Learning Long Division

Date: 2/2/96 at 16:6:19
From: Anonymous
Subject: Long Division

I'm in a 4th grade class. We are getting ready for T.A.A.S.
We are about to study long division.  I want to learn more about 
it before the rest so I can be ready instead of waiting for the math
book!

Date: 3/24/96 at 22:41:46
From: Doctor Jodi
Subject: Re: Long Division

Hi there! 

First of all, division is the opposite of multiplication.  So if I 
divide 72 by 3 I should get 24, since 3*24 = 72.  

(You might notice that our division looks sort of like the 
multiplication:

 24
X 3
___
 12
 60
----
 72

just in a different order.)

OK, back to long division.

The process of long division goes sort of like this:

1. Write the problem
2. Make a guess of what the answer will be
3. Check your guess, fix it if you need to
4. "Bring down"
5. Repeat  steps 2-4 until you're out of digits

So for 72 divided by three, the process would go like this:

1. Write the problem
  ----
3|72

That means 72 divided by 3, also called 3 into 72, etc.

2. Make a guess of what the answer is.

Let's cover up the 2 in 72 for a minute:  (This lets us ignore the place 
value, etc.)
  ----
3|7?

Now let's ask:  How many times does 3 go into 7?

You can make whatever guess you want.  But since we have a good idea of 
what the answer should be, let's guess 2. 

Now we write the 2 above the 7 like this:
  2
  ----
3|7?

Now, to check that we're right, we need to subtract 2 3's from 7.

We do this by multiplying 2X3 (to get 6) and then writing:
   2
  ----
3| 7?
  -6
  __
   1

We need the 2 from 72 again, so let's write it in again. In fact, we're
going to "bring it down" next to the 1 to make 12. Then we'll guess how 
many times 3 goes into 12, and so on.

Anyway:
   2
  ----
3| 72
  -6 |     <---that's supposed to be an arrow reminding you that we're
  __\ /        bringing down the 2 to make 12
   12       

Ok. So, how many times does 3 go into 12?  Let's guess 4 (sorry, I'm 
cheating since I know the answer already!)

   24
  ----
3| 72
  -6   
   -
   12

Now let's multiply 3 X 4.  Wow! We get 12.  If we subtract 12-12
    24
  ----
3| 72
  -6
   -
   12
-  12
   ---
    0

Now, we can check to make sure that 3 X 24 really does equal 72, and 
we're done.

Whew!  I hope this explanation makes sense.  It's pretty hard to 
explain long division over e-mail though, so write us back with 
questions if you have them.

You might also be interested in looking through our archives.  There
are some questions about division in the elementary section.  The web
address is http://www.mathforum.org/dr.math   

Enjoy!

-Doctor Jodi,  The Math Forum