# 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 = ? ANSWER BOX:   RESULTS BOX:
 2 -150 ÷ -6 = ? ANSWER BOX:   RESULTS BOX:
 3 +96 ÷ -16 = ? ANSWER BOX:   RESULTS BOX:
 4 +102 ÷ +34 = ? ANSWER BOX:   RESULTS BOX:
 5 -144 ÷ +12 = ? ANSWER BOX:   RESULTS BOX: