Integer Division

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Integer Division

Unit 5 > Lesson 7 of 11

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 = ?

ANSWER BOX:
RESULTS BOX: