The document discusses several properties of real numbers including the distributive property, identity property, zero property, inverse property, commutative property, and associative property. Each property is defined and examples are provided to illustrate how it works in algebra. Real-life analogies are also given to help explain the conceptual meaning of each property.
This presentation shows many ways that Integers (positive and negative numbers) are used in the real world.
To obtain a PowerPoint format download of this presentation, go to the following page:
http://passyworldofmathematics.com/pwerpoints/
This document discusses integers and the four basic operations that can be performed on them - addition, subtraction, multiplication, and division. It defines an integer as a positive or negative whole number including 0. It provides rules for performing each operation, such as the product of two integers with the same sign is positive and with different signs is negative for multiplication. Examples are worked through for each operation to demonstrate how to apply the rules.
This document discusses various identity and equality properties in mathematics. It defines the additive identity property as the sum of any number and 0 being equal to the number. The multiplicative identity property is defined as the product of any number and 1 being equal to the number. The multiplicative property of zero states that the product of any number and 0 is equal to 0. The reflexive, symmetric, transitive, and substitution properties of equality are also defined. Examples are provided to illustrate each property.
Math 7 lesson 11 properties of real numbersAriel Gilbuena
油
At the end of the lesson, the learner should be able to:
recall the different properties of real numbers
write equivalent statements involving variables using the properties of real numbers
08.29.2017 Daily Lesson Properities of Ratioanl Numbers.pptxArianeSantiago7
油
1. This document contains an agenda for a math lesson on rational numbers including properties of rational numbers. The agenda includes a ticket in the door and out with math problems, reviewing previous lessons, and a current lesson on applying properties of rational numbers.
2. The document defines rational numbers as real numbers that can be written as a ratio of two integers and may be terminating or repeating decimals. It then explains four properties - distributive, commutative, associative, and identity properties of one and zero - and provides examples of each.
3. The exit slip asks students to name properties illustrated in equations and simplify expressions using properties, justifying each step.
The document discusses several fundamental concepts of algebra including:
1. Different types of numbers such as integers, rational numbers, and irrational numbers.
2. Properties of operations like addition, subtraction, multiplication, and division.
3. Exponent rules for simplifying expressions with exponents like multiplying terms with the same base.
This document provides a summary of an introductory presentation on advanced JavaScript concepts including closures, prototypes, inheritance, and more. The presentation covers object literals and arrays, functions as objects, constructors and the this keyword, prototypes and the prototype chain, classical and prototypal inheritance, scope, and closures. Examples are provided to demonstrate each concept.
The document discusses properties of real numbers including commutative, associative, identity, zero, and multiplication properties of addition and multiplication. These properties allow expressions to be rewritten and compared, and are useful rules for solving problems using mental math. Examples are provided to demonstrate applying properties like commutative and associative to solve problems.
The document discusses various mathematical properties including:
- Commutative and associative properties of addition and multiplication which allow changing the order or grouping of terms.
- Identity properties which show that adding or multiplying a number by its identity (0 for addition, 1 for multiplication) does not change the number.
- The opposite property which involves changing all addition signs to subtraction or multiplying the entire expression by -1.
- The distributive property which allows multiplying a number by the terms inside parentheses.
- Properties of equality including reflexive, symmetric, transitive, and substitution properties which define when expressions can be said to be equal.
The document discusses grades being posted online and not answering questions about grades during class time. It states that grades reflect effort, not ability or intelligence. Notebooks will be graded on organization, completeness, and neatness. Students are advised to focus on learning the material rather than worrying about grades.
Quiz JavaScript Objects Learn more about JavaScriptLaurence Svekis
油
This document provides a guide to mastering JavaScript objects through a series of questions and answers. It covers topics such as creating and accessing objects, adding and deleting properties, copying and merging objects, and making objects immutable. Each question is accompanied by sample code to demonstrate the concept. The goal is to enhance understanding of objects, a key concept in JavaScript.
The document discusses various features of CoffeeScript including:
- Pattern matching for variable swaps, declarations, and object matching
- OOP styles using classes, inheritance, and mixins
- Building CoffeeScript projects and integrating with asset managers
- References for further CoffeeScript learning
This document discusses three properties of addition: the associative property, commutative property, and identity property. The associative property states that the grouping of addends does not change the sum. The commutative property says that the order of addends does not change the sum. The identity property indicates that adding zero to any number results in the original number. Examples are provided to illustrate each property.
Algebraic Properties of Matrix Operations EFREN ARCHIDE
油
This document summarizes key algebraic properties of matrix operations that are analogous to properties of real numbers. It describes the commutative, associative, identity, and inverse properties of matrix addition and multiplication. It also covers the distributive, scalar, and transpose properties as they relate to matrix operations. Examples are provided to illustrate the properties. The document serves to establish the foundational algebraic structure of matrices and their operations.
The document discusses the five properties of multiplication: the commutative property, the associative property, the identity property, the zero property, and the distributive property. It provides examples and explanations of each property using words and mathematical expressions. For example, it explains that the commutative property states that a b = b a, and the identity property indicates that any number multiplied by 1 remains the same number.
The document discusses several key properties related to identity and equality in mathematics. It defines:
- The additive identity as 0, since the sum of any number and 0 is equal to the number.
- The multiplicative identity as 1, since the product of any number and 1 is equal to the number.
- The multiplicative property of zero, where the product of any number and 0 is equal to 0.
- Multiplicative inverses or reciprocals as two numbers whose product is 1. Zero has no reciprocal.
It also discusses properties of equality like reflexive, symmetric, and transitive properties and using substitution.
The document discusses priority queues implemented using heaps. It describes a PriorityQueue class that uses a Heap to store Event objects. The PriorityQueue allows inserting new Events into the heap if not full, and removing the minimum Event from the heap. It also provides methods to check if the queue is full and get the queue length. Finding the k-th smallest element from a list using a heap is also discussed.
This document contains a 15 question quiz about properties of mathematics, specifically focusing on properties of multiplication and their applications. The quiz covers topics like the associative property, commutative property, identity property, and zero property. It tests understanding of these properties through examples of equations using multiplication and requires identifying the property being demonstrated or applying properties to rewrite expressions.
Esoft Metro Campus - Diploma in Web Engineering - (Module V) Programming with JavaScript
(Template - Virtusa Corporate)
Contents:
Introduction to JavaScript
What JavaScript Can Do?
Script tag in HTML
Noscript tag in HTML
Your First JavaScript Program
JavaScript Placement in HTML File
JavaScript Syntax
JavaScript Data Types
JavaScript Variables
JavaScript Identifiers
Arithmetic Operators
String Concatenation Operators
Assignment Operators
Comparison Operators
Logical Operators
Bitwise Operators
If Statement
If Else Statement
If Else if Else Statement
Switch Statement
The ? Operator
While Loop
Do While Loop
For Loop
Forin Loop
break Statement
continue Statement
Arrays
Functions
JavaScript Objects
JavaScript Scope
Strings
Regular Expressions
JavaScript Numbers
Math Object
Date and Time
JavaScript Events
Dialog Boxes
Error Handling in JavaScript
JavaScript Forms Validation
JavaScript HTML DOM
JavaScript BOM
The document discusses a talk titled "The Dark Side of Ruby". The talk will cover how Ruby is an awesome programming language but also discuss some weirdness, gotchas, and ah-ha moments related to Ruby. It will explore infinity in Ruby, base conversions, splat expansion, hashes and arrays, calling procs, syntax, case statements, equality comparisons, object IDs and Fixnums, and currying.
This document contains a lesson on properties of real numbers from a Holt Algebra 2 textbook. It includes examples and explanations of key properties such as additive identity, multiplicative identity, additive inverse, multiplicative inverse, closure, commutativity, associativity, and distributivity. Students are given practice identifying which properties are demonstrated in equations and applying properties to find percentages and inverses of numbers.
The document discusses basic object-oriented concepts in Java such as classes, objects, inheritance, and polymorphism. Some key points include:
- An object contains both data fields that represent its state and methods that operate on that data.
- A class defines the fields and methods common to all objects of that type. An object is an instance of a class.
- Inheritance allows subclasses to inherit and extend the functionality of parent classes. Subclass objects inherit all fields and methods of their parent classes.
- Methods can be overridden in subclasses to allow polymorphic behavior depending on an object's type. Sending a message to an object results in the execution of the corresponding method definition for that object's class.
This document discusses basic object-oriented programming concepts. It explains that an object contains both data and methods that manipulate that data. An object represents a real-world entity and has state represented by its data fields. Classes describe objects and act as templates for creating multiple similar objects. Objects inherit characteristics from their classes and can override methods. Constructors are used to create and initialize new objects. Access control determines which parts of a class are visible and accessible to other classes.
The document discusses object-oriented programming concepts in PHP, including classes, objects, methods, properties, inheritance, and polymorphism. It provides examples of defining classes and using them to instantiate objects. Key concepts covered are class definitions, creating object instances, accessing object properties and methods, inheritance between classes, and overriding methods in child classes.
The document discusses object-oriented programming concepts in PHP, including classes, objects, methods, properties, inheritance, and polymorphism. It provides examples of defining classes and using them to instantiate objects. Key concepts covered are class definitions, creating object instances, accessing object properties and methods, and extending classes to create subclass hierarchies.
The document outlines the math and financial literacy curriculum for Minarets High School's semester one, including tutorials, surveys to gather student feedback, preparing for standards-based assessments, using math stations in class, connecting to real-world math projects, and websites used as educational resources. Tutoring options are available after school and online, and students can stay connected through email.
The document discusses different types of real numbers including natural numbers which are positive but do not include zero, whole numbers which include positive numbers and zero, integers which include positive, negative and zero, rational numbers which can be expressed as a ratio of two integers, and irrational numbers which cannot be expressed as a ratio of two integers.
The document discusses various mathematical properties including:
- Commutative and associative properties of addition and multiplication which allow changing the order or grouping of terms.
- Identity properties which show that adding or multiplying a number by its identity (0 for addition, 1 for multiplication) does not change the number.
- The opposite property which involves changing all addition signs to subtraction or multiplying the entire expression by -1.
- The distributive property which allows multiplying a number by the terms inside parentheses.
- Properties of equality including reflexive, symmetric, transitive, and substitution properties which define when expressions can be said to be equal.
The document discusses grades being posted online and not answering questions about grades during class time. It states that grades reflect effort, not ability or intelligence. Notebooks will be graded on organization, completeness, and neatness. Students are advised to focus on learning the material rather than worrying about grades.
Quiz JavaScript Objects Learn more about JavaScriptLaurence Svekis
油
This document provides a guide to mastering JavaScript objects through a series of questions and answers. It covers topics such as creating and accessing objects, adding and deleting properties, copying and merging objects, and making objects immutable. Each question is accompanied by sample code to demonstrate the concept. The goal is to enhance understanding of objects, a key concept in JavaScript.
The document discusses various features of CoffeeScript including:
- Pattern matching for variable swaps, declarations, and object matching
- OOP styles using classes, inheritance, and mixins
- Building CoffeeScript projects and integrating with asset managers
- References for further CoffeeScript learning
This document discusses three properties of addition: the associative property, commutative property, and identity property. The associative property states that the grouping of addends does not change the sum. The commutative property says that the order of addends does not change the sum. The identity property indicates that adding zero to any number results in the original number. Examples are provided to illustrate each property.
Algebraic Properties of Matrix Operations EFREN ARCHIDE
油
This document summarizes key algebraic properties of matrix operations that are analogous to properties of real numbers. It describes the commutative, associative, identity, and inverse properties of matrix addition and multiplication. It also covers the distributive, scalar, and transpose properties as they relate to matrix operations. Examples are provided to illustrate the properties. The document serves to establish the foundational algebraic structure of matrices and their operations.
The document discusses the five properties of multiplication: the commutative property, the associative property, the identity property, the zero property, and the distributive property. It provides examples and explanations of each property using words and mathematical expressions. For example, it explains that the commutative property states that a b = b a, and the identity property indicates that any number multiplied by 1 remains the same number.
The document discusses several key properties related to identity and equality in mathematics. It defines:
- The additive identity as 0, since the sum of any number and 0 is equal to the number.
- The multiplicative identity as 1, since the product of any number and 1 is equal to the number.
- The multiplicative property of zero, where the product of any number and 0 is equal to 0.
- Multiplicative inverses or reciprocals as two numbers whose product is 1. Zero has no reciprocal.
It also discusses properties of equality like reflexive, symmetric, and transitive properties and using substitution.
The document discusses priority queues implemented using heaps. It describes a PriorityQueue class that uses a Heap to store Event objects. The PriorityQueue allows inserting new Events into the heap if not full, and removing the minimum Event from the heap. It also provides methods to check if the queue is full and get the queue length. Finding the k-th smallest element from a list using a heap is also discussed.
This document contains a 15 question quiz about properties of mathematics, specifically focusing on properties of multiplication and their applications. The quiz covers topics like the associative property, commutative property, identity property, and zero property. It tests understanding of these properties through examples of equations using multiplication and requires identifying the property being demonstrated or applying properties to rewrite expressions.
Esoft Metro Campus - Diploma in Web Engineering - (Module V) Programming with JavaScript
(Template - Virtusa Corporate)
Contents:
Introduction to JavaScript
What JavaScript Can Do?
Script tag in HTML
Noscript tag in HTML
Your First JavaScript Program
JavaScript Placement in HTML File
JavaScript Syntax
JavaScript Data Types
JavaScript Variables
JavaScript Identifiers
Arithmetic Operators
String Concatenation Operators
Assignment Operators
Comparison Operators
Logical Operators
Bitwise Operators
If Statement
If Else Statement
If Else if Else Statement
Switch Statement
The ? Operator
While Loop
Do While Loop
For Loop
Forin Loop
break Statement
continue Statement
Arrays
Functions
JavaScript Objects
JavaScript Scope
Strings
Regular Expressions
JavaScript Numbers
Math Object
Date and Time
JavaScript Events
Dialog Boxes
Error Handling in JavaScript
JavaScript Forms Validation
JavaScript HTML DOM
JavaScript BOM
The document discusses a talk titled "The Dark Side of Ruby". The talk will cover how Ruby is an awesome programming language but also discuss some weirdness, gotchas, and ah-ha moments related to Ruby. It will explore infinity in Ruby, base conversions, splat expansion, hashes and arrays, calling procs, syntax, case statements, equality comparisons, object IDs and Fixnums, and currying.
This document contains a lesson on properties of real numbers from a Holt Algebra 2 textbook. It includes examples and explanations of key properties such as additive identity, multiplicative identity, additive inverse, multiplicative inverse, closure, commutativity, associativity, and distributivity. Students are given practice identifying which properties are demonstrated in equations and applying properties to find percentages and inverses of numbers.
The document discusses basic object-oriented concepts in Java such as classes, objects, inheritance, and polymorphism. Some key points include:
- An object contains both data fields that represent its state and methods that operate on that data.
- A class defines the fields and methods common to all objects of that type. An object is an instance of a class.
- Inheritance allows subclasses to inherit and extend the functionality of parent classes. Subclass objects inherit all fields and methods of their parent classes.
- Methods can be overridden in subclasses to allow polymorphic behavior depending on an object's type. Sending a message to an object results in the execution of the corresponding method definition for that object's class.
This document discusses basic object-oriented programming concepts. It explains that an object contains both data and methods that manipulate that data. An object represents a real-world entity and has state represented by its data fields. Classes describe objects and act as templates for creating multiple similar objects. Objects inherit characteristics from their classes and can override methods. Constructors are used to create and initialize new objects. Access control determines which parts of a class are visible and accessible to other classes.
The document discusses object-oriented programming concepts in PHP, including classes, objects, methods, properties, inheritance, and polymorphism. It provides examples of defining classes and using them to instantiate objects. Key concepts covered are class definitions, creating object instances, accessing object properties and methods, inheritance between classes, and overriding methods in child classes.
The document discusses object-oriented programming concepts in PHP, including classes, objects, methods, properties, inheritance, and polymorphism. It provides examples of defining classes and using them to instantiate objects. Key concepts covered are class definitions, creating object instances, accessing object properties and methods, and extending classes to create subclass hierarchies.
The document outlines the math and financial literacy curriculum for Minarets High School's semester one, including tutorials, surveys to gather student feedback, preparing for standards-based assessments, using math stations in class, connecting to real-world math projects, and websites used as educational resources. Tutoring options are available after school and online, and students can stay connected through email.
The document discusses different types of real numbers including natural numbers which are positive but do not include zero, whole numbers which include positive numbers and zero, integers which include positive, negative and zero, rational numbers which can be expressed as a ratio of two integers, and irrational numbers which cannot be expressed as a ratio of two integers.
The document discusses several properties of real numbers including the distributive property, identity property, zero property, inverse property, commutative property, and associative property. Each property is defined and examples are provided to illustrate how it works in mathematics. Real-life analogies are also described to help explain the conceptual meaning of each property.
This document discusses properties of real numbers. It introduces the real number system and closure property, which is the property that the sum or product of two real numbers is also a real number. An example is provided to illustrate the closure property. The document suggests investigating properties of real numbers further and provides websites on the inverse property and property glossaries for additional information.
The document discusses properties of real numbers, including the closure property. It defines the closure property as the result of any arithmetic operation between two real numbers being a real number. An example is provided of addition closing under real numbers. The document suggests investigating properties of real numbers further by completing a slideshow and bibliography. Real-life examples and additional websites exploring properties like the inverse are also mentioned.
Real numbers have properties such as the closure property where the result of any arithmetic operation on real numbers is also a real number, and the commutative property where the order of operands does not change the result. This document discusses investigating properties of real numbers through arithmetic operations and provides websites for further information.
Mate, a short story by Kate Grenvile.pptxLiny Jenifer
油
A powerpoint presentation on the short story Mate by Kate Greenville. This presentation provides information on Kate Greenville, a character list, plot summary and critical analysis of the short story.
Computer Application in Business (commerce)Sudar Sudar
油
The main objectives
1. To introduce the concept of computer and its various parts. 2. To explain the concept of data base management system and Management information system.
3. To provide insight about networking and basics of internet
Recall various terms of computer and its part
Understand the meaning of software, operating system, programming language and its features
Comparing Data Vs Information and its management system Understanding about various concepts of management information system
Explain about networking and elements based on internet
1. Recall the various concepts relating to computer and its various parts
2 Understand the meaning of softwares, operating system etc
3 Understanding the meaning and utility of database management system
4 Evaluate the various aspects of management information system
5 Generating more ideas regarding the use of internet for business purpose
Prelims of Kaun TALHA : a Travel, Architecture, Lifestyle, Heritage and Activism quiz, organized by Conquiztadors, the Quiz society of Sri Venkateswara College under their annual quizzing fest El Dorado 2025.
Information Technology for class X CBSE skill SubjectVEENAKSHI PATHAK
油
These questions are based on cbse booklet for 10th class information technology subject code 402. these questions are sufficient for exam for first lesion. This subject give benefit to students and good marks. if any student weak in one main subject it can replace with these marks.
APM event hosted by the South Wales and West of England Network (SWWE Network)
Speaker: Aalok Sonawala
The SWWE Regional Network were very pleased to welcome Aalok Sonawala, Head of PMO, National Programmes, Rider Levett Bucknall on 26 February, to BAWA for our first face to face event of 2025. Aalok is a member of APMs Thames Valley Regional Network and also speaks to members of APMs PMO Interest Network, which aims to facilitate collaboration and learning, offer unbiased advice and guidance.
Tonight, Aalok planned to discuss the importance of a PMO within project-based organisations, the different types of PMO and their key elements, PMO governance and centres of excellence.
PMOs within an organisation can be centralised, hub and spoke with a central PMO with satellite PMOs globally, or embedded within projects. The appropriate structure will be determined by the specific business needs of the organisation. The PMO sits above PM delivery and the supply chain delivery teams.
For further information about the event please click here.
How to Configure Flexible Working Schedule in Odoo 18 EmployeeCeline George
油
In this slide, well discuss on how to configure flexible working schedule in Odoo 18 Employee module. In Odoo 18, the Employee module offers powerful tools to configure and manage flexible working schedules tailored to your organization's needs.
Database population in Odoo 18 - Odoo slidesCeline George
油
In this slide, well discuss the database population in Odoo 18. In Odoo, performance analysis of the source code is more important. Database population is one of the methods used to analyze the performance of our code.
Useful environment methods in Odoo 18 - Odoo 際際滷sCeline George
油
In this slide well discuss on the useful environment methods in Odoo 18. In Odoo 18, environment methods play a crucial role in simplifying model interactions and enhancing data processing within the ORM framework.
APM People Interest Network Conference 2025
-Autonomy, Teams and Tension: Projects under stress
-Tim Lyons
-The neurological levels of
team-working: Harmony and tensions
With a background in projects spanning more than 40 years, Tim Lyons specialised in the delivery of large, complex, multi-disciplinary programmes for clients including Crossrail, Network Rail, ExxonMobil, Siemens and in patent development. His first career was in broadcasting, where he designed and built commercial radio station studios in Manchester, Cardiff and Bristol, also working as a presenter and programme producer. Tim now writes and presents extensively on matters relating to the human and neurological aspects of projects, including communication, ethics and coaching. He holds a Masters degree in NLP, is an NLP Master Practitioner and International Coach. He is the Deputy Lead for APMs People Interest Network.
Session | The Neurological Levels of Team-working: Harmony and Tensions
Understanding how teams really work at conscious and unconscious levels is critical to a harmonious workplace. This session uncovers what those levels are, how to use them to detect and avoid tensions and how to smooth the management of change by checking you have considered all of them.
The Constitution, Government and Law making bodies .saanidhyapatel09
油
This PowerPoint presentation provides an insightful overview of the Constitution, covering its key principles, features, and significance. It explains the fundamental rights, duties, structure of government, and the importance of constitutional law in governance. Ideal for students, educators, and anyone interested in understanding the foundation of a nations legal framework.
The Constitution, Government and Law making bodies .saanidhyapatel09
油
Adding Subtracting Integers
1. Properties of油 Real Numbers by Mrs. Alvarez's油 Algebra 1 Class Period 4
2. by Katy Prather, Emma Delk and Destanee Stevenson Distributive Property
3. Definition of the Distributive Property The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. The Distributive Property is a way that you multiply one or more terms inside parentheses.
14. The Definition of Zero Property The definition of the zero property of multiplication states that if the product of one or more factors is zero than at least one of the factors is zero. The definition of the zero property of addition is if you add zero and another number you get that number.
15. Example of the Zero Property addition: 油3 + 0 = 3 multiplication: 油3 X 0 = 0
16. Real Life Example of zero property of addition When you look in a mirror you see yourself. It's just like the zero property of addition. Let's say you are a number (4 for example) and you look into a mirror (add to zero). you stay the same, but you are looking at you reflection.(this property is sometimes called the identity property of addition.)
17. Zero Property of Multiplication Anything you multiply to zero gives you... 油 油 油 油油 Z 油 油E 油 油 R 油 油O
20. 油油 油 油 油 What Is inverse property -The inverse of an operation gives the identity. - The inverse property of addition is adding its opposite and getting the identity. 6 + (-6) = 0 -The inverse property of multiplication is multiplying the reciprocal to a number to get the identity. 36 x油 n油 = 36
21. Example of Inverse Property Addition: 5+(-5)=0 Multiplication: 48 x n = 48
23. Works Cited油 "Cool math Pre-Algebra Help Lessons: Properties - The Additive Inverse Property." Cool math .com - An amusement park of math and more! Math lessons, math games, math practice, math fun! Web. 29 Sept. 2009. <http://www.coolmath.com/prealgebra/06-properties/07-properties-additive-inverse-01.htm>.油 "Math Forum: Ask Dr. Math FAQ: Glossary of Properties." The Math Forum @ Drexel University . Web. 29 Sept. 2009. <http://mathforum.org/dr.math/faq/faq.property.glossary.html>.油 Web. 29 Sept. 2009. <http://www.icoachmath.com/SiteMap/DictionaryDefinition.aspx?process=sitemap/inverseproperties&&AspxAutoDetectCookieSupport=1>.油
25. THE DEFINITION 油 油 The commutative property of addition says that we can add numbers in any order. The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result. An operation is commutative if you can change the order of the numbers involved with out changing the results. 油Addition and multiplication are both commutative. subtraction and divition is not commutative.
26. Examples油 油 3+2=2+3 油 45x15=15x45 A+B=B+A C x V=V x C 2-3=3-2 油 It doesn't work for division either油
27. picure slide The communicative property is when the numbers move but the answer stay the same. This is numbers moving on a truck油
28. BIBLIOGRAPHY "Algebra Basics - Properties of Real Numbers - In Depth."油Math.com - World of Math Online. Web. 01 Oct. 2009. <http://www.math.com/school/subject2/lessons/S2U2L1DP.html>. "Commutative property pictures - Search."油Google. Web. 01 Oct. 2009. <http://www.google.com/search?hl=en&source=hp&q=commutative+property+pictures&btnG=Google+Search&aq=f&oq=&aqi=>
30. Definition of the Associative Property Giving an equivalent expression when elements are grouped without change of order, as ( a 油+油 b ) +油 c 油=油 a 油+ ( b 油+油 c ). Your ordered sets of numbers stay the same, the only thing that changes is where the parenthesis go. Also this property is only true for addition and multiplication.油
31. Examples of Associative Property The associative property of addition will involve three or more numbers. 油 For Example (2+5)+4=11or 2+(5+4)=11 The associative property of multiplication, the product is always the same. Example: when we change the factors the product dose not change. (3x2)x4=24 or 3x(2x4)=24
32. Real Life Example油 油油 油油油 油油油 油油油 油油油 油油油 A real life example would be that three people are friends. One person is at another persons house and for what ever reason one left and went to the other persons house.
33. Bibliography "Associative Definition | Definition of Associative at Dictionary.com."油 Dictionary.com | Find the Meanings and Definitions of Words at Dictionary.com . Web. 29 Sept. 2009. <http://dictionary.reference.com/browse/associative>. "Associative Property."油 Math tutorials, resources, help, resources and Math Worksheets . Web. 29 Sept. 2009. <http://math.about.com/od/prealgebra/a/associative.htm> Rebecca S. Lindsay's Tutoring Service."油 Rebecca S. Lindsay, Tutor . Web. 29 Sept. 2009. <http://www.loisterms.com/lois10.htm>.