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Math Symbols
The Most Valuable and Important Grouping Symbols Used:

"Vertical Lines
(Absolute Value)"


Vertical Lines (Absolute Value Bars)

Math Symbols: . . . why math symbols are used . . .

Symbols are a concise way of giving lengthy instructions related to numbers and logic.


Symbols are a communication tool. Symbols are used to eliminate the need to write long, plain language instructions to describe calculations and other processes.

For example, a single symbol stands for the entire process for addition. The familiar plus sign eliminates the need for a long written explanation of what addition means and how to accomplish it.

The same symbols are used worldwide . . .

The symbols used in mathematics are universal.

The same math symbols are used throughout the civilized world. In most cases each symbol gives the same clear, precise meaning to every reader, regardless of the language they speak.

The most valuable, most frequently used Symbols in mathematics . . .

The most important, most frequently used Grouping symbols are listed below.


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Vertical Lines (Absolute Value Bars) Vertical Lines (Absolute Value Bars) -


The absolute value symbol tells you to determine the magniture of the number between the vertical lines, without regard to its sign.

If the number is negative, the negative sign is ignored. Only the magniture of the number (always positive) is returned.

The following examples compare and contrast the use of parentheses and vertical lines as grouping symbols.



vertical lines Symbols - Example 1 Math - Parentheses versus Math - Vertical Lines Grouping Symbols - comparison of Math Symbols

Grouping Symbols - Comparing Parentheses and Vertical Lines (Absolute Value) when evaluatiing the following expressions:

Vertical Lines Grouping Symbols - Example 1 versus Vertical Lines Grouping Symbols - Example 1


"PEMDAS" Order
(while reading the mathematical
expression left to right)


Vertical Lines Grouping Symbols - Example 1 Vertical Lines Grouping Symbols - Example 1


"P" (15+5) "P" |15+5|

(20) |20|

20 20

E: no exponents to evaluate E: no exponents to evaluate  

  "M"   3 x 20 "M" 3 x 20

60 Math - arrow left Math - arrow left The Same Math - arrow right Math - arrow right 60

D: no division to evaluate D: no division to evaluate  

A: no addition to evaluate A: no adddition to evaluate  

S: no subtraction to evaluate S: no subtraction to evaluate  

FINAL ANSWER: 3(15+5) = Final Answer - Sixty - Parentheses - Example 1   FINAL ANSWER: 3|15+5| = Final Answer - Sixty - Parentheses - Example 1  

Both answers are exactly the same.

Both the parentheses and the vertical line groupings can be replaced with the same number: a positive 20. This is shown on the third line under "P" (above).


Vertical Lines Grouping Symbols - Example 2 Math - Parentheses versus Math - Vertical Lines Grouping Symbols - comparison of Math Symbols

Grouping Symbols - Comparing Parentheses and Vertical Lines (Absolute Value) when evaluatiing the following expressions:

3(5-15) versus 3|5-15|


"PEMDAS" Order
(while reading the mathematical
expression left to right)


3(5-15)                               3|5-15|


"P" (5-15) "P" |5-15|

(-10) |-10|

-10 Math - arrow left Math - arrow left Different Math - arrow right Math - arrow right +10

Note: Vertical Line Groupings (absolute value) always result in a positive number

E: no exponents to evaluate E: no exponents to evaluate  

  "M"   3 x (-10) "M" 3 x (10)

-30 Math - arrow left Math - arrow left Different Math - arrow right Math - arrow right +30

D: no division to evaluate D: no division to evaluate  

A: no addition to evaluate A: no adddition to evaluate  

S: no subtraction to evaluate S: no subtraction to evaluate  

FINAL ANSWER: 3(5-15) = Final Answer - Sixty - Parentheses - Example 2   FINAL ANSWER: 3|5-15| = Final Answer - Vertical Lines Grouping Symbols - Example 2  

Both answers are not the same.

Both the parentheses and the vertical line groupings can not be replaced with the same number: the parentheses grouping is replaced by a -10, but the vertical line grouping is replaced by a +10. This is shown on the third line under "P" (above).