# Ppt on rational numbers for class 9

##### Redefining Developmental Math for Non-Algebra Core Math Courses Dr. Daryl Stephens Murray Butler East Tennessee State.

.5 Solving Equations Containing Rational Expressions Integrated Review-Summary on Rational Expressions Integrated Review-Summary on Rational Expressions 7.6 Proportion and Problem Solving with Rational Equations 7.6 Proportion and Problem Solving with Rational Equations 7.7 Simplifying Complex Fractions 7.7 Simplifying Complex Fractions 10. Radicals, Rational Exponents, and Complex Numbers 10. Radicals, Rational Exponents, and Complex Numbers 10.2 Rational Exponents 10.2 Rational Exponents 10.3 Simplifying/

##### Introduction to Rational Rose 2000 v6.5 Copyright © 1999 Rational Software, all rights reserved 1 Rational Rose 2000 Interaction Diagrams.

Realizations;  Design Classes Introduction to Rational Rose 2000 v6.5 Copyright © 1999 Rational Software, all rights reserved 9 Where are we – Subsystem Design  Realizations between the subsystem’s interfaces and contained classes are defined.  Detailed/for the remaining messages. Remember, you must add them in order.. Note: What kind of class is RegisterForCoursesForm? Note the number of messages from the actor (external) to this class. Introduction to Rational Rose 2000 v6.5 Copyright © 1999 Rational/

##### The Psychological Basis of Rationality: Examples from Games and Paradoxes Richard M. Shiffrin.

A decide. Whatever A gets, B gets also. B knows people fall into two classes, those choosing ONE and those choosing BOTH. B would very much want A to / mathematical derivations). P gets an answer or two For X =1, P gains 9 For all other X, P gains ~.2X (the larger the number of simulation trials, the closer is the convergence /answer is 1/3 (and have written journal articles saying so). What then is the rational answer? The Absent-Minded Driver Perhaps Sleeping Beauty is not such a paradox (social consensus /

##### 1 Objects and classes Classes – Encapsulate data: Attributes – Encapsulate function: Methods – Ideal for modeling real-world phenomena – Act as blueprints.

for housekeeping before Python reclaims object memory 9 Class Attributes – One copy of attribute shared by all objects of a class – Represents “class-wide” information Property of the class, not of an object of the class – Initialized once in the class/15 Rational numbers in Python Strange rounding-off errors: Create class for representing rational numbers by storing numerator and denominator >>> 2/3.0 0.6666666666666663 >>> 2/6.0 0.3333333333333331 >>> 5/6.0 0.8333333333333337 16 Rational numbers rational./

##### Class and Objects.

class Rational { friend ostream& operator<< (ostream&, const Rational&); friend istream& operator>> (istream&, Rational&); public: Rational (int n = 0, int d = 1); private: int numerator; int denominator; }; Example (Cont ..) ostream& operator<< (ostream &out, const Rational &r) { out << r.numerator << "/" << r.denominator; return out; } istream& operator>> (istream &in, Rational &r) // complete the code main() Rational rObj; cout << "Enter a rational number like 2/9: "; cin >> rObj; cout << "The rational/

##### The end is near 6 days of class left Final Exam Tuesday, December 14 th, 2-4 Decimals Ratio and Proportion Percents Problem Solving.

9.00001; 0.75 Irrational numbers A number that is not rational is called irrational. A decimal like 3.5655655565555655556… is not rational because although there is a pattern, it does not repeat. It is an irrational number. Compare this to 3.556556556556556556… It is rational because 556 repeats. It is a rational number/to find the product. Standard Algorithm for Multiplying Decimals Why do we do what we do? Multiply 2.1 × 1.3 Explain the algorithm. Dividing Decimal Numbers What model should we use? Dividing/

##### JTextArea formatting text areas. Using JTextArea JTextArea class is found in the javax.swing package. Creates an text area that can process the escape.

] Display the data Sample of program import java.awt.Container; import javax.swing.*; public class lab91 extends JApplet { double[] numbers; String output=""; public void init() { numbers = new double[9]; for (int i = 0; i < 9; i++) { numbers[i] = Double.parseDouble(JOptionPane.showInputDialog( "Enter a floating-point value" )); } for (int i = 0; i < 9; i++) { output += "number" + (i + 1) +": "+numbers[i]+" "; } JTextArea outputArea = new JTextArea(150, 300); outputArea.setText( output); Container container/

##### The end is near 5 days of class left Final Exam Tuesday, May 11 th, 11-1 Decimals Ratio and Proportion Percents.

.6666…; 0.727272… Terminating decimals: 4.8; 9.00001; 0.75 Irrational numbers A number that is not rational is called irrational. A decimal like 3.5655655565555655556… is not rational because although there is a pattern, it does not repeat. It is an irrational number. Compare this to 3.556556556556556556… It is rational because 556 repeats. It is a rational number. Comparing Decimals When are decimals equal? 3.56/

##### 1 Input/Output Stream Lesson #10 Note: CIS 601 notes were originally developed by H. Zhu for NJIT DL Program. The notes were subsequently revised by M.

<<(long); ostream& operator<<(double);... 6 Output of User-Defined Types #include class rational { int num, den; public: rational(int n=0, int d=1) { num=n; den = d/number of characters read by the last input operation 32 #include void main() {char v[20]; int n; cin.read( v, 10); n = cin.gcount() ; cout < >dec >>n; cin >>hex >>m; cout< > ws >> x; cout << tab <<"x = "<< tab << x << ENDL; }//ex10-9.cpp 41 How Does it Work? class/iostream.h u strstream.h//strstrea.h for VC++ 80 Types of ostrstream Objects/

##### Decimals and place value

.6666…; 0.727272… Terminating decimals: 4.8; 9.00001; 0.75 Irrational numbers A number that is not rational is called irrational. A decimal like 3.5655655565555655556… is not rational because although there is a pattern, it does not repeat. It is an irrational number. Compare this to 3.556556556556556556… It is rational because 556 repeats. It is a rational number. Comparing Decimals When are decimals equal? 3.56/

##### Page 1 R Copyright © 1997 by Rational Software Corporation Analysis and Design with UML.

Rational Software Corporation Multiple Systems Visual Modeling Promotes Reuse Reusable Components Page 9 R Copyright © 1997 by Rational Software Corporation What is the UML? UML stands for /Rational Software Corporation Multiplicity and Navigation Multiplicity defines how many objects participate in a relationships – Multiplicity is the number of instances of one class related to ONE instance of the other classFor each association and aggregation, there are two multiplicity decisions to make: one for/

##### Introduction to Rational Rose 1 Rational Rose Tutorial Anis Yousefi Teaching Assistant SE3KO4 / SE3MO4 Software Development for Computer and Electrical.

– some of these terms are ‘used’ interchangeably… E.g. Design model contains class diagrams, sequence diagrams, and a number of others…. Diagrams: means by which we view of the system. Different building blocks (model elements) for different types. E.g.: classes, interfaces, collaborations, components, nodes, dependencies, generalizations, and associations. Introduction to Rational Rose 17 Views Just as there are many views of a house under/

##### OverviewKindergartenEvidence:First GradeEvidence:Second GradeEvidence: Counting and Cardinality Know number names and the count sequence. (K.CC.A) 1.Count.

whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). (6.NS.B.4) (DOK 1) Apply and extend previous understandings of numbers to the system of rational numbers. (6.NS.C) 5.Understand that positive and negative numbers are/ Energy transformations Conservation of energy “Conservation of energy and increase in disorder” is an essential concept of a world-class secondary science curriculum. Included in “conservation of energy and increase in disorder” is the following content: The total /

##### Splash Screen. Chapter Menu Lesson 2-1Lesson 2-1Rational Numbers Lesson 2-2Lesson 2-2Comparing and Ordering Rational Numbers Lesson 2-3Lesson 2-3Multiplying.

Unlike Fractions Lesson 2-7Lesson 2-7Solving Equations with Rational Numbers Lesson 2-8Lesson 2-8Problem-Solving Investigation: Look for a Pattern Lesson 2-9Lesson 2-9Powers and Exponents /0.182 D.0.252 SCHOOL In Mrs. Townley’s eighth grade science class, 4 out of 22 students did not turn in their homework. Find the/ Lesson 9 Ex3 Evaluate Powers Evaluate 9 5. 9 5 = 9999 ● 9Definition of exponents Answer: 59,049 = 59,049Simplify. Check using a calculator. 9 5 59049 ENTER 1.A 2.B 3.C 4.D Lesson 9 CYP3/

##### 資訊科學數學 8 : Proof Strategy, Number and Orders 陳光琦助理教授 (Kuang-Chi Chen)

{j, k} ≠ {l, m}. Proof: Consider n = 1729, j = 9, k = 10, l = 1, m = 12. Now just check that the equalities hold. Another Constructive Existence Proof Theorem: For any integer n>0, there exists a sequence of n consecutive composite integers. - Same statement/intelligent student in the class, and Y≠X. Therefore, the premises do not imply the conclusion. Therefore, the premises do not imply the conclusion. Example : Q3 Q3: Prove that the sum of a rational number and an irrational number is always irrational. /

##### Elementary Algebra Exam 1 Material. Familiar Sets of Numbers Natural numbers –Numbers used in counting: 1, 2, 3, … (Does not include zero) Whole numbers.

our next class meeting Averaging Real Numbers To average a set of real numbers we add all the numbers and then divide by the number of numbers in the set Find the average of the following set of numbers:. Divisibility A real number is divisible by another if the division has no remainder On the following slides are tests for divisibility by all the numbers between 2 and 9, except for 7/

##### Operations with Radicals Lesson 13.3. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection.

in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to use properties of rational and irrational numbers to /properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations. Like Radicals… Two radical expressions are like radicals if they have the same radicand. For instance, /5) 2√6 + 10√18 2√6 + 10√9∙2 2√6 + 30√2 3√24 - 15√8 3√(46) - 15√(42) (32)√6 - 152√2 6√/

##### 2.1 and 2.2: RATIONAL NUMBERS. Main Idea/Vocabulary rational number terminating decimal repeating decimal bar notation Express rational numbers as decimals.

C 4.D Example 2 A.5.1 B.5.15 C.5.2 D.5.9 Example 3 AGRICULTURE A farmer lost the fruit on 8 of 15 orange trees because /148 C.0.182 D.0.252 SCHOOL In Mrs. Townley’s eighth grade science class, 4 out of 22 students did not turn in their homework. Find the fraction /3 CHEMISTRY The values for the approximate densities of various substances are shown in the table. Order the densities from least to greatest. Order Rational Numbers Write each fraction as a decimal. Example 3 Order Rational Numbers Answer: From the/

##### Page 1  Copyright © 1997 by Rational Software Corporation Computer System Business Process Order Item Ship via “ Modeling captures essential parts of.

Page 9  Copyright © 1997 by Rational Software Corporation Putting the UML to Work The ESU University wants to computerize their registration system – The Registrar sets up the curriculum for a/Rational Software Corporation Multiplicity and Navigation Multiplicity defines how many objects participate in a relationships – Multiplicity is the number of instances of one class related to ONE instance of the other classFor each association and aggregation, there are two multiplicity decisions to make: one for/

##### Page 1 R Copyright © 1998 by Rational Software Corporation Visual Modeling and the UML.

(StudentInfo) name tenureStatus ScheduleAlgorithm Page 32 R Copyright © 1998 by Rational Software Corporation Multiplicity and Navigation Multiplicity defines how many objects participate in a relationships – Multiplicity is the number of instances of one class related to ONE instance of the other classFor each association and aggregation, there are two multiplicity decisions to make: one for each end of the relationship Although associations and aggregations are/

##### CS220 Programming Principles 프로그래밍의 이해 2002 년 가을학기 Class 8 한 태숙.

(define (angle z) (cdr z)) 9 Tagged Data n In order to support both types of complex numbers we need to be able to guarantee that,/number scheme-number) (lambda (x y) (tag (* x y)))) 40 (put ’div ’(scheme-number scheme-number) (lambda (x y) (tag (/ x y)))) (put ’make ’scheme-number (lambda (x) (tag x))) ’done) ;; External constructor for ordinary numbers: ;; Sch-Num --> Number (define (make-scheme-number n) ((get ’make ’scheme-number) n)) 41 Rational Number - generic number arith. (define (install-rational/

##### Chapter 12 More on Classes. "The Practice of Computing Using Python", Punch & Enbody, Copyright © 2013 Pearson Education, Inc. The three OOP factors Remember,

9: Do the right thing A new class should be consistent with the rules of the language. It should respond to standard messages, it should behave properly with typical functions (assuming the type allows that kind of call). "The Practice of Computing Using Python", Punch & Enbody, Copyright © 2013 Pearson Education, Inc. An example Consider a Rational number class/ Education, Inc. __radd__ vs __add__ 1 + r1 try 1.__add__(r1), failure look for an __radd__ if it exists, remap 1 + r1 r1.__radd__(1) "The Practice /

##### OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 1 Building Analysis Classes.

Rational Software, all rights reserved 9 VOPC – more on last slide…  The generalization relationship has been shown because it is important to understand the relationship between the two new classes, ScheduleOfferingInfo and PrimaryScheduleOfferingInfo.  The PrimaryScheduleOfferingInfo class contains information about a primary CourseOffering that is schedule-specific.  For/ 1998-1999 Rational Software, all rights reserved 14 ClassName > Attribute : Type = InitValue CourseOffering > number :String=“100” /

##### 1-3 REAL NUMBERS AND THE NUMBER LINE I Can: - classify, graph, and compare real numbers. - find and estimate square roots.

Perfect Square  The square of an integer  For this class, you are required to memorize all perfect squares from /number is -4.5669? rational #4 Give an example of a whole number that isn’t positive. REAL NUMBERSRational numbers and irrational numbers form the set of real numbers.  Subsets of real numbers:  Natural  Whole  Integer  Rational  Irrational Inequalities An inequality is a mathematical sentence comparing the values of two expressions using an inequality symbol. 012345678-8-7-6-5-4-3-2-9/

##### Introduction to Rational Rose 2000 v6.5 Copyright © 1999 Rational Software, all rights reserved 1 Rational Rose 2000 Class Diagrams.

moment and review our preferred practices. Introduction to Rational Rose 2000 v6.5 Copyright © 1999 Rational Software, all rights reserved 23 Preferred Practices  Class Design  Relationships Generalization  Use for “is a” relationships.  Don’t use simply to make definitions visible, except for > classes. Aggregation  Use for “part of” relationships.  Don’t use in place of dependency between loosely coupled classes. Navigability  Reduce bi-directional to unidirectional relationships, where/

##### Rational Requirements Management with Use Cases v5.5 Copyright © 1998-2000 Rational Software, all rights reserved 1 Requirements Management with Use Cases.

Points 7. Relationships 8. Use-Case Diagrams 9. Other Diagrams/enclosures Use-Case Report: Template The Use-Case / Number and name sections to simplify reviewing Remember the description is for people to read, not for computers Rational Requirements Management with Use Cases v5.5 Copyright © 1998-2000 Rational Software/ Rational Requirements Management with Use Cases v5.5 Copyright © 1998-2000 Rational Software, all rights reserved 51 Exercise: Non-Functional Requirements  For your class /

##### R Copyright © 1996 by Rational Software Corporation Rose for Apex, v. 4.0, p. 1 class boy { private: int age; public: study(); } Subsystem & C++ Code Generation.

Rational Software Corporation Rose for Apex, v. 4.0, p. 8 Creating Subsystems & Views R Copyright © 1996 by Rational Software Corporation Rose for Apex, v. 4.0, p. 9 Creating New View R Copyright © 1996 by Rational Software Corporation Rose for Apex, v. 4.0, p. 10 Step 3: Select the Classes/ The default number of errors is set to 30 R Copyright © 1996 by Rational Software Corporation Rose for Apex, v. 4.0, p. 12 Error Limit (Model Property) R Copyright © 1996 by Rational Software Corporation Rose for Apex, v/

##### Page 1 R Copyright © 1997 by Rational Software Corporation Analysis and Design with UML Presentation was downloaded (and is available for free) from Rational.

that must interact with the system under development StudentRegistrarProfessorBilling System Page 9 R Copyright © 1997 by Rational Software Corporation Use Cases A use case is a pattern of /Rational Software Corporation Multiplicity and Navigation Multiplicity defines how many objects participate in a relationships – Multiplicity is the number of instances of one class related to ONE instance of the other classFor each association and aggregation, there are two multiplicity decisions to make: one for/

##### Real Numbers Miss Johnson’s 8 th Grade Math Class Standard 8.NS.1.

Class Standard 8.NS.1 Menu RATIONAL NUMBERSIRRATIONAL NUMBERS MULTIPLYING IRRATIONAL NUMBERS TERMINATING VS. REPEATING TERMINATING DECIMAL QUIZ Rational Numbers A rational number is any real number that can be expressed as the quotient or fraction of two integer Example 1.5 is a rational number because 1.5= 3/2 It can be written as a fraction More Examples NumberAs a Fraction Rational/ 2 x 11. The number of digits that repeat are referred to as the period of the repeating decimal. For example, thirds have a /

##### © 2003 Wadsworth Publishing Co. Chapter 5 The Development of Rational Choice Theory Criminology 8 th edition Larry J. Siegel.

a matter of “rational choice?” In order for behavior to be rational - must this behavior/is not limited by class or other social variables. STRENGTHS/number of motivated criminals. The strength of this approach is that it can explain fluctuations in crime and delinquency rates and shows how victim behavior can influence criminal choices. Routine activities provides a macro view of crime, rational/9. Target removal 10. Identifying property 11. Reducing temptation 12. Denying benefits Reducing Anticipated Rewards 9/

##### AGENDA: PRE-CALCULUS HONORS. MON. DAY 47; NOV. 02, 2015; (2 nd 9- WEEKS) ZEROS OF POLYNOMIAL FUNCTIONS; LEARNING OBJECTIVES: SWBAT: Use Descartes’ Rule.

, 45, 47, 49, 50, 61, 70, 72, 78. HOME LEARNING: Review for test on Friday 11/20/15. Go to review section of your textbook. AGENDA: PRE-CALCULUS HONORS. DAY 60; FRI. NOV.20, 2015; (2 nd 9- WEEKS) CHAPTER TEST: POLYNOMIAL AND RATIONAL FUNCTIONS LEARNING OBJECTIVES; SWBAT:- Solve complex numbers, quadratic functions, rational functions and direct, inverse, joint and combination variation problems. ACTIVITIES: Chapter/

##### Page 1  Copyright © 1997 by Rational Software Corporation Putting the UML to Work The ESU University wants to computerize their registration system –

() addStudent(StudentInfo) name tenureStatus ScheduleAlgorithm Page 15  Copyright © 1997 by Rational Software Corporation Multiplicity and Navigation Multiplicity defines how many objects participate in a relationships – Multiplicity is the number of instances of one class related to ONE instance of the other classFor each association and aggregation, there are two multiplicity decisions to make: one for each end of the relationship Although associations and aggregations are/

##### Object Oriented Analysis and Design using the UML Use-Case Analysis Adapted by Dr. Spiegel from Slides Provided by Rational Software.

For each use-case realization  Find Classes from Use-Case Behavior  Distribute Use-Case Behavior to ClassesFor each resulting analysis class  Describe Responsibilities  Describe Attributes and Associations  Qualify Analysis Mechanisms  Unify Analysis Classes  Checkpoints Object Oriented Analysis and Design Using the UML v2000 Copyright © 2000 Rational Software, all rights reserved 9/ Message Numbering Object Oriented Analysis and Design Using the UML v2000 Copyright © 2000 Rational Software,/

##### OOAD Using the UML - Describe Concurrency, v 4.0 Copyright  1994-1998 Rational Software, all rights reserved 1 R Thread Process X Thread Process ZProcess.

stimuli  Define a separate server thread of control for each service  Reduce number of threads to what can be supported OOAD Using the UML - Describe Concurrency, v 4.0 Copyright  1994-1998 Rational Software, all rights reserved 23 R  Class diagrams  Active classes as processes  Composition relationships from processes to classes  Composition relationships from processes to subsystem interfaces Class Name Process Name > Interface Name Process Name > Process/

##### OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 1 Use Case Analysis – continued Control Classes.

4.2 Copyright  1998-1999 Rational Software, all rights reserved 9 Course Catalog SystemRegister for CoursesStudent > RegistrationController Example: Finding Control Classes  Recommend: Identify one control class per use case Each control class is responsible for orchestrating/controlling the processing that implements /incorrect user input)  Examples of optional flows include the following: The actor decides-from a number of options-what the system is to do next The subsequent flow of events depends on /

##### ® IBM Software Group © 2013 IBM Corporation Rational Developer for System z – Distance Learning Setup Module 1 – Installing and configuring RDz Workstation.

resources for both: –RDz –COBOL 9 Welcome to Enterprise COBOL and Rational Developer for System z  COBOL runs the worlds enterprises  RDz is the way we make COBOL development easy IBM z/10 Rational Developer for System z 10 Why COBOL? Lets look at some numbers… /) specific product features to install. These are the defaults  … and they’ll work fine for the Distance Learning class  Note that CA Endevor is optional for this class Next >  Click Next > 28  Installation Process – 10 of 12 You can choose/

##### ® IBM Software Group © 2013 IBM Corporation Updated: April, 2013 Jon Sayles RDz Technical Enablement Introduction to Rational Developer.

the on-demand business logo, Rational, the Rational logo, and other IBM Rational products and services are trademarks or/And Datasets TransferSourceFiles 137 Workshop –  Workshop – Allocate PDS (Libraries) for Class  Using RDz it is simple to allocate a new PDS:  Right/ –Picture string –Non-numeric literal –Comment –Numeric literal –Sequence number OK  Click OK   If you dont like your changes/ Find all variables that end in "data" PIC.9|PIC 9( Find all numeric variable declarations  Expression See Notes/

##### Introduction to Rational Functions Dr. Shildneck Fall, 2014.

numbers except zero The graph has two symmetrical parts, called branches. For each point (x, y) on one branch, there is a corresponding point (-x, -y) on the other branch. The graph of On Your Calculator… Graph Describe what happens when… a > 1 in a < 0 in All rational/through the points, using the asymptotes as guidelines. Example 2 Graph: Real Life Uses The Junior class is sponsoring a dinner. The cost of catering the dinner is \$9.95 per person plus a delivery charge of \$18. (a)Write a model that gives the/

##### Complex Numbers, Quadratics and Rational Expressions Mathketball Review Team Test tomorrow – Thursday March 3rd.

post this power point to my FIS class files so you can use it to study #1 – Simplifying Complex Numbers (a+bi form) Simplify the following /Rational Expressions Multiply and then simplify the following rational expression. You may want to factor first. Solution #7 #8 – Adding/Subtracting Rational Expressions Add and subtract the following expressions Find the LCD (least common denominator 1 st ) Solution #8 #9 – Simplifying Rational Expressions Anyone can shoot for this problem. DOUBLE points! Solution #9/

##### COS 312 DAY 6 Tony Gauvin. Ch 1 -2 Agenda Questions? Assignment 2 Posted – Due Feb 22 prior to class Assignment 3 posted – March 5 Prior to class Capstones.

the same class as a parameter For example, the concat method of the String class takes as a parameter another String object str3 = str1.concat(str2); This drives home the idea that the service is being requested from a particular object Java Foundations, 3rd Edition, Lewis/DePasquale/Chase5 - 75 Dependency The following example defines a class called RationalNumber to represent a rational number A rational number is a/

##### 1-2 Irrational Numbers and Square Roots. Geogebra Finding square roots of perfect squares Estimating a square root Comparing square roots Surface area.

600 rounded to the nearest tenth is 24.5. The math class drops a small ball from the top of a stairwell. They/ to fall. Exploring Square Roots and Irrational Numbers LESSON 1-2 48 = 16t 2 Substitute 48 for d. d = 16t 2 Use the /number as rational or irrational. Explain. Exploring Square Roots and Irrational Numbers LESSON 1-2 d. 6.36366366636666... Irrational; the decimal does not terminate or repeat. Rational; the decimal repeats.a. –9.3333 b. 4 7979 Rational; the number can be written as the ratio. 43 9/

##### © 2004 Pearson Addison-Wesley. All rights reserved November 2, 2007 Class Relationships ComS 207: Programming I (in Java) Iowa State University, FALL 2007.

4:30-6:30pm Also see this page (for large classes like ComS 207): http://www.iastate.edu/~registrar/exams/ Addison-Wesley. All rights reserved Rule #1: 1..9 must be in each row © 2004 Pearson Addison-Wesley/class called Rational to represent a rational number A rational number is a value that can be represented as the ratio of two integers Some methods of the Rational class accept another Rational object as a parameter See RationalTester.java (page 297)RationalTester.java See Rational.java (page 299)Rational/

##### Five-Minute Review 1.What are local/instance/class variables? What about constants? 2.What is an array? 3.How do we locally declare an array of 5 integers?

digits: 0 to 9, followed by the letters A through F to indicate the values 10 to 15. The following diagrams show how the number forty-two appears in/G, T (binary/decimal) Initialization to default value for Class var’s Instance var’s Array components Not for local var’s! static data 0000 stack FFFF heap/ calculation. 1/2 + 1/3 + 1/6 = 1 public void run() { Rational a = new Rational(1, 2); Rational b = new Rational(1, 3); Rational c = new Rational(1, 6); Rational sum = a.add(b).add(c); println(a + " + " + b +/

##### Module 2: Introduction to UML

10 to 50. Unification of ideas began in mid 90’s. Rumbaugh joins Booch at Rational ’94 v0.8 draft Unified Method ’95 Jacobson joins Rational ’95 UML v0.9 in June ’96 UML 1.0 offered to OMG in January ’97 UML 1.1/attribute that are actions Identifying attributes Look for information that must be maintained about each class Several nouns rejected as classes, may now become attributes An attribute should generally contain a simple value E.g. string, number Tips about identifying and specifying valid attributes /

##### OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 1/20 Interaction Diagrams.

are related due to the controller’s logic.  Only the CourseCatalogSystem (a boundary class) class interacts with the external legacy Course Catalog System.  Note inclusion of the actors. /Rational Software, all rights reserved 20/20 More on Sequence Diagrams  Sequence diagrams  show the explicit sequence of messages and  are better for real-time specifications and for complex scenarios.  A sequence diagram includes chronological sequences, but does not include object relationships.  Sequence numbers/

##### AGENDA: PRE-CALCULUS HONORS. MON. DAY 48; 10/27/13 (2 nd 9-WEEK LEARNING OBJECTIVES; SWBAT:- Find the domains of rational functions. Identify vertical.

LEARNING: Complete review worksheet for TEST on THURSDAY (11/06/14); AGENDA: PRE-CALCULUS HONORS. THUR. DAY 55; 11/06/14 (2 nd 9-WEEK CHAPTER 2 TEST ON POLYNOMIALS & RATIONAL FUNCTIONS. LEARNING OBJECTIVES; SWBAT: Perform operations with square roots of negative numbers, solve problems involving quadratic/Discuss Pg. 501 # 74 – 83. C/W: Pg. 513 # 1 – 22 (all) HOME LEARNING: Complete class work. Go to http://killian.dadeschools.net and print & continue to work on Chapter 4.2 – 4.4.http://killian.dadeschools.net [Due/

##### J. Scott Hawker 2004-09-23p. 1 Material © IBM Rational Software Use-Case Analysis Analyze the requirements to discover what the system objects are These.

Software Use-Case Analysis - Steps  Supplement the Use-Case Description  For each use-case realization  Find classes from use-case behavior  Distribute use-case behavior to classesFor each resulting analysis class  Describe responsibilities  Describe attributes and associations  Qualify architectural analysis mechanisms  Unify analysis classes  Checkpoints Next J. Scott Hawker 2004-09-23p. 9 Material © IBM Rational Software Analysis Classes: A First Step Towards Executables Use-CasesAnalysis/

##### Jon Sayles, IBM Software Group, Rational EcoSystems Team

the IBM logo, the on-demand business logo, Rational, the Rational logo, and other IBM Rational products and services are trademarks or registered trademarks of/classes, comprising class object definitions and object definitions. The ability to define data encapsulated inside class objects and objects. The ability to define methods for class/special) 9 Only numeric data - digits (0 9) V Part of numeric definition. Assumed decimal point S Part of numeric definition. Sign – allows for negative numbers COBOL /

##### OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 1 Interaction Diagrams.

& its class are separated by a colon & underlined. Reflexive Message Object Lifeline 1.1: PerformAnother Responsibility The Anatomy of Sequence Diagrams Hierarchical Message Numbering A Sequence / 1998-1999 Rational Software, all rights reserved 9 Example: Sequence Diagram (cont.) :CourseOffering : Student : RegisterForCoursesForm : RegistrationController : Schedule : Student : PrimaryScheduleOfferingInfo Repeat for all primary course offerings. An attempt is made to register the student for all selected/

##### OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 1 Object Oriented Analysis and Design Using.

enough detail. OOAD Using the UML - Use-Case Analysis, v 4.2 Copyright  1998-1999 Rational Software, all rights reserved 9  Supplement the Use-Case Description  For each use-case realization  Find Classes from Use-Case Behavior  May be easier now to identify our candidate analysis classes for the system (candidate means first cut; possible classes) We should be able to identify a set of candidate analysis/

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