Multiplying a Number by Zero

Date: 09/14/2001 at 10:24:41
From: Almas
Subject: When zero multiply with number

When any number is multiplied by zero, why is the result zero?

Date: 09/14/2001 at 15:04:06
From: Doctor Ian
Subject: Re: When zero multiply with number

Hi Almas,

Try thinking of multiplication this way. When we multiply two numbers 
- call them A and B - we'll take a yardstick of length A, and use it 
to move B steps away from zero.  So 2 * 3 would look like this:

    2   2   2
  |---|---|---|   <-- 2 * 3
  +-------------------------
  0

Note that multiplication is commutative - that is, you can multiply 
two numbers in either order:

    2   2   3
  |---|---|---|   <- 2 * 3
  +-------------------------
  0
  |-----|-----|   <- 3 * 2
     3     3

If I multiply something by 1, I just take the one step:

        6
  |-----------|   <- 6 * 1
  +-------------------------
  0

Now, what happens if I multiply something by zero?  I start at zero, 
and jump... no times at all!  So I stay at zero, regardless of what 
the other number is. 

Does this make sense? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/