This document discusses expressions in algebra. It defines mathematical expressions and algebraic expressions, noting that algebraic expressions contain variables. It explains variables, coefficients, and constant terms. It provides examples of writing variable expressions from verbal phrases and vice versa. The document also discusses evaluating expressions by substituting values for variables and using order of operations. It includes practice problems for writing expressions, translating between verbal and algebraic forms, and evaluating expressions.
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.
Objective: Students will understand that the order of operations can be used to evaluate numerical expressions.
Key words
numerical expression
order of operations
Algebra is used in many field in many different ways to solve equation problems, and in business algebra is also used or in our day to day life it is also used. ... Algebra is a way of keeping track of unknown values, which can be used in equations.
6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.
Objective: Students will understand that the order of operations can be used to evaluate numerical expressions.
Key words
numerical expression
order of operations
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.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
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.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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.
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!
2. Objectives
Translate between verbal and symbolic representations of expressions
Simplify expressions
Evaluate expressions
3. Mathematical Expression VS Algebraic
Expression
A MATHEMATICAL EXPRESSION is any combination of numbers, symbols and
operations.
Basically mathematical expressions are the “math problems” we have worked up until
now. They contain numbers and operation symbols, parentheses, etc
An ALGEBRAIC EXPRESSIONS contains numbers, operations and one or more
VARIABLES.
A variable is a symbol that stands for an unknown number or value. Variables are
typically written as a letter in italics, like x.
4. VARIABLES, COEFFICIENTS, and
CONSTANT TERMS
5x-3=15
In the above equation, the x is the variable (representing the value we don’t know)
The “5” in front of the x is referred to as the “COEFFICIENT”. It is a multiplyer of
the x value. Basically 5x is the same as “5 times x”
The “-3” is referred to as the CONSTANT TERM in the algebraic equation.
5. WHO CARES?
Algebra and variables can help us solve many real world problems.
For example: If I know that the width of each classroom is 2 times its length, I only
need to measure the length of a classroom to determine its width.
W=width
L=length
W=2L If the L is 2 ft, the W is 4 ft. If the L in another classroom is 3 feet, the
width is 6 ft. It allows us to show relationships.
6. Write a variable expression that
represents a verbal phrase
Write the variable expression for “5 is less than twice a number.”
STEP 1.
Assign a variable to the unknown number. (the number will be referred to as “n”)
STEP 2.
Identify the operation or operations in the verbal phrase.
“5 less than” means -5
Twice means 2times
STEP 3
Write the variable expression: 2n-5
7. Write an expression that represents a real
world situation
Thomas has a cell phone plan that charges a flat rate of $35.00 per month plus
$0.25 for each text message. Write an algebraic expression that shows the
monthly fee for Thomas’s cell phone plan.
STEP 1. Assign a variable to the unknown. (let’s use “t” for number of text
messages)
STEP 2. Identify the operations in the situation
The word “plus” indicates addition
The phrase 0.25 for each text message indicates multiplication
STEP 3. Write the expression
35.00+0.25t
8. Translate an Expression into a Verbal
Phrase
3m+4
STEP 1. Identify the variable.
The variable is “m”
STEP 2. Identify the operations.
3m means 3 times m
M+4 means add 4
STEP 3. Write a verbal phrase.
9. PRACTICE
Think about math. Pg 137
Write each verbal phrase as a variable expression
1. A number increased by 12
2. $250 less than twice Rahman’s salary.
Write each variable expression as a verbal phrase
4t ÷ 2
c - 9
10. EVALUATE expressions
When you evaluate, you find the value of, an expression.
You substitute a given value for the variable and then do the math to solve.
For example
Evaluate x + 7 when x = -2
STEP 1. Substitute the given value for the variable. In this case put the (-2) into the equation
for x.
Solve the operation
(-2) + 7 = 5
11. Evaluate an expression using order of
operations
Evaluate a + 4b when a = -10 and b = 1.5
STEP 1. Substitute the given values for the variables.
(-10) + 4 (1.5)
STEP 2. Use the order of operations to solve the problem
Solve multiplication first
4 times 1.5 = 6
Solve addition next (-10) + 6 = -4
The value of a +4b when a = -10 and b = 1.5 is -4.
12. Practice
Think about math p. 138
Evaluate each expression. Use order of operations if necessary.
1) 13.6 – a, when a = 2.9
2) -3m +n , when m = 4 and n = 6
3) c + d, when c = -5 and d = 2
4) -5x ÷ 2y , when x=8 and y= -5
