From: Ralph (for Teacher2Teacher Service)
Date: Feb 04, 2008 at 10:15:02
Subject: Re: Interpreting remainders in division

Hi Sachia,

Thank you for writing to T2T.  The challenge for many teachers and students
is that when a division problem is put into a context, the remainder can
be interpreted in many different ways (and NONE of them are the usual
notation that students learn when doing division of "R___" (whatever the
remainder is!)

For example, if a car holds 5 passengers, and 32 passengers need
transportation, how many cars will be needed?  The division produces an
answer of 6 cars, with 2 passengers left over, but since you wouldn't
want to leave anyone behind, you'd need another car. Answer: 7 cars. Note
that the remainder is "rounded up" even though it's less than 1/2.

But consider this problem: You have 32 apples, and 5 apples are needed to
make an apple pie. How many pies can you make?  The answer would be
that you could make 6 pies  (and yes, there would be 2 apples left over).

Change the problem one more time. You have 32 inches of ribbon, and want to
make 5 awards. How long will each award ribbon be? In this example, you use
all 32 inches of material, so each ribbon would be 6 2/5 inches long. In this
case the "remainder" would be written as a fraction or decimal and wouldn't
really be "a remainder" at all :)

Sorry for such a long answer to such a short question, but the answer boils
down to -- how the remainder is interpreted depends on the context of the
problem.

Hope this helps,

 -Ralph, for the T2T service

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