Basic Mathematics for College Students

2.5 Dividing Integers 175

107. DECK SUPPORTS After a winter storm, a
     homeowner has an engineering firm inspect his
     damaged deck. Their report concludes that the
     original foundation poles were not sunk deep
     enough, by a factor of 3. What signed number
     represents the depth to which the poles should
     have been sunk?


108. DIETING After giving a patient a physical exam, a
     physician felt that the patient should begin a diet.
     The two options that were discussed are shown in
     the following table.

Ground level

Existing poles

6 feet deep

Poles should be

this deep

109. ADVERTISING The paid attendance for the last
     night of the 2008 Rodeo Houston was 71,906.
     Suppose a local country music radio station gave a
     sports bag, worth $3, to everyone that attended. Find
     the signed number that expresses the radio station’s
     financial loss from this giveaway.


110. HEALTH CARE A health care provider for a
     company estimates that 75 hours per week are lost
     by employees suffering from stress-related or
     preventable illness. In a 52-week year, how many
     hours are lost? Use a signed number to answer.

WRITING

111. Explain why the product of a positive number and
     a negative number is negative, using as an
     example.


112. Explain the multiplication rule for integers that is
     shown in the pattern of signs below.


113. When a number is multiplied by , the result is the
     opposite of the original number. Explain why.


114. A student claimed, “A positive and a negative is
     negative.” What is wrong with this statement?

REVIEW

115. List the first ten prime numbers.


116. ENROLLMENT The number of students attending
     a college went from 10,250 to 12,300 in one year.
     What was the increase in enrollment?


117. Divide:


118. What does the symbol mean?

175  4

 1







()()()()()

()()()()

()()()

()()

5(3)

Plan #1 Plan #2

Length 10 weeks 14 weeks

Daily exercise 1 hr 30 min

Weight loss per week 3 lb 2 lb

a. Find the expected weight loss from Plan 1.

Express the answer as a signed number.

b. Find the expected weight loss from Plan 2.

Express the answer as a signed number.

c. With which plan should the patient expect to lose

more weight? Explain why the patient might not

choose it.

1 Divide two integers.

Recall from Section 1.5 that every division has a related multiplication statement. For
example,

because 2(3) 6

6

3

 2

SECTION 2.5

Dividing Integers

In this section, we will develop rules for division of integers, just as we did earlier for
multiplication of integers.

Objectives

1 Divide two integers.

2 Identify division of 0and division

by 0.

3 Solve application problems by

dividing integers.