Basic Mathematics for College Students

644 Chapter 8 An Introduction to Algebra

Caution! When replacing a variable with its numerical value, we must often

write the replacement number within parentheses to convey the proper

meaning.

b.

Simplify:.

c. Substitute 3 for and for.

Do the multiplication:.

Do the subtraction:  60  7  60 (7)67.

Find the absolute value of 67.

d. Substitute 3 for and for.

 1 Do the division.

In the denominator, do the subtraction:

 3 (1) 3  1 4.

 4

4

x  4 y

y 0

x(1)



 4  0

3 (1)

 67

 0  670

 0  60  70 5(3)(4) 60

05 xy 70  0 5( 3 )( 4 ) 70 x  4 y

 1

 4  3 (4) 4

Substitute 4 for yand 3 for x. Don’t

yx( 4 ) (^3) forget to write the sign in front of (4).


1. 
   
   
   
   2. a.factor b.term 3. a. b. c.
   
   
   
   


2. minutes 5. amount donated to scholarship fund (in dollars);
   amount donated to building fund (in dollars) 6. number of votes
   received by the challenger; number of votes received by the incumbent


3. a. 17 b. 18 c. 0

3 x 55 

900 s  x 

(m15) s 

1, 12, 3,  4 t 80 32 T (2a15)^2

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. are letters (or symbols) that stand for
   numbers.


2. The word comes from the title of a book
   written by an Arabian mathematician around
   A.D. 800.


3. Variables and/or numbers can be combined with the
   operations of arithmetic to create algebraic
   .


4. A is a product or quotient of numbers and/or
   variables. Examples are: , , and.


5. Addition symbols separate algebraic expressions into
   parts called^.

8 x 2 t cd 3

VOCABULARY 6. A term, such as 27, that consists of a single number is

called a term.

7. The of the term is 10.


8. To for , we substitute 5 for
   and perform the necessary calculations in order.


9. CUTLERY The knife shown below is 12 inches long.
   Write an expression that represents the length of the
   blade.

h in.

CONCEPTS

(^4) x 3 x 5 x
(^10) x
SECTION 8.1 STUDY SET