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/
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