CHAPTER 1
From Arithmetic to Algebra
Source:
Elementary & Intermediate Algebra, Fourth Edition
Prepared and Edited by:
Dr. Mohamad Hammoudi

Topics of Chapter 1
1.1: Transition to Algebra.
1.2: Evaluating Algebraic Expressions.
1.3: Adding and Subtracting Algebraic Expressions.
1.4:Sets.
2

1.1: Transition to Algebra
Objectives:
1.1.1: Introduce the concept of variables
1.1.2: Identify algebraic expressions
1.1.3: Translate from English to algebra
3

1.1.1: Introduce the Concept of Variables
In
arithmetic
, calculations are performed on
numbers
using
the four basic operations of addition, subtraction,
multiplication, and division.
The addition is denoted by (+), the subtraction is denoted by
(-), and multiplication is denoted by (
×
), and the division is
denoted by (
÷
).
In
algebra
, the same four basic operations are used.
However, calculations are performed on
variables
.
The variables are letters such as
x, y, L
and
W
which
represent numerical values.
The variables represent
unknown numerical values
.
4

1.1.1: Example of Variables
Here we see two rectangles whose lengths and widths are
labeled with numbers.
If we need to represent the length and width of
any
rectangle, we can use the variables
L
for length and
W
for
width
.
5

1.1.2: Identify Algebraic Expressions
Definition of Expression
An expression
is is a meaningful collection of numbers,
variables, and symbols of operation.
Examples: Identify which are expressions and which are
not
2m + 3
x + . +
3
y =2x - 1
3a + 5b
–
4c
6

Writing Expressions That Indicate
Addition
Definition of Addition
x +
y
means the
sum
of
x
and
y
, or
x plus y.
The addition operation is
commutative
and
associative
. The
order of the added terms and the order in which the
operations are performed is
not important
.
It is
commutative
because 2 + 3 = 3 + 2 = 5
It is
associative
because (2 + 3) + 4 = 2 + (3 + 4) = 9
Examples: Write using symbols
The
sum
of
a
and 3.
L plus W
is written as.
5
more than m.
x increased by
7.
7

Writing Expressions That Indicate
Subtraction
Definition of Subtraction
x -
y
means the
difference
of
x
and
y
, or
x minus y.
The subtraction operation is neither
commutative
nor
associative
. The order of the subtracted terms and the order
in which the operations are performed is
important
.
It is not
commutative
because 5 - 3
≠ 3
- 5
It is not
associative
because (3 - 5) - 7
≠
3 - (5 - 7)
Examples: Write using symbols
r minus s.

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