# 5.3.1 Investigating Multiplication by a Negative Number

The calculator can be accessed on the left-hand side bar under Toolkit.

Now it’s time to turn detective, and write some mathematical rules.

## Activity: Being a Mathematical Detective

Use the results from the tables for the previous activity to complete the following statements:

If you multiply a negative number by a positive number, the answer is …

### Discussion

Use the evidence from your tables that you wrote in your math notebook!

### Answer

If you multiply a negative number by a positive number, the answer is negative.

gives .

You can extend these rules a little. The order of the numbers doesn’t matter, so multiplying a positive number by a negative number also gives a negative answer. And the rules work for division too.

If you multiply a negative number by a negative number, the answer is …

### Answer

If you multiply a negative number by a negative number, the answer is positive. Again this rule also works for division.

gives .

Well done, you have discovered two other important mathematical rules about negative numbers!

5.3 Multiplication and Division with Negative Numbers