Long Division

Date: 1/24/96 at 22:42:34
From: schugh
Subject: 5/7

Could you please tell me how I can divide 5 by 7.  What will be the 
answer and how you arrived at that. I am in grade 4.

Thank you in advance.

Naveen Chugh 

Date: 1/27/96 at 21:1:50
From: Doctor Ken
Subject: Re: 5/7

Hello there!

There are a couple of different ways you might want to do this problem, 
and all would give you different kinds of answers.  They are not 
really different answers, but they kind of look different, kind of 
like how .5 and 1/2 look different, but they're really the same thing.

The first way, and the way I'd usually do it, is just to say 
"5 divided by 7 equals five sevenths."  Of course, that doesn't really 
tell you any more than you knew in the first place, but it's still 
right!

Another way is to use long division with remainders:

  ____
 7)5     = 0 with a remainder of 5.

Again, that doesn't really tell you much more than you already knew.

The other way is to use long division without remainders.  Here's how
you'd do that:

  __.7_________
 7)5.000000000
   4 9
   ---
     1

  __.71________
 7)5.000000000
   4 9
   ---
     10
      7
     --
      3


  __.714_______
 7)5.000000000
   4 9
   ---
     10
      7
     --
      30
      28
      --
       2

You could keep doing this forever if you didn't grow old and die!  But 
doing it this far tells you that 5 divided by 7, which is also known as
5/7, is about .714, which is pretty useful.  Now you know that it's 
bigger than one-half, for instance.  

Thanks for the question!

-Doctor Ken,  The Geometry Forum