Adding Four 3-Digit Numbers

Date: 08/13/98 at 21:18:45
From: melisha
Subject: Addition

How do I add problems with 4 sets of numbers? For example:

   457 + 458 + 954 + 958 =

Date: 08/14/98 at 00:04:52
From: Doctor Mike
Subject: Re: Addition
   
Hi Melisha, 

I suppose you want to do it yourself and not depend on a calculator.  
That's great. When I do this by hand, I start off by lining them up 
vertically like this:
   
     457 
     458 
     954 
   + 958 
    ----- 
    
That way I see all the numbers in the "ones" column together. Do you 
know what I mean by that? The far right digits in each number stand 
for so many ones. That's the 7, 8, 4, and another 8. 

The next column over has a 5 in that column for each of the 3 numbers. 
That 5 means 5 "tens" or 50, so that's called the "tens" column. 

The far left column is where the numbers stand for so many hundreds, 
like "4" hundreds or "9" hundreds. 

So, let's go. The first thing I do is to add up all the numbers in 
the ones column: 7 + 8 + 4 + 8 = 27. Now 27 is 20 + 7, or 2 tens and 
7 ones, so I write the 7 in the ones place in the answer, and as just 
a reminder, I write the 2 on top in the tens column for the next step:

      2
     457 
     458 
     954 
   + 958 
    ----- 
       7   
   
Next I add all the stuff in the tens column: 2 + 5 + 5 + 5 + 5 = 22. 
Keep in mind that what I am doing here is adding tens - so I have 22
tens. That is 20 tens plus 2 tens. The 20 tens is 2 hundred. (In money 
terms, that is like saying that 20 dimes is 2 dollars.) What I do with 
this is write the 2 tens as a 2 in the tens place of the answer. And 
as just a reminder again I write the 2 hundreds on top in the hundreds 
column for the next step: 
      
     2
     457 
     458 
     954 
   + 958 
    ----- 
      27   
  
We are almost done. I add all the hundreds 2 + 4 + 4 + 9 + 9 = 28 
which means 28 hundreds, or 2 thousands and 8 hundreds. This I write
down like this: 
   
     457 
     458 
     954 
   + 958 
    ----- 
    2827 
   
That is the answer. 

The method depends on knowing about the "place value" system we use to 
write down numbers. That is, 1234 means 1 thousand, 2 hundred, thirty 
(3 tens) and 4 ones. Which "place" the digits are in says what they 
mean.  
   
The thing I did of writing a number temporarily on top, so I would
remember, is sometimes called "carrying." It's like carrying a number 
fron one place to another. You carry 20 ones to the tens column where 
it is 2 tens. You carry 20 tens to the hundreds column where it is 2 
hundreds.   
     
So that's what really happens when we add. Pretty fantastic! I hope 
this was what you needed to know. Please write back if you need to 
know something else.   
  
- Doctor Mike, The Math Forum
Check out our web site! http://mathforum.org/dr.math/