Math Symbols . . . Those Most Valuable and Important: Parentheses Symbols

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- Math Symbols -
The Most Valuable and Important Grouping Symbols Used:

"Parentheses Symbols
(Round Brackets)"

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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.

$Free Math Help$ $Math Help - Your Questions & Comments$ Skip to Free Math Help click here

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$Search this Site$ $Search this Site$ Search this Site click here

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

$Parentheses Symbols (also called round brackets)$ Parentheses Symbols (also called round brackets) -

Left "(" parenthesis, and right ")" parenthesis are used as math symbols together (as a pair). They can be interchanged with square brackets or braces.

If there are three levels of grouping in a nested expression, generally parentheses are used in the inner most groupings. Square brackets are used in the next higher level grouping, and braces are used in the most outer groupings (see "Nested expressions" for an example).

Background . . . Math Symbols - Why parentheses are used in mathematical expressions . . . $Parentheses Symbols (also called round brackets)$

All mathematical expressions must be evaluated in a certain order to arrive at the correct answer.

The sequential steps used are summed up in the acronym "PEMDAS" (called the order of operations).

"PEMDAS" tells you how to evaluate every mathematical expression by showing you which math symbols to use in your calculations first, second, third . . . and so on: step by step, left to right.

The order of the calculations is what is important.

The acronym "PEMDAS" stands for the procedure shown immediately below. Please note that the entire process of evaluating mathematical expressions is controlled by using math symbols in the correct order (exactly):

"P" - Parentheses: First - Evaluate every part of the expression inside every parentheses - before you do anything else.

The parentheses (or bracket) math symbols tell you what to do first. That is why they are used. (They also make every mathematical expression more readable.)

If there are several nested parentheses, begin by evaluating the innermost parentheses first - before you do anything else. After evaluating the innermost parentheses, evaluate the next innermost parentheses, and so on - until there are no parentheses left.

If there are several non-nested parentheses, evaluate every one of them separately - before you do anything else.

"E" - Exponent: Second - Evaluate every exponent which appears in the expression - before you do anything else.

"M" - Multiplication: Third - Reading the expression from left to right, complete all multiplication.

"D" - Division: Fourth - Reading the expression from left to right, complete all division.

"A" - Addition: Fifth - Reading the expression from left to right, complete all addition.

"S" - Subtraction: Sixth - Reading the expression from left to right, complete all subtraction.

$Parentheses - Example 1$ $Parentheses Symbols (also called round brackets)$ Evaluate the following expression: $Parentheses - Example 1$

short explanation . . . "PEMDAS" Order (while reading the mathematical expression left to right) $Parentheses - Example 1$ "P" (15+5) (20) "E" - no exponents to evaluate "M" 3(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) = $Final Answer - Sixty - Parentheses - Example 1$ step by step solution using PEMDAS Order of Operations . . .

$Parentheses - Example 1$ $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ $Math - arrow right$ $PEMDAS 'P' - Parentheses$ $Math - arrow right$ $Math - numbers$ evaluate the parentheses $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ $PEMDAS 'P' - Parentheses$ $PEMDAS 'E' - Exponents$ none none none none $PEMDAS 'M' - Multiplication$ $PEMDAS 'D' - Division$ $PEMDAS 'A' - Addition$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ add terms $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'S' - Subtraction$ none $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 1$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'E' - Exponents$ none $PEMDAS 'M' - Multiplication$ $Math - arrow down right$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ multiply numbers $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 1$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'D' - Division$ none $PEMDAS 'A' - Addition$ none $PEMDAS 'S' - Subtraction$ none $Math - arrow down$ $Final Answer - Sixty - Parentheses - Example 1$ - FINAL ANSWER: 3(15+5) = 60

$Parentheses - Example 2$ $Parentheses Symbols (also called round brackets)$ Evaluate the following expression: $Parentheses - Example 2$

short explanation . . . "PEMDAS" Order (while reading the mathematical expression left to right) $Parentheses - Example 2$ "P" (15+5) (20) "E" - no exponents to evaluate "M" - no multiplication to evaluate "D" $Math - numbers$ "A" - no addition to evaluate outside of
the original parentheses "S" - no subtraction to evaluate FINAL ANSWER: 3/(15+5) = $Final Answer - Parentheses - Example 2$ step by step solution using PEMDAS Order of Operations . . .

$Parentheses - Example 2$ $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ $Math - arrow right$ $PEMDAS 'P' - Parentheses$ $Math - arrow right$ $Math - numbers$ evaluate the parentheses $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ $PEMDAS 'P' - Parentheses$ $PEMDAS 'E' - Exponents$ none none none none $PEMDAS 'M' - Multiplication$ $PEMDAS 'D' - Division$ $PEMDAS 'A' - Addition$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ add terms $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'S' - Subtraction$ none $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 2$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'E' - Exponents$ none $Math - arrow down$ $PEMDAS 'M' - Multiplication$ none $PEMDAS 'D' - Division$ $Math - arrow down right$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ division $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 2$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'A' - Addition$ none $PEMDAS 'S' - Subtraction$ none $Math - arrow down$ $Final Answer - Parentheses - Example 2$ - FINAL ANSWER: 3/(15+5) = $Final Answer - Parentheses - Example 2$

$Parentheses - Example 3$ $Parentheses Symbols (also called round brackets)$ Evaluate the following expression: $Parentheses - Example 3$

short explanation . . . "PEMDAS" Order (while reading the mathematical expression left to right) $Parentheses - Example 3$ "P"              $Parentheses - Example 3$ $Parentheses - Example 3$ $Parentheses - Example 3$ "E" - no exponents to evaluate outside of
       the original parentheses "M" $Parentheses - Example 3$ $Parentheses - Example 3$ "D" - no division to evaluate "A" - no addition to evaluate outside of
       the original parentheses "S" - no subtraction to evaluate FINAL ANSWER:               = $Parentheses - Example 3$ $Final Answer - Parentheses - Example 3$ step by step solution using PEMDAS Order of Operations . . .

$Parentheses - Example 3$ $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ $Math - arrow right$ $PEMDAS 'P' - Parentheses$ $Math - arrow right$ $Math - numbers$ evaluate the parentheses $Math - arrow down$ $Math - arrow down$ $PEMDAS Order of Operations$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'P' - Parentheses$ none $Math - arrow down right$ $PEMDAS 'E' - Exponents$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ evaluate exponent $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down right$ none none $PEMDAS 'M' - Multiplication$ $PEMDAS 'D' - Division$ $PEMDAS 'A' - Addition$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ add terms $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'S' - Subtraction$ none $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 2$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'E' - Exponents$ none $Math - arrow down$ $PEMDAS 'M' - Multiplication$ $Math - arrow down right$ $Math - arrow right$ $Math - arrow right$ $Math - numbers$ multiplication $Math - arrow down$ $Math - numbers$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Math - arrow left$ $Parentheses - Example 3$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $Math - arrow down$ $PEMDAS 'D' - Division$ none $PEMDAS 'A' - Addition$ none $PEMDAS 'S' - Subtraction$ none $Math - arrow down$ $Final Answer - Parentheses - Example 3$

- FINAL ANSWER: = $Parentheses - Example 3$ $Final Answer - Parentheses - Example 3$

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- Math Symbols -
The Most Valuable and Important Grouping Symbols Used:

"Parentheses Symbols
(Round Brackets)"

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Example Problems - Geometric Sequence

Example Problems - Arithmetic Sequence

Example Problems - Rationalize the Denominator

Example Problems - Quadratic Equations

Example Problems - Work Rate Problems

Example Problems - statistics

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- Math Symbols -The Most Valuable and Important Grouping Symbols Used:"Parentheses Symbols (Round Brackets)"

- Math Symbols -
The Most Valuable and Important Grouping Symbols Used:

"Parentheses Symbols
(Round Brackets)"