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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
paper.

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

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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

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