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Chapter 2—Integers

2-8 Dividing Signed Integers

When you complete the work for this section, you should be able to:
  • Demonstrate a mastery of the procedures for dividing signed integers.

fig0208_01.jpg (9093 bytes)
Terminology for the division of signed integers.

Procedure

The procedure for dividing signed integers is basically identical to the procedure for multiplying them:

Step 1: Divide the absolute value of the terms.
Step 2: Give the appropriate sign to the quotient.
  • Positive if the terms both have the same sign.
  • Negative if the terms have opposite signs.

Note: There is no difference between the way you should handle the signs for multiplication and division--positive result for same signs, negative result for opposite signs.

Dividing Integers Having the Same Sign

Procedure

When the divisor and dividend have the same sign—both positive or both negative—the quotient is always positive.

So:

  1. Divide the two terms, disregarding the signs.
  2. Show the quotient as a positive integer.

 


Dividing integers that have the same sign.

Notice that:

When the signs of the two terms are the same, the result is positive.

Example 1

Problem

(+ 14) (+ 2) = _____

Procedure
  1. Divide the absolute value of the terms.
|+14| |+2| = 7
  1. Assign the appropriate sign to the quotient.
Both terms are positive, so the result is positive

+7

Solution

(+ 14) (+ 2) = +7

Or you might express this answer more simply as
14 2 = 7

Example 2

Problem

(– 24) (– 8) = _____

Procedure
  1. Divide the absolute value of the terms.
| –24 | | –8 | = 3
  1. Assign the appropriate sign to the quotient.
Both terms are negative, so the result is positive

+3

Solution

( – 24) ( – 8) = ( +3)

Or you might express this answer more simply as
– 24 ( – 8) = 3.

Examples and Exercises #1

Dividing Integers Having the Same Sign

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Dividing Integers Having Opposite Signs

Procedure

When the divisor and dividend  have the opposite sign—one is positive an the other is negative—the quotient is always negative.

So:

  1. Divide the absolute values of the terms.
  2. Show the quotient as a negative integer.
 


Dividing integers that have opposite signs.

Notice that:

When the signs of the two terms are different, the result is negative.

Example

Problem

( +24) ( – 8) = _____

Procedure
  1. Divide the absolute value of the terms.
| +24 | | – 8 | = 3
  1. Assign the appropriate sign to the quotient.
The terms have opposite signs, so the result is negative

–3

Solution

( +24) ( – 8) = (  – 3)

Or you might express this answer more simply as
24 ( – 8) =  – 3

Examples and Exercises #2

Dividing Integers Having Opposite Signs

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Lesson Summary

To divide integers that have the same sign (both positive or both negative):

  1. Divide the integers, disregarding the signs.
  2. Show the quotient as a positive integer.

To divide integers that have opposite signs:

  1. Divide the integers, disregarding the signs.
  2. Show the quotient as a negative integer.

Examples and Exercises #3

Dividing Signed Integers

These examples and exercises will show you that you've mastered the whole idea of dividing signed integers.

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015