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THE UNIVERSITY OF AKRON
Mathematics and Computer Science
Lesson 3: Basic Algebra, Part I
Directory
•
Table of Contents
•
Begin
Lesson 3
A
n
l
g
e
b
r
a
R
v
i
w
Iam
DP
S
N
⊆
Z
⊆
Q
⊆
R
⊆
C
a
3
a
4
=
a
7
(
ab
)
10
=
a
10
b
10
−
(
ab
−
(3
ab
−
4))=2
ab
−
4
(
ab
)
3
(
a
−
1
+
b
−
1
)=(
ab
)
2
(
a
+
b
)
(
a
−
b
)
3
=
a
3
−
3
a
2
b
+3
ab
2
−
b
3
2
x
2
−
3
x
−
2=(2
x
+ 1)(
x
−
2)
1
2
x
+13=0 =
⇒
x
=
−
26
G=
{
(
x, y
)

y
=
f
(
x
)
}
f
(
x
)=
mx
+
b
y
= sin
x
T
L
s
o
Copyright c
°
1995–2000
D. P. Story
Last Revision Date: 2/2/2000
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View Full Document Lesson 3: Basic Algebra, Part I
Table of Contents
3.
Basic Algebra, Part I
•
You are manipulating Numbers
3.1.
The Basics
•
The Arithmetical Operations
•
Terms vs Factors
•
Paren
theses, Brackets, and Braces
•
How to Negate Correctly
•
How to Invert Correctly
3.2.
How to Add/Subtract Algebraic Expressions
•
Adding/Subtracing Grouped Expressions
3. Basic Algebra, Part I
Algebra is the language of mathematics, engineering and the sciences.
We use algebra to express our thoughts, ideas, and to communicate
with others who understand the language of algebra.
Algebra is a language in which we can precisely pose ourselves ques
tions; Algebra is a set of tools for answering those questions.
•
You are manipulating Numbers
When we manipulate algebraic quantities, we are, in fact, manipu
lating
numbers
. This point must be ever kept in mind. The rules for
manipulating algebraic quantities reﬂect the properties of the
number
system
. This is an important point. Therefore, when you manipulate
symbolic quantities in a questionable way, you must ask yourself the
question, “Is what I have just done valid when I replace the symbols
by numbers?”
This should be your guiding principle.
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View Full Document Section 3: Basic Algebra, Part I
A Fundamental Guiding Principle of Algebra
:
“Is the algebraic manipulation that I just performed valid
when I replace the symbols by numbers?”
3.1. The Basics
In this section we take a brief survey of the arithmetical operations
and some of the properties of these operations that are exploited to
perform algebraic manipulations.
•
The Arithmetical Operations
Let the letters
a
,
b
, and
c
represent (real) numbers. As you well know
we can add, subtract, multiply, and divide these numbers. In algebra,
these operations are carried out
symbolically
:
1.
Addition.
The sum of
a
and
b
is
a
+
b
. The number
a
is called
a
term
of the expression
a
+
b
. (Of course,
b
is a term too.)
Section 3: Basic Algebra, Part I
2.
Subtraction.
The diference oF
a
and
b
is
a
−
b
. The number
a
is called a
term
oF
a
−
b
. (OF course,
b
is a term too.)
3.
Mulitplication.
Product oF
a
and
b
is
ab
or
a
·
b
, or sometimes,
a
×
b
. The numbers
a
and
b
are called
factors
oF the product
ab
.
4.
Division.
The quotient oF
a
by
b
is
a
b
,or
a/b
, or less Frequently
(in algebra),
a
÷
b
. Division is only de±ned when the denominator
b
±
= 0. The number
a
is the
numerator
, and
b
is the
denominator
.
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This note was uploaded on 09/24/2009 for the course CHEM 333 taught by Professor Baird during the Spring '09 term at UC Davis.
 Spring '09
 Baird

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