Multiplying by 0

Date: 03/09/2001 at 04:23:12
From: Bruce Griffis
Subject: Multiplying by 0

This may be a stupid question, but why, when multiplying any number by 
0, do you get 0? 

If I have a dollar in my hand and multiply it by 0, won't I still have 
a dollar? If not, then who took my dollar?

Date: 03/09/2001 at 08:41:28
From: Doctor Rick
Subject: Re: Multiplying by 0

Hi, Bruce.

They say the only stupid question is the one that you don't ask. Even 
"stupid questions" can lead to interesting insights if they make us 
look at the obvious in a new way. I don't know if I'll do that, but it 
could happen!

What does your illustration mean? If I have a dollar and multiply it 
by 2, I have $2. I could just as well ask where the second dollar came 
from, as you can ask where your dollar went.

Let's fix your picture to make it clear where money is coming from. 
Let's say you're a barber and every customer tips you a dollar. At the 
end of the day, how much have you made in tips? Multiply a dollar by 
the number of customers you had. If you had 10 customers, you made 
$10. If you had 20 customers, you made $20.

So, what about the day that your shop was closed because of a 
blizzard? By your reasoning, you'd still make a buck, even though you 
had zero customers. 

No, it's clear that you make $0: $1 times 0 customers is $0.

- Doctor Rick, The Math Forum
  http://mathforum.com/dr.math/ 

Date: 03/09/2001 at 08:48:18
From: Doctor Peterson
Subject: Re: Multiplying by 0

Hi, Bruce.

Picture multiplication by a whole number as making that many piles, 
each containing the original amount. If I start with a dollar and 
multiply by 5, I make 5 piles with a dollar in each. If I multiply by 
zero instead, I have zero piles; and zero piles (no matter how much I 
claim "each of them" has) will contain zero dollars.

You can also go in the other direction, multiplying zero by anything; 
this should give the same result. So start with 0 dollars, and make 57 
piles, each containing zero dollars. Again, the total is zero.

I'm wondering if you are confusing "multiplying by 0" with "adding 
zero times as much." If you have a dollar in your hand and multiply it 
by ONE, you will still have the same amount; multiplying by one 
doesn't change anything. Multiplying by 2 takes what you had, makes 
another copy of it, and gives you back twice what you started with. 
But multiplying by zero takes away what you had and gives you none of 
it back.

- Doctor Peterson, The Math Forum
  http://mathforum.com/dr.math/