Adding Numbers in the 100s

Date: 7/31/96 at 17:42:23
From: Anonymous
Subject: Adding Big Numbers

How do you add 500 + 995? I just don't understand.

Thank you,
   Taylor

Date: 8/1/96 at 17:1:40
From: Doctor Mike
Subject: Re: Adding Big Numbers

Hello Taylor,
  
Here is the usual way this problem is written down and solved.
  
      500 
     +995 
    ------
     1495 
  
You start from the right.  You find 0 and 5 is the "units"
position, which add together to give 5 for that position in
the answer.  Move to the left one place to the "tens" position.
There, the 0 and 9 add together to give 9 in a similar way.
Next move to the left one more place to the "hundreds" position.
There, 5 and 9 add together to give 14.  Now ask yourself what
14 means there.  We are working with hundreds at this point, so
this is 14 hundreds, or 1400, which is the same as 400 and 1000
added together.  I wrote that as a 4 in the hundreds position,
and a one in the thousands position.  
  
But now let's think of it in a couple of different ways so you
can better see what's going on.  Because 500 is 495 + 5 , the
original problem is really the same as adding 495 + 5 + 995.
If you add these three numbers up starting with the two numbers
on the right, you see that the problem is really the same as  
adding 495 + 1000.  That's because 5+995 is one thousand.  Now,
it's easy to see that 495 + 1000 is 1495, as we got before.
  
Finally, think of these numbers as representing pennies.  500 is
500 pennies, or 5 dollars.  1000 is 1000 pennies, or ten dollars.
I could go through the same analysis as in the previous paragraph.
I will do that, but with a slight change.  I'm going to write the
money amounts using the dollar sign "$" and decimal point instead
of writing them as a whole number of pennies.  Here goes : 
  
      $5.00 + $9.95         is the same as 
      $4.95 + $0.05 + $9.95 which is the same as
      $4.95 + $10.00        which is the same as
      $14.95                which is the same as
       1495  pennies, which is the answer.
  
I hope this helps to get you started.  Please write back to us
if you need any more help. 

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/