Basic Mathematics for College Students

176 Chapter 2 The Integers

and

because

We can use the relationship between multiplication and division to help develop

rules for dividing integers. There are four cases to consider.

Case 1: A positive integer divided by a positive integer

From years of experience, we already know that the result is positive. Therefore,the

quotient of two positive integers is positive.

Case 2: A negative integer divided by a negative integer

As an example, consider the division. We can find? by examining the related

multiplication statement.

Related multiplication statement Division statement

Therefore,. This example illustrates that the quotient of two negative integers

is positive.

Case 3: A positive integer divided by a negative integer

Let’s consider. We can find? by examining the related multiplication statement.

Related multiplication statement Division statement

Therefore,. This example illustrates that the quotient of a positive integer and

a negative integer is negative.

Case 4: A negative integer divided by a positive integer

Let’s consider .We can find? by examining the related multiplication statement.

Related multiplication statement Division statement

Therefore,. This example illustrates that the quotient of a negative integer

and a positive integer is negative.

We now summarize the results from the previous examples and note that they are

similar to the rules for multiplication.

 212  6

So the quotient is 6.

 12

2

?

This must be 6 if the

product is to be 12.

?(2) 12

 212 ?

(^) ^122  6
So the quotient is 6.

12

 2

?

This must be 6 if the

product is to be

positive12.

?(2) 12

(^) ^122 ?

^122  6

So the quotient

is positive6.

 12

 2

?

This must be positive 6

if the product is to be

negative12.

?(2) 12

^122 ?

4(5) 20

20

5

 4

Dividing Two Integers

To divide two integers, divide their absolute values.

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


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