Remainders

Date: 07/02/98 at 10:54:59
From: Ted
Subject: Question

Dear Dr.Math,

I am doing very good at school. In math, I can do addition, 
subtraction, multiplication, and division. But I don't know how to do 
remainders. Can you help me?

Date: 07/02/98 at 12:25:27
From: Doctor Mike
Subject: Re: Question
  
Dear Ted, 
   
I'm glad you are doing well. Things we are good at are more fun. 
  
I'm not sure whether you need to know what remainders are all about, 
or whether you need to know how to do a certain kind of problem. If 
you need specific information about a problem after you read my e-mail 
to you, please write back giving a particular problem you would like 
us to work out in detail.
  
As far as the "idea" of remainder, consider this situation. You have a 
pile of eggs and you are asked to put them into egg cartons, and you 
must completely fill up a carton before you move on to the next one.  
Let's say you have 50 eggs. By the way, egg cartons can hold exactly a 
dozen (12) eggs.   
    
   Step 1: Start with 50 eggs, put 12 in first carton, 38 eggs left
   Step 2: Start with 38 eggs, put 12 in second carton, 26 eggs left
   Step 3: Start with 26 eggs, put 12 in third carton, 14 eggs left
   Step 4: Start with 14 eggs, put 12 in fourth carton, 2 eggs left 
   Step 5: Start with 2 eggs, not enough to fill another carton, quit.
    
The way you would say this in the language of division and remainders
is that "12 goes into 50 a total of 4 times, with a remainder of 2"
or "50 divided by 12 gives a quotient of 4 with a remainder of 2". In
symbols, this is often written something like the following :   
     
                  4  R=2
                ----         
            12 / 50 
           ----      
  
Notice that if I had started out with 48 eggs, there would have been
zero eggs left at the end of Step 4, and the remainder would have
been zero. When this happens, we say that 12 goes into 48 evenly.
   
I hope this helps.  Have a good summer.  Bye for now. 

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