Putting Division into Words

Date: 04/06/99 at 09:55:28
From: nicole thiel
Subject: Division

How many times does 4 go into 600?  I know the answer is 150, but I 
I have to explain how I got the answer and I am having a hard time 
putting it into words.

Date: 04/06/99 at 12:57:16
From: Doctor Peterson
Subject: Re: Division

Hi, Nicole.

Since I don't know how YOU got the answer, I can't put it into words 
for you, but I can suggest how I might do it without having learned 
division yet.

Suppose I have 600 sticks, and I want to divide them among four 
people. Rather than count them out individually, I want to make use of 
what I know from the number: that they come in 6 bundles of 100.

I can start by giving each person a bundle, so each has 100 sticks and 
I have 2 bundles left over. I've divided 6 by 4 and gotten a quotient 
of 1, with a remainder of 2.

Now how can I divide the remaining 2 bundles among four people? I have 
to untie the bundles. Luckily, I find that each bundle is really ten 
bundles of ten sticks tied together - that is, 1 hundred is the same 
as 10 tens. So now I have 20 bundles of 10.

I can divide 20 by 4 to get exactly 5, so I give each person 5 bundles 
of ten. Now each of them has 1 hundred and 5 tens, making a total of 
100 + 50 = 150. Since I have none left, we're done, and you have your 
answer.

This is just what we do when we divide numbers with several digits. I 
don't know whether you've learned this yet, so I'll just write it out 
and you can figure out what it means by comparing it with what I've 
said:

      _150_
    4 )600
       4     <-- 4 hundreds (1 x 4) distributed
       -
       20    <-- 2 hundreds (20 tens) left
       20    <-- 20 tens (5 x 4) distributed
       --
        00   <-- nothing left
         0   <-- nothing more distributed
        --
         0

Does that fit with your own reasoning at all? If not, it's a good way 
to think.

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