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The Forgiving Method of Division

Date: 05/14/2002 at 16:29:01
From: Dan Bruce
Subject: Solving division problems using the "forgiving" method

My son has been asked to solve his division problems using the 
forgiving method, but he doesn't recall what this process is, and
judging by the answers he's arriving at, he's way off base.  Have you
ever heard of this method and could you demonstrate it using the
example 100/6?


Date: 05/15/2002 at 09:49:17
From: Doctor Mitteldorf
Subject: Re: Solving division problems using the "forgiving" method

I'd never heard of the forgiving method, and couldn't find references
to it in our archives.  From a reference that I found in a discussion
group on the net, I gather that it's about piecing together whatever
multiplication facts you are comfortable with to solve the problem at

Suppose you want to know how many 6's there are in 100.  You
can remember that 7*6=42, so you write down the 7 as part of your
answer, then take the 42 away from 100 and have 58 left.

Next step: you might say the same thing.  There's another 42 in
there, so there's another 7 sixes.  Write down another 7 under the
first one, and subtract 42 from 58.

Now you've got 16 left, and you know you can squeeze 2 sixes out of
16, but not 3.  So you write down the 2 under your 7's and add them
up:  7+7+2=16.  

You've pulled 16 sixes out of 100 (with 4 left over that wasn't enough
to make another 6).  You did it in groups of 7, 7 and 2, but someone
else might have done 5 and 5 and 5 and 1, and the "standard" method
would have been to do 10 + 6.  The method is forgiving in the sense
that your partial guesses don't have to be anything in particular, as
long as you don't overshoot.

- Doctor Mitteldorf, The Math Forum 
Associated Topics:
Elementary Division

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