This document discusses direct proportion and methods for solving direct proportion problems. Direct proportion exists when two quantities change at a constant rate with respect to each other. The cross-multiplication method can be used to solve direct proportion problems by setting up a proportion between the known quantities and cross-multiplying to solve for the unknown quantity. Graphs of direct proportion relationships will always produce a straight line passing through the origin.
This tutorial provides fundamental concepts such as:
- Absolute Values
- Basic Operations with Signed Numbers
- PEMDAS rule
in order to properly handle simplification of mathematical expressions.
This tutorial provides fundamental concepts such as:
- Absolute Values
- Basic Operations with Signed Numbers
- PEMDAS rule
in order to properly handle simplification of mathematical expressions.
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
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
Why linear programming is a very important topic?
• A lot of problems can be formulated as linear
programmes
• There exist efficient methods to solve them
• or at least give good approximations.
• Solve difficult problems: e.g. original example given
by the inventor of the theory, Dantzig. Best
assignment of 70 people to 70 tasks.
A Summary of Concepts Needed to be Successful in Mathematics
The following sheets list the key concepts that are taught in the specified math course. The sheets
present concepts in the order they are taught and give examples of their use.
WHY THESE SHEETS ARE USEFUL –
• To help refresh your memory on old math skills you may have forgotten.
• To prepare for math placement test.
• To help you decide which math course is best for you.
Este taller vamos a ver una rama de las matemáticas que se ocupa del estudio de las propiedades de las figuras en el plano o el espacio, incluyendo: puntos, rectas, planos etc
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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.
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!
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.
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.
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.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
3. The FindinThe Findingg One Method.One Method.
Example 1.
If it costs 85p for 5 Mars bars, what is the cost of 3 Mars bars ?
Solution.
Find the cost of 1 Mars bar.
Cost of 1 mars bar :
85 ÷5 = 17 p
Find the cost of 3 Mars bars.Cost of 3 Mars bars.
17 x 3 = 51p
3 Mars bars cost 51p.
4. Example 2.
If you are paid £261 for 18 hours work, how much will you be
paid for 23 hours work ?
Solution.
Find the pay for 1 hour .I hours pay
261 ÷ 18 = £ 14.50
Calculate 23 hours pay.14.5 x 23 = 333.5
You are paid £333.50 for 23 hours work.
5. Example 3.
It takes a production line 90 hours to make 120 cars. How long does
it take to make 330 cars ?
Solution.
Calculate the time to make 1 car .Time for 1 car.
90 ÷ 120 = 0.75 hours. Note :0.75 hours = 45 minutes .
Calculate the time to make 330 cars.0.75 x 330 = 247.5 hours
It takes 247 hours and 30 minutes to make 330 cars.
6. What Goes In The Box ?What Goes In The Box ?
Calculate the following:
(1) It costs £21.06 for a hotel to buy 27 boxes of cereal . How
much will 35 boxes cost at the same price per box ?
(2) 35 cars are produced in 87.5 hors by a car factory. How
long will it take to produce 142 cars at the same rate of
working ?
(3) If you earn £139.20 for 16 hours of work, what will you
earn for 9 hours work paid at the same rate ?
£27.30
355 hours
£78.30
7. The Cross-MultiThe Cross-Multipplication Method .lication Method .
This method is a more sophisticated way of solving direct
proportion questions but it has two advantages:
• It establishes a very strong routine to solve the problems.
• It makes Inverse Proportion questions easier to handle.
Think back to the Mars Bar problem and answer the following questions:
If you have twice as many Mars Bars what happens to the price ?
The price doubles.
If you have three times as many Mars Bars what happens to the price?
The price trebles.
What about ten times the number of Mars Bars? Ten times the price.
8. Key Point.
Whenever you have two quantities and when one is doubled or trebled
etc the other quantity doubles or trebles etc , then you have
direct proportion .
The problem can then be solved by the method demonstrated in the
following slides.
9. Example 1.
If you are paid £ 190.21 for 23 hours work, then what is your pay
for 17 hours work ?
Solution. Identify the two quantities being
talked about:
Pay Hours
Identify the two amounts that go
together.190.21 23
Ask yourself “ If the first
quantity is doubled , trebled etc,
what happens to the second
quantity ?
It doubles , trebles etc also.
Determine what is being asked for
and what other info’ you have.
P 17
Cross multiply to solve.
Use arrows..
17
23
p
190.21
=
23 x p = 17 x 190.21
23
190.2117
p
×
=
p = £140.59 for 17 hours.
11. Example 3.
Find the area
of the sector
OAB of this
circle if angle
AOB is 100o
Solution.
100o
O
A B
5cm
Find the area of the whole circle.
A = ∏ r2
A = 3.14 x 5 x 5
A = 78.5cm2
Now decide on the two
quantities in the problem:
Area Angle
What angle goes with 78.5cm2
?
78.5 360o
Add the other information:
A 100o
Cross multiply and solve:
100
360
A
78.5
=
A = 21.8cm2
( to 1 d.p)
If you double treble etc the angle
what happens to the area ?
12. Example 3.
172o
O
A
B12cm
Calculate the arc
length AB on this
circle.
Solution.
Find the circumference of the circle.
C = 2 ∏ r
C = 2 x 3.14 x 12
C = 75.36 cm
Now decide on the two
quantities in the problem:
Arc Length Angle
What angle goes with 75.36cm ?
75.36 360o
A 172o
If you double treble etc the angle
what happens to the arc length ?
Cross multiply and solve:
172
360
A
75.36
=
A = 36cm (to 1 d.p)
13. What Goes In The Box ? 2What Goes In The Box ? 2
(1) The shadow of a tree 7.4m high is 10.6m . How long will the
shadow of a tree 8.9m high be at the same time ?
(2) Calculate the area of the sector AOB . 100o
O
A B
23cm
(3) Calculate the arc length AB.
(4) You get 14 out of 23 in a test. What would you get out of 100 for
the same test score ?
12.7m
461.4cm2
to 1 d.p
40.1cm to 1 d.p
60.9% to 1 d.p
15. 0 2 4 6 8 10 12
2
4
6
8
10
No of ladders.
Hours
Graph Of Ladders Made against Time Taken.
16. L
T
o
Key Fact.
All Direct Proportion graphs are straight
line graphs passing through the origin:
Look at the table of values again:
Ladders 0 1 2 3 4 5
Hours 0 2 4 6 8 10
If you divide the number of hours by the given number of ladders ,
what do you find each time ? ( Hours divided by ladders)
The answer is 2 every time.
We only need one point on the table to complete the whole table.
17. Complete the tables below given that they form direct proportion graphs:
(1) F 0 1 2 3 4 5
G 80 4 12 16 20
(2) D 0 3 6 10 20
E 240 18 40 80
(3) R 0 2 7 10 100
W 350 10 50 500
(4) W 0 3 7 8 12
M 120 4.5 10.5 18
18. 0 1 2 3 4 5
10
20
30
G
H
What Goes In The Box ? 3What Goes In The Box ? 3
Complete the tables below for direct proportion and draw the graph.
G 0 1 2 3 4 5
H 180 6 12 24 30
