Q&A #19309

Interpreting remainders in division

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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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