Q&A #19452

Teachers' Lounge Discussion: Remainders in long division


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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2009113012:13:02
Subject: Re: fractions as remainders in long division

On 2009112015:00:58, Megan wrote:
>What is the mathematical reasoning behind not using "R" before a
>remainder expressed in fraction form?  We use an "R" followed by a
>whole number to represent a remainder in long division, so why is it
>considered "wrong" to write the "R" before representing the remainder
>as a fraction.  I need to know why the "R" is not acceptable -
>"because it is just not done" is not a good enough explanation!!!
>Thank you for your help!

In the first place, R is not used in math much beyond the teaching of
fractions.  But division is first learned in about the 3rd and 4th
grade and the students are not always adapted to thinking in fractions
so someone came up with the use of R for the younger students.  

Gail gave an example of 37 divided by 7.  The result is 5 whole groups
with a fraction of a group left over.  So, the result should be 5
whole groups and a 2/7 of a group left over which we write as   5 and
2/7 = 5 2/7 = 5+2/7.  The later being the form that is used in all
math at and above the 5th grade.  The R means nothing to me in algebra
and other higher mathematics. 

So, one would not write 5 R 2/7 but simply 5+2/7.  When someone writes
5 R 2, it neglects the use of the divisor which is 7.  

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