The document describes the number line and how it assigns numbers to points on a line. It explains that 0 is assigned to the center or origin of the line. Positive numbers are assigned to points to the right of 0, and negative numbers to points on the left. The number line defines the relative size of numbers based on their position, with numbers to the right being greater than those to the left. Intervals on the number line, such as -1 < x < 3, represent all the numbers between and including the bounds.
Prompt, complete, accurate and self-explanatory visual presentation of the concepts of various types of numbers and number line. A brief description of numbers with diagrammatic representation so that students can understand. How these numbers can be represented on the number line.
Prompt, complete, accurate and self-explanatory visual presentation of the concepts of various types of numbers and number line. A brief description of numbers with diagrammatic representation so that students can understand. How these numbers can be represented on the number line.
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
let us revise - 3 digit numbers- number name , place value,expanded form, numbers on abacus ,comparing numbers, ascending and descending order, even and odd numbers , cardinal and ordinal numbers , addition, subtraction , multiplication and division.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
2. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
3. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
0
the origin
4. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East)
20 1 3
+
the origin
5. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
the origin
6. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
the origin
2½
7. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½
the origin
8. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..–π –3.14..
the origin
9. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..
This line with each position addressed by a number is called
the number line.
–π –3.14..
the origin
10. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..
This line with each position addressed by a number is called
the number line. Given two numbers and their positions on the
number line, we define the number R to the right to be greater
than the number L to the left and we write that “L < R”.
–π –3.14..
the origin
+– L R
11. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..
This line with each position addressed by a number is called
the number line. Given two numbers and their positions on the
number line, we define the number R to the right to be greater
than the number L to the left and we write that “L < R”.
–π –3.14..
the origin
+– L R<
12. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..
This line with each position addressed by a number is called
the number line. Given two numbers and their positions on the
number line, we define the number R to the right to be greater
than the number L to the left and we write that “L < R”.
–π –3.14..
the origin
+– –1–2
<For example,
–2 is to the left of –1,
so written in the natural–form “–2 < –1”.
0
L R<
13. The Number Line
Just like assigning address to houses on a street we assign
addresses to points on a line.
We assign 0 to the “center” of the line, and we call it the origin.
We assign the directions with signs, positive numbers to the
right (East) and negative numbers to the left (West).
-2 20 1 3
+
-1-3
–
2/3 2½ π 3.14..
This line with each position addressed by a number is called
the number line. Given two numbers and their positions on the
number line, we define the number R to the right to be greater
than the number L to the left and we write that “L < R”.
–π –3.14..
the origin
+– –1–2
<For example,
–2 is to the left of –1,
so written in the natural–form “–2 < –1”. This may be written
less preferably in the reversed direction as –1 > –2.
0
L R<
14. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
The Number Line
15. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
The Number Line
16. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x".
The Number Line
17. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a.
The Number Line
18. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
The Number Line
19. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
a < x
The Number Line
20. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x.
a < x
The Number Line
21. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x. In picture
+–
a
solid dot
a < x
a < x
The Number Line
22. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x. In picture
+–
a
solid dot
a < x
a < x
The numbers x fit the description a < x < b where a < b are all
the numbers x between a and b.
The Number Line
23. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x. In picture
+–
a
solid dot
a < x
a < x
The numbers x fit the description a < x < b where a < b are all
the numbers x between a and b.
+–
a b
The Number Line
24. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x. In picture
+–
a
solid dot
a < x
a < x
The numbers x fit the description a < x < b where a < b are all
the numbers x between a and b.
+–
a a < x < b b
The Number Line
25. Example A. 2 < 4, –3< –2, 0 > –1 are true statements
and –2 < –5 , 5 < 3 are false statements.
If we want all the numbers greater than 5, we may denote them
as "all number x where 5 < x". We write "a < x" for all the
numbers x greater than a, but not including a. In picture,
+–
a
open dot
If we want all the numbers x greater than or equal to a
(including a), we write it as a < x. In picture
+–
a
solid dot
a < x
a < x
The numbers x fit the description a < x < b where a < b are all
the numbers x between a and b. A line segment as such is
called an interval.
+–
a a < x < b b
The Number Line
27. Example B.
a. Draw –1 < x < 3.
It’s in the natural form.
The Number Line
28. Example B.
a. Draw –1 < x < 3.
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
The Number Line
29. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
The Number Line
x
30. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
The Number Line
–1 ≤ x < 3
31. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
Put it in the natural form –3 < x < 0.
The Number Line
–1 ≤ x < 3
32. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
Put it in the natural form –3 < x < 0.
Then mark the numbers and x in order accordingly.
The Number Line
–1 ≤ x < 3
33. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
0
+
-3
–
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
Put it in the natural form –3 < x < 0.
Then mark the numbers and x in order accordingly.
The Number Line
–1 ≤ x < 3
34. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
0
+
-3
–
Put it in the natural form –3 < x < 0.
Then mark the numbers and x in order accordingly.
The Number Line
–1 ≤ x < 3
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
–3 < x < 0
35. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
0
+
-3
–
Expressions such as 2 < x > 3 or 2 < x < –3 do not have any
solution meaning that there isn’t any number that would fit the
description hence there is nothing to draw.
Put it in the natural form –3 < x < 0.
Then mark the numbers and x in order accordingly.
The Number Line
–1 ≤ x < 3
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
–3 < x < 0
36. Example B.
a. Draw –1 < x < 3.
0 3
+
-1
–
b. Draw 0 > x > –3
0
+
-3
–
Expressions such as 2 < x > 3 or 2 < x < –3 do not have any
solution meaning that there isn’t any number that would fit the
description hence there is nothing to draw.
Put it in the natural form –3 < x < 0.
Then mark the numbers and x in order accordingly.
The Number Line
–1 ≤ x < 3
It’s in the natural form. Mark the numbers and x on the line
in order accordingly.
–3 < x < 0
The number line converts numbers to picture and in order for
the pictures to be helpful, certain accuracy is required when
they are drawn by hand.
37. Following are two skills for drawing and scaling a line segment.
The Number Line
38. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
The Number Line
39. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
The Number Line
40. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
41. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
42. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two.
43. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two.
44. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two.
45. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
46. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
To cut a line segment K into 6 pieces, cut K in half, then cut
each half into 3 pieces.
K
47. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
To cut a line segment K into 6 pieces, cut K in half, then cut
each half into 3 pieces.
K
48. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
To cut a line segment K into 6 pieces, cut K in half, then cut
each half into 3 pieces.
K
49. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
To cut a line segment K into 6 pieces, cut K in half, then cut
each half into 3 pieces. Each smaller segment is 1/6 of K.
K
50. Following are two skills for drawing and scaling a line segment.
* Find the midpoint that cuts the segment in two equal pieces.
* Find the two points that cut the segment in three equal pieces.
The Number Line
To cut a line segment into 4 pieces, cut it in half, then cut each
half into two. Each small segment is 1/4 of the original.
To cut a line segment K into 6 pieces, cut K in half, then cut
each half into 3 pieces. Each smaller segment is 1/6 of K.
K
If we divide each segment into two again, we would have
12 segments which may represent a ruler of one foot divided
into 12 inches.
51. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers.
52. The Number Line
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers.
53. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
54. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first:
55. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
56. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable.
57. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
0o
58. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40.
0o
40o
–40o
59. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30.
0o
40o
–40o
60. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30.
0o
40o
–40o
61. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30.
0o
40o
–40o
62. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30.
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
63. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30. Use this scale to plot the numbers to
obtain a reasonable picture as shown.
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
–40o
64. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30. Use this scale to plot the numbers to
obtain a reasonable picture as shown.
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
–40o
–25o
65. The Number Line
To plot a list of numbers on a number line, first select a suitable
scale based on the numbers. For example, based on the list,
we may set the size between two markers on the line
to be 5, or 10, or 50, or 100, etc.. for easier plotting,
Example C. We record the following temperatures
during the year: 35o, –40o, 27o, –25o, 16o, 21o.
Draw a vertical scale with appropriate spacing
representing temperature then plot these numbers.
Order the numbers first: –40, –25, 16, 21, 27, and 35.
The furthest we need to plot from the origin is –40
hence using 10 as the spacing between the markers is
reasonable. Draw a line and label its center as 0.
Draw two markers close to the two ends and label them
as ±40. Divide each segment into fourths for ±10,
±20, and ±30. Use this scale to plot the numbers to
obtain a reasonable picture as shown.
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
35o
–40o
–25o
16o
21o
27o
67. The Number Line
Here are two important formulas about the number line.
Using a ruler we compute the length of a stick S by subtraction.
S
68. The Number Line
Ruler
Here are two important formulas about the number line.
Using a ruler we compute the length of a stick S by subtraction.
3
S
44
69. The Number Line
Ruler
Here are two important formulas about the number line.
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
44
70. The Number Line
Ruler
Here are two important formulas about the number line.
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
44
71. The Number Line
Ruler
Here are two important formulas about the number line.
Example D.
a. Town A and town B are as shown on a map. What is the
distance between them?
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
35 mi 97 mA B
44
0
72. The Number Line
Ruler
Here are two important formulas about the number line.
Example D.
a. Town A and town B are as shown on a map. What is the
distance between them?
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
35 mi 97 mA B
44
0
The distance between them is 97 – 35 = 62 miles.
73. The Number Line
Ruler
Here are two important formulas about the number line.
Example D.
a. Town A and town B are as shown on a map. What is the
distance between them?
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
35 mi 97 mA B
44
0
The distance between them is 97 – 35 = 62 miles.
b. What is the distance between the points u = –3 and v = 25?
u v
–3 25
0
74. The Number Line
Ruler
Here are two important formulas about the number line.
Example D.
a. Town A and town B are as shown on a map. What is the
distance between them?
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
35 mi 97 mA B
44
0
The distance between them is 97 – 35 = 62 miles.
b. What is the distance between the points u = –3 and v = 25?
The point v = 25 is to the right of u = –3,
so the distance is the 25 – (–3) = 28.
u v
–3 25
0
75. The Number Line
Ruler
Here are two important formulas about the number line.
Example D.
a. Town A and town B are as shown on a map. What is the
distance between them?
Using a ruler we compute the length of a stick S by subtraction.
For example, the length of S
shown here is 44 – 3 = 41
which is the also distance from one end to the other.
3
S
I. The Distance Formula.
The distance between two positions on the number line is
R – L where R is number to the right and L is number to the left.
35 mi 97 mA B
44
0
The distance between them is 97 – 35 = 62 miles.
b. What is the distance between the points u = –3 and v = 25?
The point v = 25 is to the right of u = –3,
so the distance is the 25 – (–3) = 28. R – L = 28
u v
–3 25
0
76. The Number Line
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
77. The Number Line
a
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
b
78. The Number Line
a a + b
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
b
2
the midpoint
79. The Number Line
a a + b b
2
the midpoint
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
80. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b b
2
the midpoint
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
81. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b b
The average of the two quizzes is
(4 + 7)/2 = 11/ 2 = 5.5
which is the midpoint of 4 and 7.
2
the midpoint
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
82. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b
4
b
The average of the two quizzes is
(4 + 7)/2 = 11/ 2 = 5.5
which is the midpoint of 4 and 7.
2
the midpoint
7
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
83. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b
4
b
the midpointThe average of the two quizzes is
(4 + 7)/2 = 11/ 2 = 5.5
which is the midpoint of 4 and 7.
2
the midpoint
7
5.5
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
84. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b
4
b
the midpointThe average of the two quizzes is
(4 + 7)/2 = 11/ 2 = 5.5
which is the midpoint of 4 and 7.
b. Find the midpoints between u = –3 and v = 25?
2
the midpoint
7
5.5
–3 0 25
the midpoint
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
85. The Number Line
Example D.
a. Joe obtained 4 points on the 1st quiz and 7 points on the 2nd
quiz, what is the average of the two quizzes? Draw.
a a + b
4
b
the midpointThe average of the two quizzes is
(4 + 7)/2 = 11/ 2 = 5.5
which is the midpoint of 4 and 7.
b. Find the midpoints between u = –3 and v = 25?
Their midpoint is (25 + (–3))/2 = 22/2 = 11.
2
the midpoint
7
5.5
–3 0 25
11
the midpoint
II. The Midpoint Formula.
The midpoint between two points a and b is (a + b)/2,
this is also the average of a and b.
86. Exercise. A. Draw the following Inequalities. Indicate clearly
whether the end points are included or not.
1. x < 3 2. –5 ≤ x 3. x < –8 4. x ≤ 12
B. Write in the natural form then draw them.
5. x ≥ 3 6. –5 > x 7. x ≥ –8 8. x > 12
C. Draw the following intervals, state so if it is impossible.
9. 6 > x ≥ 3 10. –5 < x ≤ 2 11. 1 > x ≥ –8 12. 4 < x ≤ 2
13. 6 > x ≥ 8 14. –5 > x ≤ 2 15. –7 ≤ x ≤ –3 16. –7 ≤ x ≤ –9
D. Solve the following Inequalities and draw the solution.
17. x + 5 < 3 18. –5 ≤ 2x + 3 19. 3x + 1 < –8
20. 2x + 3 ≤ 12 – x 21. –3x + 5 ≥ 1 – 4x
22. 2(x + 2) ≥ 5 – (x – 1) 23. 3(x – 1) + 2 ≤ – 2x – 9
24. –2(x – 3) > 2(–x – 1) + 3x 25. –(x + 4) – 2 ≤ 4(x – 1)
26. x + 2(x – 3) < 2(x – 1) – 2
27. –2(x – 3) + 3 ≥ 2(x – 1) + 3x + 13