Mental Math

Date: 07/25/2003 at 13:35:27
From: Charlie
Subject: Mental Math

I would like to find a trick for multiplying by 3367.

3367*27
3367*33
3367*32
3367*18
3367*17
3367*14
3367*15

Date: 07/31/2003 at 09:42:23
From: Doctor Stephanie
Subject: Re: Mental Math

Hi Charlie,

When I have seen these problems on tests that are specially designed 
for mental math, I have tried to find similarities or trends from 
other problems like them. You really are on the right track. When I 
have seen a problem that has multiplied 3367 by another number, I 
have noticed that almost always the other number is a multiple of 3. 
When you multply 3367 by three you then find a number that is very 
common in the "mental math world," 10101.  

An example of how to use this would be to not view 3367 as 3367, but 
as 10101 * (1/3).

Here is an example of how you might be able to use this to your 
advantage:

          3367 X 15 = 
 
 10101 X (1/3) X 15 =
   
          10101 X 5 =

          50505 

Keep in mind that this trick is only useful if the other number is 
divisible by 3. 

I hope this perspective has helped you find another way to approach 
the problem or even find an even better "trick". If you have any more 
questions or if this is unclear, feel free to write back!     

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