Basic Mathematics for College Students











138 Chapter 2 The Integers

The symbol is used to indicate a negative number, the opposite of a number,

and the operation of subtraction. The key to reading the symbol correctly is to

examine the context in which it is used.





EXAMPLE (^5) Simplify each expression: a. b. c.
StrategyWe will find the opposite of each number.
WHYIn each case, the symbol written outside the grouping symbols means “the
opposite of.”
Solution
a. means the opposite of. Since the opposite of is 44, we write
b. means the opposite of the absolute value of 11. Since , and the
opposite of 11 is , we write
c. means the opposite of the absolute value of. Since ,
and the opposite of 225 is , we write
 0  2250  225

 225

 0  2250  225 0  2250  225

 0110  11

 11

 0110 0110  11

(44) 44

(44)  44  44



(44)  0110  0  2250

Self Check 5

Simplify each expression:

a.

b.

c.

Now TryProblems 55, 65, and 67

 0  990

 040

(1)

1. 
   
   
   
   2. a. b.
   
   
   
   


2. a.false b.true c.true d.false 4. a. 9 b. 4 5. a. 1 b. 4 c. 99

− 4 − 3 − 2 − 101234  

ANSWERS TO SELF CHECKS

Reading the Symbol

Negative twelve A symbol directly in front of a number

is read as “negative.”

The opposite of The first symbol is read as “the opposite

negative twelve of” and the second as “negative.”

Twelve minus five Notice the space used before and after the

symbol. This indicates subtraction and

is read as “minus.”



12  5

(12) 

 12 





Number Opposite

57 Read as “negative fifty-seven.”

Read as “the opposite of negative eight is eight.”

0 Read as “the opposite of 0 is 0.”

The concept of opposite can also be applied to an absolute value. For example, the

opposite of the absolute value of can be written as. Think of this as a two-

step process, where the absolute value symbol serves as a grouping symbol. Find the

absolute value first, and then attach a sign to that result.

First, find the absolute value.

Read as “the opposite of the absolute value

of negative eight is negative eight.”

Then attach a sign.

 0  80  8



 8  0  80

 0  0

 8 (8) 8

 57