is twice as far to the left of the origin as -1.
Similarly, is twice as far to the left of the origin as -5.
In general, for any two numbers a and b, we have .
We say "a positive times a negative is negative".
By the commutative law:
and in general
So we say "a negative times a positive is negative".
Using the properties and we obtain
(-a)(-b) = ab
So we say "a negative times a negative is positive".
The following table of signs is useful in remembering these rules:
Look at some examples of multiplying negative numbers below:
Here are some further examples of multiplying three numbers:
Try multiplying some negative numbers yourself.
Got that down? Then try these harder exercises: