Basic Mathematics for College Students

2.1 An Introduction to the Integers 139

SECTION 2.1 STUDY SET

10. a. If a number is less than 0, what type of number
    must it be?

b. If a number is greater than 0, what type of number

must it be?

11. On the number line, what number is

a. 3 units to the right of?

b. 4 units to the left of 2?

12. Name two numbers on the number line that are a
    distance of

a. 5 away from.

b. 4 away from 3.

13. a. Which number is closer to on the number line:
    2 or?

b. Which number is farther from 1 on the number

line: or 8?

14. Is there a number that is both greater than 10 and less
    than 10 at the same time?


15. a. Express the fact using an symbol.

b. Express the fact using an symbol.

16. Fill in the blank: The opposite of the of a
    number is that number.


17. Complete the table by finding the opposite and the
    absolute value of the given numbers.

 4  5 

 12  15 

 5

 7

 3

 3

 7

VOCABULARY

Fill in the blanks.

1. numbers are greater than 0 and
   numbers are less than 0.


2. is called
   the set of.


3. To an integer means to locate it on the
   number line and highlight it with a dot.


4. The symbols and are called
   symbols.


5. The of a number is the distance
   between the number and 0 on the number line.


6. Two numbers that are the same distance from 0 on
   the number line, but on opposite sides of it, are called
   .

CONCEPTS

7. Represent each of these situations using a signed
   number.

a. $225 overdrawn

b. 10 seconds before liftoff

c. 3 degrees below normal

d. A deficit of $12,000

e. A 1-mile retreat by an army

8. Represent each of these situations using a signed
   number, and then describe its opposite in words.

a. A trade surplus of $3 million

b. A bacteria count 70 more than the standard

c. A profit of $67

d. A business $1 million in the “black”

e. 20 units over their quota

9. Determine what is wrong with each number line.
   a.

b.

c.

d.

− 3 − 2 − 1 01234

− 3 − 2 − 1 12345

− 3 − 2 − 1 02468

− 3 − 2 − 1 0123 4

 

{... , 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... }

Number Opposite Absolute value

39

0

 25

18. Is the absolute value of a number always positive?

NOTATION

19. Translate each phrase to mathematical symbols.

a. The opposite of negative eight

b. The absolute value of negative eight

c. Eight minus eight

d. The opposite of the absolute value of negative

eight