Multiplying and Dividing Positive and Negative Numbers
Multiplication and division of integers both work in a very similar pattern to adding and subtracting. The short description of the process is that we multiply or divide like normal, and if the signs match (both positive or both negative) the answer is positive. If the signs don't match (one positive and one negative), the answer is negative.
Here are examples of multiplication and division of integers with matching signs:
In each example, since the two integers have matching signs, we multiply or divide the two numbers, and write the product or quotient as a positive number.
The product or quotient of two positive numbers is positive. The product or quotient of two negative numbers is also positive.
Here are some examples of multiplication and division of integers with opposite signs:
In these examples, the two integers have opposite signs: one is positive and the other is negative. We multiply or divide the two numbers, and write the product or quotient as a negative numbers.
The product or quotient of a positive and negative number is negative.
There are a few things to be careful of when working with integers. First, be sure not to confuse a problem like - 3 - 8 with -3 (-8). The second problem is a multiplication problem, because there is nothing between the 3 and the parenthesis. If there is no operation written in between the parts, then we assume that means we are multiplying. The - 3 - 8 problem is subtraction, because the subtraction separates -3 from what comes after it. Another item to watch out for is to be careful not to mix up the pattern for adding and subtracting integers with the pattern for multiplying and dividing integers. They can look very similar, for example if the signs match on addition, we keep the sign, even if it is negative: - 3 + (- 7) = - 10. However, if the signs match in multiplication, the answer is always positive: (-3)(-7) = 21.
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT: HTTP://WALLACE.CCFACULTY.ORG/BOOK/BOOK.HTML