This document provides instruction and examples for evaluating algebraic expressions by substituting values for variables. It explains how to evaluate expressions like 3x + 7y^2 by substituting values for x and y based on the numbers provided in the problem. Examples are provided of evaluating expressions with fractions and formulas. The document walks through practice problems on pages 121-125 of the book that involve evaluating expressions after substituting values. It also previews upcoming lessons on the quadratic formula.
Identify basic properties of equations
Solve linear equations
Identify identities, conditional equations, and contradictions
Solve for a specific variable (literal equations)
Identify basic properties of equations
Solve linear equations
Identify identities, conditional equations, and contradictions
Solve for a specific variable (literal equations)
This learner's module discusses and help the students about the topic Systems of Linear Inequalities. It includes definition, examples, applications of Systems of Linear Inequalities.
This learner's module discusses and help the students about the topic Systems of Linear Inequalities. It includes definition, examples, applications of Systems of Linear Inequalities.
Algebraic Expression and Expansion.pptxMisbahSadia1
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Algebraic expressions are fundamental mathematical constructs that play a crucial role in representing and solving a wide range of mathematical and real-world problems. They are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions are a bridge between the abstract world of mathematics and the practical world of problem-solving.
Key components of an algebraic expression:
Variables: These are symbols (usually letters) that represent unknown values or quantities. Common variables include "x," "y," and "z." Variables allow us to generalize mathematical relationships and solve problems with unknowns.
Constants: These are fixed numerical values that do not change within the expression. Examples include numbers like 2, 5, Ļ (pi), or any other specific constant value.
Mathematical Operations: Algebraic expressions include operations like addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^ or **). These operations define how the variables and constants interact within the expression.
Coefficients: Coefficients are the numerical values that multiply variables. For example, in the expression 3x, 3 is the coefficient of the variable x.
Algebraic expressions can take various forms, from simple linear expressions like 2x + 3 to more complex ones like (x^2 - 4)(x + 1). They are used in a wide range of mathematical contexts, including equations, inequalities, and functions.
Expansion of Algebraic Expressions:
Expanding an algebraic expression involves simplifying it by removing parentheses and combining like terms. This process is essential for solving equations, simplifying complex expressions, and gaining a better understanding of the underlying mathematical relationships.
Here's how to expand algebraic expressions:
Distribute: When an expression contains parentheses, you distribute each term within the parentheses to every term outside the parentheses using the appropriate mathematical operation (usually multiplication or addition).
Example: To expand 2(x + 3), you distribute the 2 to both terms inside the parentheses: 2x + 6.
Combine Like Terms: After distributing and simplifying, you look for like terms (terms with the same variable(s) and exponent(s)) and combine them.
Example: In the expression 3x + 2x, you combine the like terms to get 5x.
Remove Parentheses: If there are nested parentheses, continue to distribute and simplify until no parentheses remain.
Expanding algebraic expressions is a crucial step in solving equations and simplifying complex expressions. It allows mathematicians and scientists to manipulate and analyze mathematical relationships efficiently, making it an essential tool in various fields, including physics, engineering, and computer science.
* Solve a system of nonlinear equations using substitution.
* Solve a system of nonlinear equations using elimination.
* Graph a nonlinear inequality.
* Graph a system of nonlinear inequalities.
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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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.
1. Skill #22 Evaluating an Algebraic Expression
page 121 to 126 in your book
This is a classic type of algebra problem where you are given an algebraic expression
such as 3x + 7y2 and told to evaluate the expression if some numbers (made up by the
problem maker) are assigned to x and y. Letās evaluate this expression if x = 4 and y = -1.
3x + 7y2
3(4) + 7(-1)2
12 + 7 (1)
12 + 7
19
I used the order of operations
(PEMDAS)
2. Look at page 121. The first example is easy.
Look at the next example. It is more like what I expect you to see on the GED.
You may be given a fraction to substitute. Think about what that would look like.
I would change the fraction to a decimal first. Then use the order of operations.
3. You should be able to evaluate a fraction.
Just get a number for the top and a number for the bottom. Then simplify.
Sometimes the problem maybe be set in the context of a word problem given a
formula. Look at this example. You do not need to understand the formula. Just
put in the given numbers and simplify by the order of operations.
4. Now look at page 122 in the book. It is a puzzle giving formulas and numbers to
substitute for the letters in the formula. Each formula has two different sets of
numbers to substitute. Try each formula. The answers are at the right.
You should get one of these numbers for each problem.
Try number 13. Let e = 2 so that you get w = 0.03 (2)3 This gives w = 0.03 (8) or
w = 0.24
5. Now look at page 123 problem 7. This is a geometry formula you might see on the test.
It is on the formula page as the volume of a cone.
V = 1/3 (3.14) (6)2 (10) Everything is basically multiplied after the exponent
is simplilfied.
V = 1/3 (3.14)(36)(10) You can multiply the three numbers on the right.
Then multiply by 1/3 or change 1/3 to .33.
V = 376.8 or close to it. One the test, choose the answer closest to 376.8.
6. On page 124, just look at the problems beginning with number 10. They are just
practice evaluating.
One page 125, I made up a bunch of expressions leading up to the quadratic formula
which we will be looking at in the next several lessons. A few things may look new.
For example, the plus or minus symbol (Ā±) is just a way to say two things at once.
3 Ā± 4 means 3 + 4 or 7 and also 3 ā 4 or -1 at the same time. You save paper and ink!
I just picked three easy numbers for a b, and c. The answers you should get are on
the next page. Try some of them but donāt worry too much.
We will get lots of practice in the next few lessons.
Thanks for trying this lesson without me actually being in the room. I will
be checking the account for your questions during the 5;30-7:00 time slot
on Tuesday night. I will try to answer them in emails.
