Here are examples of the Associative Property and Commutative Property:
Associative Property:
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication: 3 × (4 × 2) = (3 × 4) × 2
Commutative Property:
Addition: 2 + 5 = 5 + 2
Multiplication: 3 × 4 = 4 × 3
The Associative Property shows that changing the grouping of numbers or variables does not change the sum or product. The Commutative Property shows that changing the order of numbers or variables does not change the sum or product.
This learner's module discusses about the topic of Radical Expressions. It also discusses the definition of Rational Exponents. It also teaches about writing an expression in a radical or exponential form. It also teaches about how to simplify expressions involving rational exponents.
This learner's module discusses or talks about the topic Radical Expressions. It also teaches how to recognize basic radical notation. It also teaches the multiplication and division of Radical Expressions.
This learner's module discusses about the topic of Radical Expressions. It also discusses the definition of Rational Exponents. It also teaches about writing an expression in a radical or exponential form. It also teaches about how to simplify expressions involving rational exponents.
This learner's module discusses or talks about the topic Radical Expressions. It also teaches how to recognize basic radical notation. It also teaches the multiplication and division of Radical Expressions.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
1. Describe the pattern in each sequence.
1. 2, 22, 42, 62, . . . 2. 2.8, 6, 9.2, 12.4, . . .
Write the next three terms of each sequence.
3. 4, 12, 20, 28, . . . 4. 2.1, 2.8, 3.5, 4.2, . . .
5. Every 18 months, National Surveys conducts a population
survey of the United States. If they conducted a survey in
September 2003, when will they conduct the next four
surveys?
6. What is the next term in the sequence 3.2, 12.8, 22.4, 32, …?
Course 2, Lesson 5-3
2. Answers
1. Add 20 to the previous term.
2. Add 3.2 to the previous term.
3. 36, 44, 52
4. 4.9, 5.6, 6.3
5. March 2005, September 2006, March 2008,
September 2009
6. 41.6
Course 2, Lesson 5-3
3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-3
6. • To identify properties of operations
• To determine if conjectures are true or false
and provide counterexamples for false
conjectures
• To use properties to simplify algebraic
expressions
Course 2, Lesson 5-3
Expressions and Equations
8. Course 2, Lesson 5-3
Expressions and Equations
Words The Commutative Property states that the order in which
the numbers are added or multiplied does not change the
sum or product.
Addition Multiplication
Symbols a + b = b + a a • b = b • a
Examples 6 + 1 = 1 + 6 7 • 3 = 3 • 7
9. Course 2, Lesson 5-3
Expressions and Equations
Words The Associative Property states that the way in which
numbers are grouped when they are added or multiplied
does not change the sum or product.
Addition Multiplication
Symbols a + (b + c) = (a + b) + c a • (b • c) = (a • b) • c
Examples 2 + (3 + 8) = (2 + 3) + 8 3 • (4 • 5) = (3 • 4) • 5
10. 1
Need Another Example?
Step-by-Step Example
1. Name the property shown by the statement
2 • (5 • n) = (2 • 5) • n.
The order of the numbers and variable did not change,
but their grouping did. This is the Associative Property
of Multiplication.
11. Answer
Need Another Example?
Name the property shown by the statement
(3 • m) • 2 = 2 • (3 • m).
Commutative Property of Multiplication
12. 1
Need Another Example?
2
Step-by-Step Example
2. State whether the following conjecture is true or false.
If false, provide a counterexample.
Write two division expressions using the Commutative Property.
Division of whole numbers is commutative.
15 ÷ 3 = 3 ÷ 15
5 ≠
State the conjecture.
Divide.
?
The conjecture is false. We found a counterexample. That is,
15 ÷ 3 ≠ 3 ÷ 15. So, division is not commutative.
13. Answer
Need Another Example?
State whether the following conjecture is true
or false. If false, provide a counterexample.
Subtraction of whole numbers is associative.
false; Sample answer: (12 – 5) – 3 ≠ 12 – (5 – 3)
14. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Alana wants to buy a sweater that costs $38,
sunglasses that costs $14, a pair of jeans that costs
$22, and a T-shirt that costs $16. Use mental math to
find the total cost before tax.
Write an expression for the total cost. You can rearrange the
numbers using the properties of math. Look for sums that are
multiples of ten.
Commutative Property of Addition
Associative Property of Addition
The total cost of the items is $90.
38 + 14 + 22 + 16
= 38 + 22 + 14 + 16
= (38 + 22) + (14 + 16)
Add.
Simplify.
= 60 + 30
= 90
15. Answer
Need Another Example?
In a garden, a decorative pool in the shape
of a box is 2 feet deep, 17 feet long, and
5 feet wide. Use mental math to find the
volume of water in the pool.
170 ft3
16. 1
Need Another Example?
2
3
Step-by-Step Example
4. Simplify (7 + g) + 5. Justify each step.
Commutative Property of Addition
Associative Property of Addition
(7 + g) + 5 = (g + 7) + 5
Simplify.= g + 12
= g + (7 + 5)
17. Answer
Need Another Example?
Simplify 6 + (d + 8). Justify each step.
6 + (d + 8) = 6 + (8 + d) Commutative (+)
= (6 + 8) + d Associative (+)
= 14 + d Simplify.
18. 1
Need Another Example?
2
3
Step-by-Step Example
5. Simplify (m • 11) • m. Justify each step.
Commutative Property of Multiplication
Associative Property of Multiplication
(m • 11) • m
Simplify.= 11m2
= (11 • m) • m
= 11 • (m • m)
19. Answer
Need Another Example?
Simplify a • (9 • b). Justify each step.
a • (9 • b) = (a • 9) • b Associative (×)
= (9 • a) • b Commutative (×)
= 9ab Simplify.
20. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-3
Expressions and Equations
21. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-3
Expressions and Equations
Sample answers:
• Using numbers and symbols to represent mathematical
properties
• Finding a counterexample to show a conjecture is false
• Applying properties and use mental math when solving
real-world problems
22. Give examples of both
the Associative Property and
the Commutative Property.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2, Lesson 5-3
