# 5.3.2 Rules for Multiplication and Division of Signed Numbers

These rules for multiplication and division are really useful, so be sure to add them to your math notebook and take a little time to learn them.

1. or = Negative
2. or = Negative
3. = Positive
4. = Positive

Let’s think some more about what is happening here.

When you used your calculator, you found that , this was the same as four lots of , or , which gives an answer of 8.

You also found that . The product of any two negative numbers can be shown to be positive.

Now, consider . An alternative way of considering this problem is to say: “What do I have to multiply 2 by to get ...” ? Since 2 is positive, and 6 is a negative number, the answer must be negative. Because , then .

Similarly, for , since you would need to multiply by 3 to get , you can deduce that .

Now let’s get some practice without your calculator—you can do it! Look back at the rules if you need to.

5.3.1 Investigating Multiplication by a Negative Number

5.3.3 Working with Negative Numbers by Hand