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Signed Numbers

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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