Basic Mathematics for College Students

2.4 Multiplying Integers 167

Self Check 2

Multiply:

a.

b.

c.

d.

Now TryProblems 33, 37, 41, and 43

4,100(20,000)

34(15)

12(2)

9(7)

Multiplying Two Integers

To multiply two nonzero integers, multiply their absolute values.

1. The product of two integers that have the same (like) signs is positive.


2. The product of two integers that have different (unlike) signs is negative.

We now summarize the multiplication rules for two integers.



Using Your CALCULATOR Multiplication with Negative Numbers

At Thanksgiving time, a large supermarket chain offered customers a free

turkey with every grocery purchase of $200 or more. Each turkey cost the

store $8, and 10,976 people took advantage of the offer. Since each of the

10,976 turkeys given away represented a loss of $8 (which can be expressed

as $8), the company lost a total of 10,976($8). To perform this

multiplication using a calculator, we enter the following:

Reverse entry: 10976 8

Direct entry: 10976 8

The negative result indicates that with the turkey giveaway promotion, the

supermarket chain lost $87,808.

 () ENTER  87808

 /   87808

3 Perform several multiplications to evaluate expressions.

To evaluate expressions that contain several multiplications, we make repeated use of
the rules for multiplying two integers.

EXAMPLE (^2) Multiply:
a. b. c. d.
StrategyWe will use the rule for multiplying two integers that have the same
(like) signs.
WHYIn each case, we are asked to multiply two negative integers.
Solution
a.Find the absolute values: and.
Multiply the absolute values, 5 and 9, to get 45.
The final answer is positive.
b.Find the absolute values: and.
Multiply the absolute values, 8 and 10, to get 80.
The final answer is positive.
c.Find the absolute values: and.
Multiply the absolute values, 23 and 42, to get 966.
The final answer is positive.
d.We can extend the method discussed in Section 1.4 for multiplying whole-
number factors with trailing zeros to products of integers with trailing zeros.
Attach six 0’s after 75.
Multiply 25 and 3 to get 75.

2,500(30,000)75,000,000

42

 23

126

840

966

23(42) 966

0  230  23 0  420  42

8(10) 80

0  80  8 0  100  10

5(9) 45

0  50  5 0  90  9

5(9) 8(10) 23(42) 2,500(30,000)