Dividing Two-Digit Numbers

Date: 03/01/2002 at 17:32:40
From: Callie
Subject: Math

How do you divide 2-digit numbers?

Date: 03/01/2002 at 18:46:01
From: Doctor Ian
Subject: Re: Math

Hi Callie,

You know how multiplication is just repeated addition?

  12*11 = 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 

  11*12 = 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 

Well, division is kind of like repeated subtraction. For example, if I 
want to divide 121 by 11, I can do this:

  121 
 - 11     Subtract 1st time
  ---
  110
 - 11              2nd
  ---
   99
 - 11              3rd
  ---
   88
 - 11              4th
  ---
   77
    .
    .
  ---
   22             11th
 - 11
  ---
   11
 - 11             12th
  ---
    0

That is, the following are just two ways of saying the same thing:
          _____
  1)   11 ) 121  = 12          

  2)   11 subtracted 12 times from 121 is zero

So when you don't know what else to do, you can use this definition.  
For example,

        1
        1
        1 
     ____
  24 ) 79
       24    That's 1
       --
       55
       24    That's 2
       --
       31
       24    That's 3
       --
        7    Remainder

             Answer = 3 remainder 7

Now, note that you don't _have_ to do the subtractions 1 at a time.  
In this example, you might see right away that 2 * 24 must be less 
than 79:

        1
        2
     ____
  24 ) 79
       48    That's 2
       --
       31
       24    That's 3
       --
        7    Remainder

             Answer = 3 remainder 7

Or - and this is what your teacher _wants_ you to do - you might do 
enough math in your head to figure out that 3 is the LARGEST value it 
could possibly be:

        3
     ____
  24 ) 79
       72    That's 3
       --
        7    Remainder

             Answer = 3 remainder 7

But that _is_ kind of a pain, and the more digits that are involved, 
the bigger pain it is.  

In the end, you get the same answer no matter how many subtractions 
you have to do. As you get more practice, you'll get better at 
guessing things like how many times 24 will go into 79; but I would 
say, at first, don't sweat it. It's more important to understand 
what's actually going on, even if it means you do a few more steps, 
than to memorize 'how to do division' without understanding it. 

Does this make sense?  Write back if any of this isn't clear, or if 
you'd like to talk about it some more. 

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