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Fractions: Sheets of Paper Left

Date: 08/07/97 at 11:57:37
From: Barton, Dana
Subject: Word Problem

I have a question about a word problem involving fractions. Maybe you
can help.

An office got a new copier and was given 800 sheets of paper. On the
first day they used 1/3 of the paper. On the second day they used 1/5
and on the 3rd they used 1/6 of the paper. How many sheets of paper 
were left?

Dana Barton

Date: 08/30/97 at 11:34:42
From: Doctor Sonya
Subject: Re: Word Problem

Dear Dana,

To solve word problems it is necessary to translate mathematical 
thoughts expressed in words into mathematical symbols that we can 
manipulate and simplify.  

For instance, the words "1/3 of the paper" can be written 
mathematically as 800/3.

If we look at what is going on in this office, as paper is used it is 
being subtracted from the original amount of 800 sheets.  We want an 
expression that models what is going on. If we understand the 
situation we can arrive at the correct answer. So if on day one, one 
third of the paper is used, we are left with 800 - 800/3 sheets of 

On day two we use 1/5 of the paper, which is 800/5.  Thus after day 
two, we will have (800 - 800/3) - 800/5 sheets of paper.

If you do the same type of calculation for day three, you can find out 
how much paper was used that day, and subtract that also to get the 
final answer.

There is another possible interpretation of your word problem, one 
that makes it a little bit more complicated. We did the problem 
assuming that "on the second day they used 1/5 of the paper" means 
that they used 1/5 of the original 800 sheets. It might also mean 
that they used 1/5 of the number of sheets that were left over after 
the first day.  If you remember, after the first day there were 
800 - 800/3 sheets of paper left.  If we use up 1/5 of that on the 
second day, how much would be left?

If you have any more questions, please write us back.

-Doctors Cheryl and Sonya,  The Math Forum
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Associated Topics:
Middle School Word Problems

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