Adding Six-digit Numbers

Date: 12/23/96 at 09:49:37
From: Sarah Hobbs
Subject: Adding

I've done everything I can to try and figure out the sum of 
100,234 and 678,123.

Date: 12/24/96 at 01:27:54
From: Doctor Mike
Subject: Re: Adding

Hi Sarah,   

Sometimes you can add numbers easily by just adding the numbers in the 
"ones" place, then the numbers in the "tens" place, then the numbers 
in the "hundreds" place, and so on.  In this problem you are in luck!  
Let's take a look.  The first number ends with 4 ones, and the second 
number ends with 3 ones.  That makes 7 ones.  We start writing it down 
like this: 
  
       100234
      +678123
     ---------
            7
   
Now look at the tens place, where the first number has 3 tens and
the second number has 2 tens.  That makes 5 tens, so we continue: 
   
       100234
      +678123
     ---------
           57
  
You just keep on like this until you get to the left end, like this: 
   
       100234
      +678123
     ---------
       778357 
   
For your problem, that is absolutely all you need to do.  However, I 
should warn you that it can get more complicated than this.  What if 
the 2 numbers were 100,294 and 678,153 ?  Then you still start the 
same way, and after you do, the ones place it looks like this: 
  
       100294
      +678153
     ---------
            7 
  
So now we look at the tens place where we have 9 tens in the first
number and 5 tens in the second number.  Add that together and you
get 9+5 tens, or 14 tens.  We cannot write 14 in a place with room
just for one digit.  What to do?  No big problem, really.  14 tens
is just 10 tens plus 4 tens, right?  That's the same as 1 hundred 
plus 4 tens.  What we'll do is just write down the 4 tens for right
now, and make SURE to remember to add on an extra hundred when we
get to that step.  Okay, let's do that: 
  
       100294
      +678153
     ---------
           47
   
We wrote down 4 in the tens place of the answer, but we had better
remember to make up for that in the "hundreds" step coming up: 
   
       100294
      +678153
     ---------
          447
  
Normally, we would add 2+1 to get 3 in the hundreds place, but we
instead needed to add on an extra one from the previous step when we 
were doing the tens.  When you start getting this in school, you will 
probably hear the word "carry" or "carrying" used.  What we just did 
would be called "carrying a 1 to the hundreds place".  If you really 
understand what is happening, like we do in this problem, then it is 
fine to talk like it that way.  Anyway, from here on the problem is 
exactly the same as before: 
  
       100294
      +678153
     ---------
       778447
  
This answer may be a bit longer than you expected, but look on it as 
an advance warning of what is coming up soon.  Have fun. 
  
I hope this helps.

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