**Division of Integers: Negative and Positive Forms**

Division of Integers is similar to division of whole numbers (both positive) except the sign of the quotient needs to be determined.

- RULE 1: The quotient of a positive integer and a negative integer is negative.
- RULE 2: The quotient of two positive integers is positive.
- RULE 3: The quotient of two negative integers is positive.

If both the dividend and divisor are positive, the quotient will be positive.

(+16) ÷ (+4) = +4

If both the dividend and divisor are negative, the quotient will be positive.

(-16) ÷ (-4) = +4

If only one of the dividend or divisor is negative, the quotient will be negative.

(+16) ÷ (-4) = -4 or (-16) ÷ (+4) = -4

In other words, if the signs are the same the quotient will be positive, if they are different, the quotient will be negative.

**Explanation**

Dividing positive and negative numbers follows the same rules as multiplying positive and negative numbers. We’ll repost them here for you, using division examples instead of multiplication:

**Rule 1:** A positive number divided by a positive number gives you a positive number.

Example 1: This is the kind of division you’ve been doing for years, positive numbers divided by positive numbers. It would look like this: 12/3 = 4. 12 is positive, 3 is positive, thus, 4 is positive. We know that 12 and 3 are both positive because there are no negative signs in front of them.

**Rule 2:** A positive number divided by a negative number gives you a negative number

**Example 2:** This is new – for example, you might have 12/-3. The 12 is positive, but the 3 is negative, so our answer has to be negative. Thus, we divide the numbers as we normally would, and then put a negative sign in front of our answer. So, 12/-3 = -4. Please note that this also works when the negative number comes first and the positive number is second. For example, you may see it written -12/3 = -4, but don’t get confused. The combination of one positive and one negative number, no matter which order they come in, means your answer is going to be negative.

**Rule 3:** A negative number divided by a negative number gives you a positive number.

**Example 3:** This is also new—and doesn’t seem to make much sense, but it is a rule we have to follow when dividing negative numbers. So, for example, we may have the problem -12/-4. Both the 12 and the 4 are negative, so we know our answer is going to be positive. Therefore, -12/-4 = 3.

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