Dividing 800 by 500

From: Anonymous
Date: Mon, 7 Nov 1994 10:38:30 -0500
Subject: Re: Ask Dr. Math: on-line math problem solvers

Dear Doctor Math,

My name is Damon T Stallings and I am 9 years old.
I go to the William Monroe Trotter School,in Roxbury, Mass.
I have a math problem for you.

How can I divide 800 by 500?

Your friend,  Damon     

From: Dr. Sydney
Date: Mon, 7 Nov 1994 11:14:24 -0500 (EST)
Subject: Re: Ask Dr. Math: on-line math problem solvers

Dear Damon,

        Thanks for writing to Dr. Math!  Your question about dividing 800 
by 500 is a good question.  I'm not sure how you usually think of 
division, but I usually think of it in 2 ways:

1) as a fraction:  So the problem of dividing 800 by 500 is equivalent to
reducing the fraction :     
                        
                        800
                        ---
                        500

into simpler terms.  One way to do this is to factor the number in the
numerator (top) of the fraction and the number in the denominator 
(bottom) of the fraction, and then cancel common factors.  When I say 
factor the number, I mean write the number as the product of smaller 
numbers.  Keep in mind when we factor 800 and 500 we are looking 
for common factors.  So, let's try... 800=8x100   and 500=5x100, right? 
So we can rewrite our fraction as:

800  8x100  8  100
---= -----=-- x---
500  5x100  5  100

But 100 
    --- = 1, right?
    100

So, 800  8       8
    ---= - x 1 = -
    500  5       5

We can leave our answer like this or we can write it as 1 and 3/5 (do you
know why 8/5 = 1 and 3/5?)

2) The other way to do this is using long divison:

   The problem becomes:
           _________
       500|800       = ?

Well, the way I usually do problems like this is to move the decimal point
over the same number of spaces in both 800 and 500.  If we move the decimal
point over 2 spaces in each (so 500. becomes 5. and 800 becomes 8.)  our
problem becomes:
 ____
5|8

(Note this step is the counterpart to factoring out a 100 the way we did in
the first part).

So, now we proceed as usual with long division.  5 goes into 8 one time with
3 left over so we have:

 _1__
5|8
 -5
 ---
  3.

So our answer is 1 with a remainder of 3 or 1 and 3/5.

Both of these methods for division are good, so go with whichever makes more
sense to you.  If you have any questions about what I said, or if you have
any other math questions, feel free to write back.  

--Sydney