Basic Mathematics for College Students

2.4 Multiplying Integers 165

SECTION 2.4

Multiplying Integers

Multiplication of integers is very much like multiplication of whole numbers. The only
difference is that we must determine whether the answer is positive or negative.
When we multiply two nonzero integers, they either have different signs or they
have the same sign. This means that there are two possibilities to consider.

Objectives

1 Multiply two integers that have

different signs.

2 Multiply two integers that have

the same sign.

3 Perform several multiplications to

evaluate expressions.

4 Evaluate exponential expressions

that have negative bases.

5 Solve application problems by

multiplying integers.

1 Multiply two integers that have different signs.

To develop a rule for multiplying two integers that have different signs, we will find
, which is the product of a positive integer and negative integer. We say that the
signs of the factors are unlike.By the definition of multiplication, means that we
are to add four times.

Write 3 as an addend four times.

Use the rule for adding two integers that have the same sign.

The result is negative. As a check, think in terms of money. If you lose $3 four times, you
have lost a total of $12, which is written $12.This example illustrates the following rule.

 12

4(3)(3)(3)(3)(3)

 3

4(3)

4(3)

Multiplying Two Integers That Have Different (Unlike) Signs

To multiply a positive integer and a negative integer, multiply their absolute

values. Then make the final answer negative.

EXAMPLE (^1) Multiply:
a. b. c. d.
StrategyWe will use the rule for multiplying two integers that have different
(unlike) signs.
WHYIn each case, we are asked to multiply a positive integer and a negative integer.
Solution
a.Find the absolute values: and.
Multiply the absolute values, 7 and 5, to get 35.
Then make the final answer negative.
b.Find the absolute values: and.
Multiply the absolute values, 20 and 8, to get 160.
Then make the final answer negative.
c.Find the absolute values: and.
Multiply the absolute values, 93 and 16, to get 1,488.
Then make the final answer negative.
d.Recall from Section 1.4, to find the product of a whole number and 10, 100,
1,000, and so on,attach the number of zeros in that number to the right of the
whole number.This rule can be extended to products of integers and 10, 100,
1,000, and so on.
34(1,000)34,000 Since 1,000 has three zeros, attach three 0’s after 34.
93
 16
558
930
1,488

 93  16 1,488

0  930  93 0160  16

20(8) 160

0200  20 0  80  8

7(5) 35

070  7 0  50  5

7(5) 20(8)  93  16 34(1,000)

Self Check 1

Multiply:

a.

b.

c.

d.

Now TryProblems 21, 25, 29, and 31

98(1,000)

 75  17

30(4)

2(6)