate Arithmetic Expression3:45
- Example 2: Evaluate Arithmetic Expression7:28
- Example 3: Evaluate Arithmetic Expression10:11
- Example 4: Evaluate with Variables13:12

Distributive Property

9m 50s

- Intro0:00
- Distributive Property Statements0:23
- Moving Forward0:49
- Rule for Subtraction1:14
- Reverse Order1:40
- Several Numbers2:17
- Example 1: Evaluate Using Distributive Property2:56
- Example 2: Multiply Using Distributive Property4:10
- Example 3: Simplify Using Distributive Property4:59
- Example 4: Simplify Using Distributive Property7:03

Real Number System

17m 58s

- Intro0:00
- Real Number System0:31
- Natural Numbers0:39
- Whole Numbers1:11
- Integers1:23
- Rational Numbers1:52
- Cannot Divide by Zero2:18
- Decimals2:27
- Example: Terminating or Repeating2:39
- Real Number System, Cont.3:37
- Square Roots3:42
- Examples3:54
- Irrational Numbers4:36
- Examples5:02
- Perfect Square5:54
- Real Number System, Cont.6:49
- Example: Number Line7:02
- Example 1: Which Set of Numbers7:54
- Example 2: Graph on Number Line10:04
- Example 3: Approximate Irrational Number12:47
- Example 4: Order Largest to Smallest13:57

Functions and Graphs

34m 39s

- Intro0:00
- Functions0:15
- Example: Function0:29
- Example: Not Functions (Relations)1:15
- Graphs4:44
- Visual Display4:53
- Example: X and Y5:03
- Coordinate Pairs5:53
- Discrete Function8:19
- Continuous Function8:55
- Vertical Line Test10:55
- Test if Function11:12
- Example: Pass Through Points11:43
- Domain and Range14:13
- Example14:43
- Example 1: Function Given by Table16:24
- Example 2: Cost of Gas18:46
- Example 3: Cost of Gas23:15
- Example 4: Cost of Mail29:07

II. Solving Linear Equations

From Sentences to Equations

16m 5s

- Intro0:00
- Real World Applications0:18
- Strategy0:26
- Using Variables0:32
- Translate Phrases0:48
- Identity Equality Words1:07
- Example 1: Write Equation1:32
- Example 2: Write Equation4:14
- Example 3: Sisters' Ages8:26
- Example 4: Surface Area of Cylinder12:52

Addition and Subtraction Techniques

15m 24s

- Intro0:00
- Techniques0:21
- Addition Principle0:24
- Example0:37
- Subtraction Principle1:44
- Example1:48
- Strategy2:33
- Isolate the Variable2:41
- Example2:55
- Example 1: Solve Equation3:39
- Example 2: Solve Equation5:38
- Example 3: Word Problem7:38
- Example 4: Word Problem11:14

Multiplication and Division Techniques

15m 41s

- Intro0:00
- Isolating the Variable0:08
- Techniques0:34
- Multiplication Principle0:41
- Example0:57
- Division Principle2:32
- Example2:47
- Strategy3:12
- Example3:30
- Opposite Operation3:53
- Example 1: Solve Equation5:07
- Example 2: Solve Equation6:50
- Example 3: Solve Equation10:05
- Example 4: Word Problem12:07

Techniques for Multistep Equations

14m 31s

- Intro0:00
- What are Multistep Equations0:06
- Addition/Subtraction and Multiplication/Division0:31
- Strategy0:43
- Identify Last Operation0:47
- Example 1: Solve Equation1:51
- Example 2: Solve Equation5:27
- Example 3: Find Numbers7:39
- Example 4: Solve Equation11:27

When the Variable is on Both Sides of the Equation

20m 17s

- Intro0:00
- Solving More Complicated Equations0:28
- Distributive Property0:41
- Review of Distributive Property0:55
- Factoring1:28
- Subtracting1:50
- Applying with Addition/Subtraction2:08
- Possible Outcomes2:45
- Exactly One Solution2:52
- No Solution3:08
- True for All Real Numbers4:45
- Identities5:01
- Example 1: Solve Equation6:03
- Example 2: Solve Equation9:08
- Example 3: Solve Equation14:06
- Example 4: Solve Equation17:28

Ratios and Proportion

16m 5s

- Intro0:00
- Definitions0:07
- Ratio0:10
- Different Representations0:14
- Proportion0:33
- Example0:40
- Cross Product1:08
- Cross Multiplication1:32
- Example2:13
- Rates3:33
- Rates in Real Life3:46
- Example 1: Form a Proportion4:43
- Example 2: Cross Multiply7:15
- Example 3: How Long to Drive9:00
- Example 4: Cross Products12:13

Applications of Percents

13m 46s

- Intro0:00
- Definitions0:15
- Percent of Increase0:27
- Percent of Decrease0:34
- Examples0:42
- Sales Tax1:48
- Discount2:44
- Example 1: Temperature Change3:12
- Example 2: Sales Tax5:44
- Example 3: Clothing Discount7:04
- Example 4: Sales and Discount9:15

More Than One Variable

20m 38s

- Intro0:00
- More Than One Variable0:21
- Real Life Examples0:30
- Strategy1:08
- Possible Techniques1:17
- Typical Application1:43
- Solving for a Different Variable1:59
- Example 1: Solve for Y5:06
- Example 2: Solve for Q7:38
- Example 3: Solve for H12:56
- Example 4: Solve for X16:04

III. Functions

Relations

16m 58s

- Intro0:00
- Definition0:04
- Relation0:06
- Table0:18
- Set of Ordered Pairs1:01
- Graph1:38
- Domain and Range2:40
- Example: Relation2:51
- Example: Broader Cases3:48
- Inverse of a Relation4:42
- Example4:59
- Example 1: Relation as Table/Graph6:15
- Example 2: Domain and Range8:41
- Example 3: Table, Graph, Domain, Range10:36
- Example 4: Inverse of a Relation13:36

Functions

19m 27s

- Intro0:00
- Definition0:14
- Review of Relations0:27
- Violation of Function1:43
- Example: Function2:00
- Vertical Line Test3:18
- Example3:41
- Function Notation6:15
- Using f(x)6:26
- Example: Value Assigned7:12
- Example 1: Relation a Function8:10
- Example 2: Relation a Function9:39
- Example 3: Using f(x) Notation12:20
- Example 4: g(x) Notation15:01

Linear Functions

20m 15s

- Intro0:00
- Definition0:07
- Standard Form0:18
- Example0:52
- Graph and Intercepts2:39
- Example: Graph2:48
- X-Intercept2:56
- Y-Intercept3:35
- Graphing Linear Equations4:29
- Example4:47
- Linear Functions7:51
- Example8:15
- Example 1: Linear10:16
- Example 2: Linear Equation12:58
- Example 3: Intercepts14:23
- Example 4: Equation from Intercepts16:47

IV. Linear Functions and Their Graphs

Slope and Rate of Change

19m 46s

- Intro0:00
- Rate of Change0:06
- Other Words0:14
- Example0:24
- Slope2:12
- Two Points2:39
- Steepness of a Line2:57
- Possible Slopes4:29
- Positive Slope5:02
- Negative Slope5:29
- Zero Slope (Horizontal Line)6:23
- Undefined Slope (Vertical Line)7:08
- Example 1: Rate of Change of Table8:19
- Example 2: Slope Through Points10:52
- Example 3: Increasing/Decreasing13:06
- Example 4: Slope Through Points16:02

Direct Variation

13m 54s

- Intro0:00
- Definitions0:10
- Constant of Variation k0:21
- Example: Gas and Miles Driven0:59
- Graph1:50
- k is Slope2:04
- Examples2:27
- Applications2:47
- Write, Graph, Solve2:58
- Example 1: Constant of Variation3:11
- Example 2: Graph Direct Variation4:59
- Example 3: Direct Variation6:50
- Example 4: Distance Car Travels9:18

Slope Intercept Form of an Equation

12m 6s

- Intro0:00
- Slope Intercept Form0:12
- m (Slope) and b (Y Intercept)0:31
- Example1:12
- Example 1: Slope Intercept Form Equation2:39
- Example 2: Graph the Equation5:11
- Example 3: Slope Intercept Form Equation6:51
- Example 4: Slope Intercept Form Equation8:50

Point Slope Form of an Equation

9m 7s

- Intro0:00
- Point Slope Form0:07
- Manipulating to Other Forms0:35
- m (Slope), x1 y1 (Point)0:47
- Example 1: Point Slope Form Equation1:03
- Example 2: Point Slope Form Equation2:50
- Example 3: Point Slope Form Equation4:18
- Example 4: Point Slope Form Equation6:50

Parallel Lines and Perpendicular Lines

18m 2s

- Intro0:00
- Parallel Lines0:08
- Example0:15
- Vertical Lines0:40
- Perpendicular Lines1:19
- Negative Reciprocal1:31
- Example2:05
- Example 1: Slope Intercept Form3:25
- Example 2: Parallel or Perpendicular6:15
- Example 3: Slope Intercept Form9:27
- Example 4: Slope Intercept Form12:35

V. Systems of Equations

Graphing Systems of Equations

22m 45s

- Intro0:00
- Systems of Equations0:10
- Definition0:15
- Example0:31
- Solution0:47
- Solving by Graphing1:23
- Points of Intersection1:36
- Example1:56
- Number of Solutions3:09
- Independent3:20
- Dependent3:50
- Inconsistent4:46
- Example 1: Solve by Graphing5:45
- Example 2: Solve by Graphing9:50
- Example 3: Solve by Graphing14:17
- Example 4: Solve by Graphing18:03

Solving by Substituting

22m 41s

- Intro0:00
- Substitution0:09
- Example0:45
- Number of Solutions2:47
- Infinite Solutions3:11
- No Solutions4:28
- Example 1: Solve by Substitution5:44
- Example 2: Solve by Substitution10:01
- Example 3: Solve by Substitution15:17
- Example 4: Solve by Substitution19:41

Solving by Addition and Subtraction

16m 13s

- Intro0:00
- Fundamental Principle0:10
- Example0:23
- Example 1: Solve the System1:52
- Example 2: Solve the System5:53
- Example 3: Solve the System10:15
- Example 4: Solve the System14:08

VI. Inequalities

Addition & Subtraction Techniques

11m 34s

- Intro0:00
- Fundamental Principle0:09
- Example0:36
- Solutions of Inequalities1:51
- Inequality1:59
- Set Builder Notation2:02
- Graph on a Number Line2:08
- Examples2:18
- Example 1: Solve the Inequality4:59
- Example 2: Solve the Inequality7:00
- Example 3: Solve the Inequality8:10
- Example 4: Solve the Inequality9:47

Multiplication & Division Techniques

10m 49s

- Intro0:00
- Fundamental Principle0:10
- Only Positive Numbers0:23
- Example0:51
- Fundamental Principle, Cont.2:01
- Negative Numbers2:12
- Reverse Inequality Sign2:28
- Example2:48
- Example 1: Solve the Inequality4:26
- Example 2: Solve the Inequality5:45
- Example 3: Solve the Inequality6:50
- Example 4: Solve the Inequality8:28

Techniques for Multistep Inequalities

16m 56s

- Intro0:00
- Similarity to Multistep Equations0:16
- Negative Numbers0:32
- Example0:49
- Inequalities Containing Grouping Symbols1:24
- Example1:35
- Special Cases2:45
- Example: All Real Numbers3:04
- Example: Empty Set4:10
- Example 1: Solve the Inequality6:05
- Example 2: Solve the Inequality7:39
- Example 3: Solve the Inequality9:57
- Example 4: Solve the Inequality13:56

Compound Inequalities

21m 32s

- Intro0:00
- What is a Compound Inequality0:07
- Joined by 'And' or 'Or'0:16
- Inequalities Combined by 'And'0:36
- Intersection/Overlap0:53
- Example1:08
- Inequalities Combined by 'Or'4:23
- Union4:41
- Example5:27
- Example 1: Solve the Inequality6:39
- Example 2: Solve the Inequality11:30
- Example 3: Solve the Inequality13:43
- Example 4: Solve the Inequality18:19

Equations with Absolute Value

24m 16s

- Intro0:00
- Absolute Value0:06
- Number Line0:22
- Example0:41
- Absolute Value is N1:52
- Absolute Value Function3:17
- Example3:40
- g(x) and f(x)4:31
- Solving Absolute Value Equations6:23
- Absolute Value in Words6:39
- Split Into Two Parts7:58
- Solve Both Equations8:22
- Example 1: Solve the Absolute Value10:34
- Example 2: Solve the Absolute Value13:09
- Example 3: Solve the Absolute Value14:52
- Example 4: Solve the Absolute Value20:23

Inequalities with Absolute Values

17m 37s

- Intro0:00
- Inequalities of the Form |x|< n0:07
- Values that Satisfy Both Inequalities0:46
- Example1:27
- Inequalities of the Form |x|> n3:58
- Values that Satisfy Either Inequalities4:19
- Example4:47
- Example 1: Solve the Inequality6:38
- Example 2: Solve the Inequality9:54
- Example 3: Solve the Inequality12:05
- Example 4: Solve the Inequality14:50

Graphing Inequalities with Two Variables

24m 33s

- Intro0:00
- Graph0:08
- Half Plane and Boundary0:51
- Technique for Graphing1:57
- Graph Equation2:01
- Solid Line or Dashed Line2:07
- Example2:32
- Choosing a Test Point5:10
- Example5:26
- Example 1: Solve the Inequality7:49
- Example 2: Solve the Inequality11:37
- Example 3: Solve the Inequality15:44
- Example 4: Solve the Inequality19:10

Graphing Systems of Inequalities

24m 4s

- Intro0:00
- System of Inequalities0:05
- Example0:22
- Solving a System of Inequalities0:38
- Solution Set0:46
- Graph Each Inequality0:57
- Area of Overlap1:45
- Example 1: Solve the System of Inequalities2:44
- Example 2: Solve the System of Inequalities6:33
- Example 3: Solve the System of Inequalities11:40
- Example 4: Solve the System of Inequalities17:36

VII. Polynomials

Multiplying Monomials

22m 19s

- Intro0:00
- What is a Monomial0:09
- Examples0:17
- Power0:55
- Base and Exponent1:52
- Properties of Exponents2:16
- Add Exponents2:25
- Multiply Exponents4:00
- Product Exponent4:39
- Simplified Form7:26
- Examples7:47
- Example 1: Simplify the Monomial8:26
- Example 2: Simplify the Monomial10:32
- Example 3: Simplify the Monomial12:48
- Example 4: Simplify the Monomial17:33

Dividing Monomials

24m 2s

- Intro0:00
- Properties of Exponents0:05
- Dividing with Same Base0:15
- Example0:53
- Quotient Raised to Power2:22
- Example2:53
- Raising to 0 Power4:00
- Example4:21
- Negative Exponents5:45
- Example6:05
- Example 1: Simplify the Monomial7:33
- Example 2: Simplify the Monomial14:56
- Example 3: Simplify the Monomial13:30
- Example 4: Simplify the Monomial17:35

Polynomials

8m 56s

- Intro0:00
- What is a Polynomial0:07
- Monomial0:40
- Binomial1:15
- Trinomial1:25
- Degree of a Polynomial1:56
- Example: Degree of Monomial2:13
- Example: Degree of Polynomial2:47
- Ordering Polynomials3:32
- Example3:47
- Example 1: Trinomial or Binomial4:44
- Example 2: Find the Degree5:27
- Example 3: Increasing Powers6:11
- Example 4: Decreasing Powers7:27

Adding and Subtracting Polynomials

15m 51s

- Intro0:00
- Adding Polynomials0:07
- Like Terms0:18
- Example1:02
- Subtracting Polynomials2:44
- Example2:58
- Example 1: Add Polynomials5:11
- Example 2: Subtract Polynomials7:30
- Example 3: Add and Subtract9:35
- Example 4: Add and Subtract12:09

Multiplying Polynomials by Monomials

18m 17s

- Intro0:00
- Distributive Property0:07
- Example0:54
- Solving Equations1:36
- Isolate Variable and Solve1:46
- Example 1: Multiply1:59
- Example 2: Simplify3:33
- Example 3: Simplify7:20
- Example 4: Solve13:37

Multiplying Polynomials

18m 2s

- Intro0:00
- Distributive Property0:08
- Example0:54
- FOIL Method2:44
- First, Outer, Inner, Last3:20
- Example 1: Multiply5:32
- Example 2: Multiply7:27
- Example 3: Multiply9:41
- Example 4: Multiply13:56

Special Products

17m

- Intro0:00
- Square of a Sum0:06
- Example1:09
- Square of a Difference2:46
- Example3:22
- Difference of Two Squares4:50
- Example5:31
- Example 1: Multiply6:24
- Example 2: Multiply8:34
- Example 3: Multiply11:03
- Example 4: Multiply12:54

VIII. Factoring

Special Product

17m 51s

- Intro0:00
- Prime and Composite Numbers0:09
- Prime Number0:12
- Composite Number0:42
- Factored Forms1:39
- Prime Factored Form1:40
- Factored Form2:21
- Greatest Common Factor3:55
- Example: GCF for Number4:19
- Example: GCF for Monomial6:00
- Example 1: Prime Factored Form7:51
- Example 2: Factored Form9:34
- Example 3: GCF11:12
- Example 4: GCF13:28

Factoring Using Greatest Common Factor

25m 21s

- Intro0:00
- Distributive Property0:05
- Example: Binomial0:49
- Example: Trinomial2:18
- Factoring by Grouping4:17
- Example: Four Terms4:40
- Zero Product Property8:21
- Example9:01
- Example 1: Factor the Polynomial10:38
- Example 2: Factor the Polynomial13:43
- Example 3: Factor the Polynomial19:59
- Example 4: Solve the Polynomial22:58

Factoring Trinomials with Leading Coefficient of 1

27m 11s

- Intro0:00
- Factoring Trinomials0:07
- Leading Coefficient0:11
- Example1:20
- Rules for Signs2:42
- P and Q Both Positive2:55
- P and Q Both Negative3:39
- P and Q Opposite Signs4:30
- Solving Equations5:18
- Example6:44
- Example 1: Factor the Polynomial7:41
- Example 2: Factor the Polynomial12:33
- Example 3: Factor the Polynomial16:39
- Example 4: Solve the Polynomial21:35

Factoring General Trinomials

46m 9s

- Intro0:00
- Factoring Trinomials0:15
- Example2:42
- Grouping7:20
- Example7:35
- Rules for Signs10:51
- Same as Leading Coefficient is 111:05
- Greatest Common Factor12:29
- Use Whenever Possible12:41
- Example12:59
- Prime Polynomials13:58
- Example14:33
- Solving Equations16:55
- Example17:25
- Example 1: Factor the Polynomial18:46
- Example 2: Factor the Polynomial25:23
- Example 3: Factor the Polynomial32:37
- Example 4: Solve the Polynomial36:18

Factoring the Difference of Two Squares

24m 3s

- Intro0:00
- Difference of Two Squares0:08
- Example0:36
- Factoring Using Several Techniques2:23
- Factoring the GCF2:30
- Example3:22
- Solving Equations5:24
- Example5:50
- Example 1: Factor the Polynomial7:34
- Example 2: Factor the Polynomial9:11
- Example 3: Factor the Polynomial12:00
- Example 4: Solve the Polynomial18:31

Factoring Perfect Squares

18m 10s

- Intro0:00
- Perfect Squares0:07
- Example: Perfect Square Trinomials1:12
- Solving Equations2:57
- Square Root Property3:09
- Example3:28
- Example 1: Factor the Polynomial5:09
- Example 2: Factor the Polynomial6:13
- Example 3: Solve the Polynomial8:43
- Example 4: Solve the Polynomial13:35

IX. Quadratic Functions

Graphing Quadratic Functions

35m 45s

- Intro0:00
- Parabolas0:14
- Standard Form of Quadratic Function0:28
- Examples1:05
- Absolute Value of 'a'2:19
- Parabolas That Open Upward3:14
- Minimum3:48
- Example3:57
- Parabolas That Open Downward6:57
- Example7:17
- Maximum9:23
- Vertex9:53
- Example10:40
- Axis of Symmetry14:16
- Example15:03
- Example 1: Graph the Quadratic19:54
- Example 2: Graph the Quadratic24:12
- Example 3: Vertex Maximum or Minimum28:32
- Example 4: Axis of Symmetry31:13

Solving Equations by Graphing

40m 42s

- Intro0:00
- Solving a Quadratic Equation0:08
- Example0:56
- Two Distinct Solutions/Roots8:10
- Roots8:23
- Example: Graphs8:40
- One Double Root9:19
- Example: One X-Intercept9:54
- No Real Roots14:03
- Example14:53
- Estimating Solutions18:41
- Example: Not Integers19:18
- Example 1: Solve by Graphing20:18
- Example 2: Solve by Graphing26:36
- Example 3: Solve by Graphing30:18
- Example 4: Estimate by Graphing34:59

Solving Equations by Completing the Square

28m 13s

- Intro0:00
- Perfect Square Trinomials0:15
- Example0:36
- Completing the Square4:55
- Example6:20
- Completing the Square to Solve Equations9:19
- Example9:40
- When the Leading Coefficient is Not 113:17
- Example14:01
- Example 1: Solve the Equation15:05
- Example 2: Complete the Square20:16
- Example 3: Solve by Completing the Square22:31
- Example 4: Solve by Completing the Square25:02

Solving Equations Using the Quadratic Formula

17m 17s

- Intro0:00
- Quadratic Formula0:17
- Standard Form0:24
- Example1:00
- Discriminant3:14
- Two Solutions and Both Real3:40
- One Real Solution4:07
- No Real Solutions4:28
- Example 1: Solve the Equation6:25
- Example 2: Solve the Equation8:42
- Example 3: Solve the Equation12:02
- Example 4: Number of Real Roots15:23

X. Radical Expressions and Equations

Simplifying Radical Expressions

41m 30s

- Intro0:00
- Radical Expression0:12
- Example: Radicand Simplest Form0:29
- Example: Not Simplest Form1:16
- Principal Square Root (Positive)2:43
- Product Property3:40
- Examples4:05
- Square Roots of Variables with Even Powers7:01
- Eliminate Radical Sign7:42
- Divide Exponent by 27:57
- Absolute Value of Result8:29
- Examples8:52
- Quotient Rule14:12
- Example14:31
- Rationalizing Denominators16:08
- Example16:43
- Conjugates18:33
- Example19:53
- Simplest Radical Form20:58
- Three Criteria21:10
- Example 1: Simplify Expression21:57
- Example 2: Simplify Expression25:12
- Example 3: Simplify Expression31:37
- Example 4: Simplify Expression35:29

Operations with Radical Expressions

21m 52s

- Intro0:00
- Adding and Subtracting Radical Expressions0:13
- Like Radicals0:28
- Distributive Property1:10
- Multiplying Radical Expressions4:24
- Example: Use FOIL4:44
- Example 1: Simplify Expression7:07
- Example 2: Simplify Expression8:51
- Example 3: Simplify Expression12:14
- Example 4: Simplify Expression16:06

Solving Radical Equations

27m

- Intro0:00
- Radical Equations0:15
- Examples0:30
- Solving a Radical Equation1:13
- Isolate Radical1:18
- Square Both Sides1:38
- Example1:44
- Extraneous Solutions2:57
- Example: Check Solutions3:30
- Example 1: Solve Equation6:29
- Example 2: Solve Equation9:52
- Example 3: Solve Equation14:29
- Example 4: Solve Equation20:53

Pythagorean Theorem

17m 24s

- Intro0:00
- Right Triangles0:06
- Vertex0:32
- Hypotenuse0:56
- Legs1:11
- Pythagorean Theorem1:21
- Graphical Representation1:37
- Example2:39
- Pythagorean Triples3:40
- Example3:56
- Converse of the Pythagorean Theorem4:36
- Example6:23
- Example 1: Length of Hypotenuse7:24
- Example 2: Length of Legs9:02
- Example 3: Area of Triangle12:00
- Example 4: Length of Side14:59

Distance Formula

26m 50s

- Intro0:00
- Distance Formula0:09
- Similarity to Pythagorean Theorem0:21
- Missing Coordinates5:50
- Example6:22
- Example 1: Distance Between Points11:43
- Example 2: Distance Between Points14:05
- Example 3: Distance Between Points18:18
- Example 4: Missing Coordinate21:57

XI. Rational Expressions and Equations

Inverse Variation

24m 13s

- Intro0:00
- Direct Variation0:12
- Inverse Variation0:24
- Constant of Variation k0:50
- Y Varies Inversely as X0:59
- Graphing Inverse Variation3:09
- Real World Applications3:24
- Example3:59
- Product Rule10:19
- Alternate Form11:10
- Finding Missing 4th Point11:24
- Example 1: Graph Inverse Variation11:36
- Example 2: Graph Inverse Variation14:47
- Example 3: Find Missing Point19:39
- Example 4: Find Missing Point21:53

Rational Expressions

34m 22s

- Intro0:00
- Rational Expressions0:10
- Examples0:28
- Excluded Values1:03
- Dividing by 01:29
- Example2:49
- Simplifying Rational Expressions7:12
- Eliminating the GCF7:17
- Example: Regular Fraction7:30
- Example: Rational Expression8:12
- Simplifying and Excluded Values10:15
- Original Rational Expression10:24
- Example10:47
- Example 1: Find Excluded Values13:47
- Example 2: Simplify and Find Excluded Values16:10
- Example 3: Simplify and Find Excluded Values22:04
- Example 4: Simplify and Find Excluded Values26:29

Multiplying Rational Expressions

22m 58s

- Intro0:00
- Procedure0:08
- Examples0:29
- Cancel Before Multiplication1:53
- Example2:04
- Rational Expressions Containing Polynomials3:18
- Example3:46
- Example 1: Multiply Rational Expressions6:04
- Example 2: Multiply Rational Expressions9:11
- Example 3: Multiply Rational Expressions11:19
- Example 4: Multiply Rational Expressions17:36

Dividing Rational Expressions

21m 49s

- Intro0:00
- Procedure0:10
- Reciprocal of Expression0:22
- Example: Regular Fractions0:44
- Example: Rational Expressions1:46
- Cancel Before Multiplying3:23
- Why Cancel3:45
- Example4:15
- Rational Expressions Containing Polynomials6:46
- Example7:06
- Example 1: Divide Rational Expressions9:15
- Example 2: Divide Rational Expressions13:11
- Example 3: Divide Rational Expressions15:39

Dividing Polynomials

35m 57s

- Intro0:00
- Dividing a Polynomial by a Monomial0:11
- Example: Regular Fractions0:36
- Example: Polynomials1:24
- Dividing a Polynomial by a Binomial2:56
- Example: Dividend and Divisor3:30
- Long Division5:28
- Example: Regular Numbers5:49
- Example: Polynomials7:17
- Missing Terms12:20
- Definition12:40
- Example12:55
- Example 1: Divide the Polynomials18:42
- Example 2: Divide the Polynomials20:54
- Example 3: Divide the Polynomials23:28
- Example 4: Divide the Polynomials28:52

Adding and Subtracting Rational Expressions with Like Denominators

17m 38s

- Intro0:00
- Adding with Like Denominators0:09
- Example: Regular Numbers0:19
- Example: Rational Expressions1:05
- Subtracting with Like Denominators2:35
- Example: Regular Fractions2:52
- Example: Rational Expressions3:05
- Denominators That Are Additive Inverses4:08
- What Are Additive Inverses4:35
- Example5:53
- Example 1: Add Rational Expressions7:54
- Example 2: Subtract Rational Expressions8:43
- Example 3: Add Rational Expressions10:39
- Example 4: Subtract Rational Expressions11:48

Adding and Subtracting Rational Expressions with Unlike Denominators

37m 16s

- Intro0:00
- Least Common Multiple of Polynomials0:21
- Example: Regular Fractions0:42
- Example: Rational Expressions5:18
- Equivalent Rational Expressions Using LCM7:23
- Example8:09
- Adding and Subtracting14:24
- Summary of Techniques14:32
- Example 1: Find the LCM15:09
- Example 2: Add Rational Expressions17:53
- Example 3: Subtract Rational Expressions22:19
- Example 4: Add Rational Expressions30:44

Complex Fractions

25m 38s

- Intro0:00
- Mixed Expressions0:10
- Analogy to Mixed Fractions0:23
- Polynomial and Rational Expression0:59
- Example: Combining1:55
- Converting to Rational Expression2:29
- Complex Fraction5:16
- Examples5:30
- Simplifying Complex Fractions6:08
- Example6:27
- Example 1: Write as Rational Expression9:43
- Example 2: Simplify Complex Fractions12:44
- Example 3: Simplify Complex Fractions15:03
- Example 4: Simplify Complex Fractions19:55

Rational Equations

38m 9s

- Intro0:00
- Definition0:11
- Example: Cross Multiplication0:39
- Example: Rational Expressions1:13
- Solving Rational Equations3:12
- Multiply by LCM of Denominators3:33
- Example4:02
- Work Problems7:19
- Example: Complete a Project8:17
- Extraneous Solutions12:41
- Check All Solutions13:18
- Example13:54
- Example 1: Solve Rational Equation17:28
- Example 2: Solve Rational Equation19:45
- Example 3: Work Problem27:15
- Example 4: Solve Rational Equation31:10

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For more information, please see full course syllabus of Algebra 1

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1 answer

Last reply by: Dr Carleen Eaton

Tue Apr 26, 2016 7:45 PM

Post by Raymond Hayden on April 24, 2016

Regarding Ex #3, the right side of the equation = 20 because the difference between the two ages is 5 and 5sq = 25 and 25-5 = 20. The left side of the equation is a problem because the are no multiples of 20 that have a difference of 5 between them. This makes the equation untrue. Am I correct?

1 answer

Last reply by: Dr Carleen Eaton

Wed Jun 26, 2013 11:38 PM

Post by Taylor Wright on June 17, 2013

In example 3:

Wouldn't (m-(m-5)) be (m-m+5) which would be 5 ?

Shouldn't the minus sign in front of the parentheses distribute to the 5, turning it into a positive #?

2 answers

Last reply by: Raymond Hayden

Sun Apr 24, 2016 11:43 PM

Post by Taylor Wright on June 17, 2013

What are some good indicators that parentheses needs to be present?

1 answer

Last reply by: Dr Carleen Eaton

Thu Dec 27, 2012 12:15 AM

Post by bo young lee on December 17, 2012

i dont understand the example 1 and 2 can you explain more specific and more easy

1 answer

Last reply by: Dr Carleen Eaton

Tue May 11, 2010 11:56 PM

Post by eric filler on April 21, 2010

I enjoy this it is a whole diffrent way of looking at math thanks oh is their any work problems I can get for each lesson