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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/

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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