This document provides a lesson on adding and subtracting rational numbers. It begins with a warm up problem and example of adding decimals. It then teaches how to add and subtract rational numbers with like denominators by adding or subtracting the numerators and keeping the denominator. Several examples are provided using number lines and evaluating expressions. The document ends with a two part lesson quiz to assess understanding.
Powerpoint presentation about Division of Integers. Best for demo teaching. Designed for an online class and face-to-face with review, motivation, groupings, quiz, and homework.
Powerpoint presentation about Division of Integers. Best for demo teaching. Designed for an online class and face-to-face with review, motivation, groupings, quiz, and homework.
The 2014 Mercedes-Benz SL-Class is available at Walter’s Automotive, a trusted Mercedes-Benz dealer serving Corona. Schedule a test-drive in this thrilling roadster today.
Slides of polling from the Resolution Foundation and YouGov which gives fresh insight into what voters think the Conservatives can (and can’t) achieve on the economy and in relation to living standards at the 2015 election.
Launched at the Resolution Foundation event - Living Standards: the 2015 challenge with Jesse Norman MP and Rob Halfon MP http://res-fdn.org/1arhtFp
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Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
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Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
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How can you help your company evolve, adapt, and succeed using Artificial Intelligence and the Metaverse to stay ahead of the competition? What are the potential issues, complications, and benefits that these technologies could bring to us and our organizations? In this session, Jen Stirrup will explain how to start thinking about these technologies as an organisation.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
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• What is SAP Fiori and why it matters to you
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• How to get started with SAP Fiori today
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Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
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Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
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- How to remove silos in DevSecOps
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GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
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The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
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Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
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While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
3 2 adding and subtracting rational numbers lesson
1. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers3-2
Adding and Subtracting
Rational Numbers
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
2. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Problem of the Day
Four sprinters run a race. In how many
different ways can they arrive at the finish
line, assuming there are no ties?
3. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Problem of the Day
Four sprinters run a race. In how many
different ways can they arrive at the finish
line, assuming there are no ties?
24
5. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
The 100-meter dash is measured in
thousandths of a second, so runners
must react quickly to the starter pistol.
If you subtract a runner’s reaction time
from the total race time, you can find the
amount of time the runner took to run
the actual 100-meter distance.
6. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
In August 2001 at the World University
Games in Beijing, China, Jimyria Hicks ran
the 200-meter dash in 24.08 seconds. Her
best time at the U.S. Senior National Meet in
June of the same year was 23.35 seconds.
How much faster did she run in June?
She ran 0.73 second faster in June.
24.08
–23.35
0.73
Align the decimals.
Additional Example 1: Sports Application
7. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Tom ran the 100-meter dash in 11.5 seconds
last year. This year he improved his time by
0.568 seconds. How fast did Tom run the
100-meter dash this year?
Try This: Example 1
Tom ran the 100-meter dash in 10.932 seconds
this year.
Subtract 0.568 from 11.5 to determine the new time.
10.932
–0.568
11.5 Add 2 zeros so the
decimals align.
00
8. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 0.3 + (–1.2)
Move right 0.3 units.
0.4–1.0 –0.4 0
From 0.3, move left 1.2 units.
–1.2
0.3
Use a number line to find the sum.
Additional Example 2A: Using a Number Line to Add
Rational Decimals
–1.4
You finish at –0.9, so 0.3 + (–1.2) = –0.9.
9. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
0
1
5
+
2
5
1
5
2
5
1
5
3
5
2
5
Use a number line to find the sum.
Additional Example 2B: Using a Number Line to Add
Rational Decimals
Move right units.
1
5
B.
4
5
1
You finish at , so
1
5
+
2
5
3
5
= .
3
5
From , move right units.
1
5
2
5
10. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 1.5 + (–1.8)
Move right 1.5 units.
1.6–0.4 0 0.8
From 1.5, move left 1.8 units.
–1.8
1.5
Use a number line to find the sum.
Try This: Example 2A
You finish at –0.3, so 1.5 + (–1.8) = –0.3.
0.4 1.4
11. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
0
3
8
+
1
8
3
8
1
8
1
8
3
8
1
4
1
2
5
8
B.
Try This: Example 2B
Use a number line to find the sum.
Move right units.
3
8
From , move right units.
3
8
1
8
You finish at ,
which simplifies to .
1
2
4
8
12. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
ADDING AND SUBTRACTING WITH
LIKE DENOMINATORS
Words Numbers
To add or subtract
rational numbers
with the same
denominator, add or
subtract the
numerators and keep
the denominator.
= , or ––2
7
2
7
4
7
+ – =
2 + (–4)
7
2
7
13. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
ADDING AND SUBTRACTING WITH
LIKE DENOMINATORS
Words Algebra
To add or subtract
rational numbers
with the same
denominator, add or
subtract the
numerators and keep
the denominator.
=+
a
d
a + b
d
b
d
14. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Additional Example 3: Adding and Subtracting
Fractions with Like Denominators
Subtract numerators.
Keep the denominator.
2
9
– –
5
9
2
9
– –
5
9
= –
7
9
=
3
7
6
7
+ –
3
7
–2 – 5
9
=
6 + (–3)
7
=
can be written as .–
3
7
–3
7
Add or subtract.
6
7
+
–3
7
A.
B.
15. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
=
1
9
5
9
+ –
4
9
5 + (–4)
9
=
5
9
+
–4
9
Try This: Example 3
Subtract numerators.
Keep the denominator.
1
5
– –
3
5
1
5
– –
3
5
= –
4
5
–1 – 3
5
=
Add or subtract.
A.
B. can be written as .–
4
9
–4
9
16. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 12.1 – x for x = –0.1
Substitute –0.1 for x.12.1 – (–0.1)
12.2 Think: 12.1 – (–0.1) =
12.1 + 0.1
Evaluate the expression for the given value of
the variable.
Additional Example 4A: Evaluating Expressions with
Rational Numbers
17. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
4
5
= 3
+
7
10
31
10
Add numerators,
keep the denominator.
7 + 31
10
Simplify.
+ m for m = 3
7
10
1
10
38
10
=
+ 3
7
10
1
10
Substitute 3 for m.1
10
3(10) + 1
10
3 = =
31
10
1
10
B.
Evaluate the expression for the given value of
the variable.
Additional Example 4B: Evaluating Expressions with
Rational Numbers
18. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
52.3 – y for y = –7.8
Substitute –7.8 for y.52.3 – (–7.8)
60.1
Think: 52.3 – (–7.8) =
52.3 + 7.8
Try This: Example 4A
A.
Evaluate the expression for the given value of
the variable.
19. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
+
5
8
47
8
Add numerators,
keep the denominator.
5 + 47
8
Simplify.
+ m for m = 5
5
8
7
8
52
8
=
+ 5
5
8
7
8
Substitute 5 for m.7
8
5(8) + 7
8
5 = =
31
8
7
8
B.
Try This: Example 4B
Evaluate the expression for the given value of
the variable.
1
2
= 6
21. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Simplify.
1. –1.2 + 8.4
2. 2.5 + (–2.8)
7.2
–0.3
3.
4. 62.1 + x for x = –127.0
1
2
–
3
4
+
5
4
–
–64.9
Lesson Quiz: Part 1
Evaluate.
22. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Sarah’s best broad jump is 1.6 meters,
and Jill’s best is 1.47 meters. How much
farther can Sarah jump than Jill?
Lesson Quiz: Part 2
5.
23. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Sarah’s best broad jump is 1.6 meters,
and Jill’s best is 1.47 meters. How much
farther can Sarah jump than Jill?
Lesson Quiz: Part 2
5.
0.13 m