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. Negative multiplication Positive or Positive multiplication Negative = Negative
  2. Negative division Positive or Positive division Negative = Negative
  3. Negative multiplication Negative = Positive
  4. Positive division Positive = Positive

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

When you used your calculator, you found that equation left hand side open two minus close multiplication four equals right hand side eight minus, this was the same as four lots of open two minus close, or sum with, 4 , summands open two minus close plus open two minus close plus open two minus close plus open two minus close, which gives an answer of 8.

You also found that open four minus close multiplication open two minus close equals eight. The product of any two negative numbers can be shown to be positive.

Now, consider open six minus close division two equals minus three. An alternative way of considering this problem is to say: “What do I have to multiply 2 by to get ...” open six minus close? Since 2 is positive, and 6 is a negative number, the answer must be negative. Because equation left hand side two multiplication open three minus close equals right hand side open six minus close, then equation left hand side open six minus close division two equals right hand side three minus.

Similarly, for open six minus close division open two minus close, since you would need to multiply open two minus close by 3 to get open six minus close, you can deduce that open six minus close division open two minus close equals three.

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