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## Multiplication is twice as far to the left of the origin as -1. Thus, .

Similarly, is twice as far to the left of the origin as -5. Thus, .

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:

 a b a x b + + + - + - + - - - - +
• The product of two numbers of the same sign is positive
• The product of two numbers of opposite signs is negative

### Example 3.

Look at some examples of multiplying negative numbers below:

 × =

Here are some further examples of multiplying three numbers:

 × × =

### Exercise 4.

Try multiplying some negative numbers yourself.

 × =

Got that down? Then try these harder exercises:

 × × × =

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