Algebra Demystified 2nd Ed

46 algebra De mystif ieD

deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter2

A variable is a symbol for a number whose value is unknown. A variable might

represent quantities at different times. For example if you are paid by the hour

for your job and you earn $10 per hour, letting x represent the number of hours

worked would allow you to write your earnings as “10x.” The value of your

earnings varies depending on the number of hours worked. If an equation

has one variable, we can use algebra to determine what value the variable is

representing.

Variables are treated like numbers because they are numbers. For instance

2 +x means two plus the quantity x and 2x means the quantity two times x

(when no operation sign is given, the operation is assumed to be multiplica-

tion). The expression 3x + 4 means three times x plus four. This is not

the same as 3x + 4x which is three x’s plus four x’s for a total of seven x’s:

3 x + 4x = 7x.

Simplifying Fractions Containing Variables

We can simplify fractions containing variables with the same techniques

that we used to simplify ordinary fractions. If a variable appears as a factor

in the numerator and denominator, we can simplify the fraction. We sim-

plify fractions containing variables with the same strategy that we used in

Chapter 1; that is, we divide common factors from the numerator and

denominator.

EXAMPLES

Write the fraction in lowest terms.

22

1

x 2

x

x

x

=⋅=

6

9

6

9

6

9

2

3

x

x

x

x

=⋅==

7

5

7

5

7

5

xy

x

yx

x

=⋅= y

EXAMPLES

Write the fraction in lowest terms.