**Multiplication of Integers: Negative and Positive**

Multiplication of Integers is similar to multiplication of whole numbers (both positive) except the sign of the product needs to be determined.

RULE 1: The product of a positive integer and a negative integer is negative.

RULE 2: The product of two positive integers is positive.

RULE 3: The product of two negative integers is positive.

Examples:

Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10

Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12

Rule 3: 1. (-6) x (-8) = +48 2. (-2) x (-4) = +8

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

**Explanation**

Multiplying positive and negative numbers has far less rules than adding or subtracting positive and negative numbers, in fact there are only three that you’ll have to remember:

**Rule 1:** A positive number times a positive number gives you a positive number.

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

**Rule 2:** A positive number times a negative number gives you a negative number.

**Example 2:** This is new – for example, you might have 4 x -3. The 4 is positive, but the 3 is negative, so our answer has to be negative. Thus, we multiply the numbers together as we normally would, and then put a negative sign in front of our answer. So, 4 x -3 = -12. 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 -3 x 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 times 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 multiplying negative numbers together. So, for example, we may have the problem -3 x -4. Both the 3 and the 4 are negative, so we know our answer is going to be positive. Therefore, -3 x -4 = 12.

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