Page 132 - Basic College Mathematics with Early Integers

INTRODUCTION TO VARIABLES AND ALGEBRAIC Objectives
2.1 EXPRESSIONS
Evaluate Algebraic Expressions
Given Replacement Values.
Objective Evaluating Algebraic Expressions
Translate Phrases into Variable
Perhaps the most important quality of mathematics is that it is a science of patterns.
Expressions.
Communicating about patterns is often made easier by using a letter to represent
all the numbers fitting a pattern. We call such a letter a variable. For example, in
Section 1.3 we presented the addition property of 0, which states that the sum of 0
and any number is that number.We might write

0 + 1 = 1
0 + 2 = 2
0 + 3 = 3
0 + 4 = 4
0 + 5 = 5
0 + 6 = 6
o
continuing indefinitely. This is a pattern, and all whole numbers fit the pattern. We
can communicate this pattern for all whole numbers by letting a letter, such as a,
represent all whole numbers.We can then write

0 + a = a
Using variable notation is a primary goal of learning algebra. We now take
some important first steps in beginning to use variable notation.
A combination of operations on letters (variables) and numbers is called an
algebraic expression or simply an expression.

Algebraic Expressions
#
#
3 + x 5 y 2 z - 1 + x
If two variables or a number and a variable are next to each other, with no
operation sign between them, the operation is multiplication. For example,
2x means 2 x
#
and
xy or x1y2 means x y
#
Also, the meaning of an exponent remains the same when the base is a variable.
For example,
5
# # # #
2
x = x x and y = y y y y y
#
u
r
2 factors of x 5 factors of y
Algebraic expressions such as 3x have different values depending on replace-
ment values for x. For example, if x is 2, then 3x becomes
Î
#
3x = 3 2
= 6

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