What is 12/18 ?

Date: 27 Apr 1995 13:16:46 -0400
From: Jennifer La
Subject: (none)

Dear Dr. Math,

Our third grade class is learning division and remainders. I want to ask 
you a math problem. 12/18 = ?
From,
Jennifer La

Date: 9 May 1995 22:08:48 -0400
From: Dr. Sydney
Subject: Re: your mail

Dear Jennifer,

Hello!  I'm glad you wrote to Dr. Math!

Long divison is a helpful tool in figuring out problems like what is 12
divided by 18.  

Write out your problem like this:
  ____
18|12

First notice that 12 is smaller than 18.  That means that 12 divided by 18
is going to be less than one!  Whenever you divide a smaller number by a
larger number, you get a number that is less than one.  You can think of
12/18 as being a part of a whole -- a fraction (hence the name fraction,
which you may not have heard yet) of the number 1.  If you were to look at a
number strip, the number 12/18 would fall in between the markings for 0 and
1.  

That said, we should now move on to the problem.  When dividing a smaller
number by a bigger number, we must take a few more extra steps than we do
when dividing a bigger number by a smaller number.  There are several
approaches we can take.  One way to figure out the answer is to deal with
decimal points.   Write the problem like this:
  _____
18|12.0

We can do this because 12 = 12.0 
(If you want to know why this is, write us back!)

Then write a decimal point above the 12.0 exactly above the decimal point in
the 12.0.  Now go ahead with long-division as if you were dividing 120 by
18.  Keep pulling down 0's and repeating the divison process until you can't
go any further or until a pattern emerges.  If you get a pattern, you can
ask your teacher or write back, and we'll tell you what that pattern means
and how to write it down!  

I hope it goes well!  Enjoy, and write back if you have any questions.

--Sydney, "Dr. Math"