Associated Topics || Dr. Math Home || Search Dr. Math

### Equations from Word Problems, and Units

```Date: 05/19/2003 at 10:46:20
From: Colin
Subject: Number placement in fraction and decimal word problems

In a fraction or decimal word problem, how do I know where to place
the numbers from the sentence when I'm writing the equation? Example:
In 2 1/4 hours the temperature dropped 13 1/9 degrees. How many
degrees did the temperature drop per hour?

I understand how to pick the operation, just not where to place the
numbers. Thank you.
```

```
Date: 05/19/2003 at 12:17:05
From: Doctor Peterson
Subject: Re: Number placement in fraction and decimal word problems

Hi, Colin.

It would be more helpful if you had shown us what operation you expect
to use, and where you think the numbers should be placed in your
expression; that would tell me where you are having trouble. I myself
can't separate the two aspects; an operation is meaningless without
numbers to operate on. Let's instead think about what you are being
asked to find, and what it means in terms of the quantities you are
given.

You are given

the total time, 2 1/4 hours
the total drop in temperature, 13 1/9 degrees

You want to find

the rate of temperature drop, in degrees per hour.

That is, in each hour (on the average), how many degrees did it drop?

One way to solve this is to think as if the degrees were objects you
could count. If I get a certain number of apples every hour, then the
total number of apples I get in a certain number of hours is found by
multiplying. Do you see that? If I get 5 apples per hour, for 3
hours, then I have 3 piles of 5 apples for a total of 3*5 = 15 apples.
Then to reverse the problem, we have to divide: the number of apples
per pile (or per hour) is the total number of apples divided by the
number of piles (or hours). Thinking in this way can make it clearer
what you want to divide.

You can just think of this as a rate problem, using the formula

d = rt  [distance = rate times time]

In this case, the "distance" is not a physical distance, but a change
in temperature; but the same equation is valid. Solving for r, you
have

r = d/t

So the rate is found by dividing the total "distance" traveled by the
time it took.

You can also think in terms of units; you have to do so at some point
anyway. The units of "degrees per hour" can be written as a fraction:

deg
---
hr

So we want to divide a number of degrees by a number of hours to get
the number of degrees per hour.

If you had used the rate equation, you would have divided degrees by
hours, so you would see that the answer is in degrees per hour. If the
problem had asked you for, say, degrees per minute, you would have to
convert. And if you had accidentally divided the time by the
temperature change, you would find that your units were hours per
degree, and you would know you were wrong. That's why I say you have
to check the units no matter how you do it.

So there are three different ways to approach this sort of question,
all of which tell you not only to divide, but what to divide by what.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Terms & Units of Measurement
Elementary Word Problems
Middle School Terms/Units of Measurement
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search