Math Symbols . . . Those Most Valuable and Important: Vertical Lines (Absolute Value)

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Math Symbols
The Most Valuable and Important Grouping Symbols Used:

"Vertical Lines
(Absolute Value)"

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Background - why math symbols are used. . .

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

Math Symbols are an invention, not a discovery. They are a communication tool. Symbols are used to eliminate the need to write long, plain language instructions to describe calculations and other processes.




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

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

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Grouping Symbols (delimiters) - click symbol $Math - all symbols$ To See All Symbols click here $Math - Parentheses Symbols (also called Round Brackets)$ $Math - Square Brackets (also called Box Brackets)$ $Math - Curly Brackets (also called Braces)$ $Math - Overbar Symbol (also called a Vinculum)$ $Vertical Lines (Absolute Value Bars)$ $Math - Angle Brackets$ $Nested Groupings (nested Brackets)$

$Vertical Lines (Absolute Value Bars)$ 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.

$Vertical Lines Grouping Symbols - Example 1$ $Math - Parentheses$ $Math - Vertical Lines Grouping Symbols$ Grouping Symbols - Comparing Parentheses and Vertical Lines (Absolute Value) when evaluatiing the following expressions: versus - comparison of Math Symbols $Vertical Lines Grouping Symbols - Example 1$ versus $Vertical Lines Grouping Symbols - Example 1$

"PEMDAS" Order (while reading the mathematical expression left to right) $Vertical Lines Grouping Symbols - Example 1$ "P" (15+5) (20) 20 "E" - no exponents to evaluate "M" 3 x 20 60 "D" - no division to evaluate "A" - no addition to evaluate outside of
the original parentheses "S" - no subtraction to evaluate FINAL ANSWER: 3(15+5) = $Final Answer - Sixty - Parentheses - Example 1$

$Vertical Lines Grouping Symbols - Example 1$ "P" $Vertical Lines Grouping Symbols - Example 1$ $Vertical Lines Grouping Symbols - Example 1$ 20 "E" - no exponents to evaluate "M" 3 x 20 60 "D" - no division to evaluate "A" - no addition to evaluate outside of
the original vertical line grouping "S" - no subtraction to evaluate FINAL ANSWER: = $Vertical Lines Grouping Symbols - Example 1$ $Final Answer - Vertical Lines Grouping Symbols - Example 1$

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).

The Same $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$

$Vertical Lines Grouping Symbols - Example 2$ $Math - Parentheses$ $Math - Vertical Lines Grouping Symbols$ Grouping Symbols - Comparing Parentheses and Vertical Lines (Absolute Value) when evaluatiing the following expressions: versus - comparison of Math Symbols $Vertical Lines Grouping Symbols - Example 2$ versus $Vertical Lines Grouping Symbols - Example 2$

"PEMDAS" Order (while reading the mathematical expression left to right) $Vertical Lines Grouping Symbols - Example 2$ "P" (5-15) (-10) -10 "E" - no exponents to evaluate "M" 3 x (-10) -30 "D" - no division to evaluate "A" - no addition to evaluate outside of
the original parentheses "S" - no subtraction to evaluate FINAL ANSWER: 3(5-15) = $Final Answer - Sixty - Parentheses - Example 2$

$Vertical Lines Grouping Symbols - Example 2$ "P" $Vertical Lines Grouping Symbols - Example 2$ $Vertical Lines Grouping Symbols - Example 2$ +10 Vertical Line Groupings (absolute value) always result in a positive number "E" - no exponents to evaluate "M" 3 x 10 30 "D" - no division to evaluate "A" - no addition to evaluate outside of
the original vertical line grouping "S" - no subtraction to evaluate FINAL ANSWER: = $Vertical Lines Grouping Symbols - Example 2$ $Final Answer - Vertical Lines Grouping Symbols - Example 2$

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).

Different $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$ $Math - arrow right$

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Math Symbols
The Most Valuable and Important Grouping Symbols Used:

"Vertical Lines
(Absolute Value)"

+1 Solving-Math-Problems

+1 Solving-Math-Problems

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

Math Symbols
The Most Valuable and Important Grouping Symbols Used:

"Vertical Lines
(Absolute Value)"