Integer Division

Problem: Mrs. Jenson owes $8,000 on her car loan. Each of her 4 children is willing to pay an equal share of this loan. Using integers, determine how much money each of her children will pay.

Solution: Owing $8,000 can be represented by –8,000. We must divide –8,000 by 4 in order to solve this problem. However, we need rules for dividing integers in order to continue.

Rule 1: The quotient of a positive integer and a negative integer is a negative integer.

Rule 2: The quotient of two negative integers or two positive integers is a positive integer.

We can now use Rule 1 to solve the problem above arithmetically:   –8,000 ÷ +4 = –2,000. Each of Mrs. Jenson’s four children will pay $2,000. Let’s look at some more examples of dividing integers using the above rules.


Example 1: Find the quotient of each pair of integers.

Dividing Integers
Integers Quotient Rule Used
+24 ÷ +12 = +2 Rule 2
+24 ÷ –12 = –2 Rule 1
–24 ÷ +12 = –2 Rule 1
–24 ÷ –12 = +2 Rule 2

Example 2: Find the quotient of each pair of integers.

Dividing Integers
Integers Quotient Rule Used
+27 ÷ +3 = +9 Rule 2
+27 ÷ –3 = –9 Rule 1
–27 ÷ +3 = –9 Rule 1
–27 ÷ –3 = +9 Rule 2

Example 3: Find the quotient of each pair of integers.

Dividing Integers
Integers Quotient Rule Used
+99 ÷ +11 = +9 Rule 2
+80 ÷ –16 = –5 Rule 1
–72 ÷ +12 = –6 Rule 1
–91 ÷ –13 = +7 Rule 2

Summary: The quotient of a positive integer and a negative integer is a negative integer, and the quotient of two negative integers or two positive integers is a positive integer.


Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. –81 ÷ +3 = ?

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2. –150 ÷ –6 = ?

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3. +96 ÷ –16 = ?

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4. +102 ÷ +34 = ?

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5. –144 ÷ +12 = ?

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RESULTS BOX: