Question 120827
Think of yourself standing on the number line at Zero.  You perform multiplications of {{{a*b}}} by taking {{{a}}} steps that are {{{b}}} units long each.  (you need long legs if b is large).


Now, the signs on {{{a}}} and {{{b}}} tell you the direction you are facing when you start and whether you walk forwards or backwards respectively.


Here's the rule:  if {{{a}}} is positive, you face to the right, and if {{{a}}} is negative, you face to the left.  Then, if {{{b}}} is positive you walk forwards, in the direction that you are facing, but if {{{b}}} is negative, you walk backwards, away from the direction that you are facing.


Examples:  Multiply 2 times 3.  Face RIGHT and take 2 steps FORWARD, each step being 3 units.  You end up at positive 6.


Multiply -2 times 3.  Face LEFT and take 2 steps FORWARD, each step being 3 units.  You end up at negative 6.


Multiply 2 times -3.  Face RIGHT and take 2 steps BACKWARD, each step being 3 units.  You end up at negative 6.


Multiply -2 times -3.  Face LEFT and take 2 steps BACKWARD, each step being 3 units.  You end up at positive 6.


Hope that helps.
John