Basic Mathematics for College Students

2.5 Dividing Integers 179

Self Check 3

Divide, if possible:

a. b.

Now TryProblems 45 and 47

0 (6)

 12

0

Self Check 4

SELLING BOATSThe owner of a sail

boat reduced the price of the boat

by an equal amount each month,

because there were no interested

buyers. After 8 months, and a $960

reduction in price, the boat sold.

By how much was the price of the

boat reduced each month?

Now TryProblem 81

3 Solve application problems by dividing integers.

Problems that involve forming equal-sized groups can be solved by division.

EXAMPLE (^4) Real Estate Over the
course of a year, a homeowner reduced the
price of his house by an equal amount each
month, because it was not selling. By the end
of the year, the price was $11,400 less than at
the beginning of the year. By how much was
the price of the house reduced each month?
Analyze

• The homeowner dropped the price $11,400 in 1 year. Given


• The price was reduced by an equal amount each month. Given


• By how much was the price of the house reduced each month? Find

Form We can express the drop in the price of the house for the year as.
The phrase reduced by an equal amount each monthindicates division.
We translate the words of the problem to numbers and symbols.

is equal to divided by

11,400  12

SolveTo find the quotient, we use the rule for dividing two integers that have
different signs. First, we find the absolute values: and.

Divide the absolute values, 11,400 and 12,

to get 950. Then make the final answer

negative.

StateThe negative result indicates that the price of the house was reducedby $950
each month.

CheckWe can use estimation to check the result. A reduction of $1,000 each
month would cause the price to drop $12,000 in 1 year. It seems reasonable that a
reduction of $950 each month would cause the price to drop $11,400 in a year.

11,400 12  950

0 11,400 0 11,400 0120  12

The amount the

price was reduced

each month

the number

of months in

1 year.

the drop in the

price of the house

for the year

The amount the

price was reduced

each month

$11,400

David McNew/Getty Images

950

12 11,400

 10 8

60

 60

00

 00

0



EXAMPLE 3

Divide, if possible: a. b.

StrategyIn each case, we need to determine if we have division of0 or division
by0.

WHYDivision of 0by a nonzero integer is defined, and the answer is 0. However,
division of a nonzero integer by 0is undefined; there is no answer.

Solution

a. is undefined. This is division by 0.

b. 0 (8) 0 because 0(8) 0. This is division of 0.

 4

0

0 (8)

 4

0