Practical Applications of Absolute Value
Date: 09/26/2000 at 13:25:49 From: Anne Marie Garrett Subject: Practical applications of absolute value My 8th grade students would like to know the real world applications of the concept of absolute value. I have explained it as a distance to zero on the number line. They are not convinced of its importance and why we need it. Now that they've asked and I've thought about it, I'd like to know too!
Date: 09/26/2000 at 15:10:16 From: Doctor Douglas Subject: Re: Practical applications of absolute value Hi Anne Marie, Thanks for sending your question to Ask Dr. Math. Your choice of explanation as a "distance" is a very good one, since that kind of quantity is one that doesn't depend on its sign. I think that your students may be objecting to the "distance from zero" because that's a mathematics example. Here are some "real-world" applications that I've come up with by brainstorming with Dr. Tony here at the Math Forum. 1. Distances in real life: suppose you go three blocks east, then six blocks west, then eleven blocks east again. Now we can ask two questions: Where are you relative to where you started? This requires us to retain the sign information, and is not answered by the absolute value. The other obvious question is "How far did you go?" Now every student in your class should add 3 + 6 + 11, each of them doing at least one absolute value operation in their minds (for the -6). Of course distances are useful in many real world applications, such as navigation and transport ("Do we have enough fuel to get there AND back?"), architecture, engineering and science, and sports ("How many consecutive 15-yard penalties can the referees call before it becomes 'half-the-distance-to-the goal-line", if we start at midfield?"). 2. Suppose you are driving a car. Going too fast is obviously a hazard and might earn a speeding ticket. Going too slow is also a hazard, and can earn a ticket also. What matters is how different one's speed is from what everyone else is doing. This type of "difference" is fundamental to all sorts of concepts in statistics, where the absolute value is used in various ways of quantifying how well or how poorly one thing predicts another. Statistics is used in many important real world applications also, including medicine and finance. 3. Suppose you are exchanging currency, say dollars and pesos. The bank or exchange will charge a commission based on how much is exchanged (sometimes there will be a flat fee as well). This commission is applied no matter whether you buy dollars or buy pesos. In your pocket, it could be D dollars and P pesos, and D could go up (or down) while P goes down (or up). But the commission on a given transaction is the absolute value of either D or P, times the exchange rate. I hope that these examples helps to get you started. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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