# 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 = ? |

2. |
^{–}150 ÷ ^{–}6 = ? |

3. |
^{+}96 ÷ ^{–}16 = ? |

4. |
^{+}102 ÷ ^{+}34 = ? |

5. |
^{–}144 ÷ ^{+}12 = ? |