## Math Symbols The Most Valuable and Important Grouping Symbols Used: "Vertical Lines (Absolute Value)"

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 symbols are listed below.

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Grouping Symbols (delimiters) - click description

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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.

versus - comparison of Math Symbols

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

versus

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

"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 The Same 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: 3|15+5| =

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).

versus - 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 Different +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 Different +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: 3|5-15| =

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).