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mathematical expressions

by EVE NORTH
(BOYNTON BEACH, FLORIDA, USA)











































The following matematical question involves the use of a vertical line (|) ; i.e. a line lying north to south as contrasted with a minus sign ( - ) which goes east to west.

You should note that the vertical line to which I am referring appears on a computer keyboard below the Backspace key.

The question is: Which of the following exprfesions is true?

A:

- |5| = 5


B:


| -1/3 | = 1/3


C:


- | - 2 | = 2

D.


- | 6 | = 6


If you sish, I can be reached at 561-375-XXXX







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Dec 25, 2010
Mathematical Expressions - Absolute Value
by: Staff

The question:

by EVE NORTH
(BOYNTON BEACH, FLORIDA, USA)

The following matematical question involves the use of a vertical line (|) ; i.e. a line lying north to south as contrasted with a minus sign ( - ) which goes east to west.

You should note that the vertical line to which I am referring appears on a computer keyboard below the Backspace key.

The question is: Which of the following exprfesions is true?

A:

- |5| = 5


B:


| -1/3 | = 1/3


C:


- | - 2 | = 2

D.


- | 6 | = 6


If you sish, I can be reached at 561-375-xxxx


The answer:

The double vertical lines (| |) you are referring to stand for ABSOLUTE VALUE.

The absolute value of the expression between the double vertical lines is the MAGNITUDE of the expression WITHOUT REGARD TO THE SIGN.

For example: If you are standing 2 feet away from a flag pole due south, what is the absolute value of your distance from the flag pole? Absolute Value of the distance (magnitude only) = 2 feet. |2 feet to the south | = 2 feet

Now suppose you move so you are standing 2 feet to the north of the flag pole. What is the absolute value of your distance from the flag pole? Absolute Value of the distance (magnitude only) = 2 feet. |2 feet to the north | = 2 feet

Now suppose you move again, so you are standing 2 feet to the east of the flag pole. What is the absolute value of your distance from the flag pole? Absolute Value of the distance (magnitude only) = 2 feet. |2 feet to the east | = 2 feet

The concept of absolute value: No matter where you stand, you are still exactly 2 feet from the flag pole. The direction makes no difference at all.


Now, let’s apply the idea of absolute value to your problem:


A: - |5| = 5

Is this true? NO. - |5| does not = 5, - |5| actually = -5 (The absolute value [magnitude only] of |5| is 5. However a – sign is outside the double vertical lines, so it does apply to the final answer)

B: | -1/3 | = 1/3

Is this true? YES. | -1/3 | does = 1/3 (The absolute value [magnitude only] of |-1/3| is 1/3 The – sign is inside the double vertical lines, so it does not affect the magnitude of the 1/3)

C: - | - 2 | = 2

Is this true? NO. - | - 2 | does not = 2; |-2| = 2, but -|-2| = -2. (The absolute value [magnitude only] of |-2| is 2. However a – sign is also outside the double vertical lines, so it does apply to the final answer)


D: - | 6 | = 6

Is this true? NO. - |6| does not = 6, - |6| actually = -6 (The absolute value [magnitude only] of |6| is 6. However a – sign is outside the double vertical lines, so it does apply to the final answer)


The final answer is: only choice B is correct.




You can see some other examples of absolute value at:

http://www.solving-math-problems.com/math-symbols-vertical-lines.html


Thanks for writing.


Staff
www.solving-math-problems.com

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