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

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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Grouping Symbols (delimiters) - click description

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$Math - Parentheses Symbols (also called Round Brackets)$

Parentheses Symbols
(also called
"Round Brackets")

$Math - Square Brackets (also called Box Brackets)$

Square Brackets
(also called
"Box Brackets")

$Math - Curly Brackets (also called Braces)$

Curly Brackets
(also called
"Braces")

$Math - Overbar Symbol (also called a Vinculum)$

Overbar Symbol
(also called
a "Vinculum",
or an "Overline")

$Vertical Lines (Absolute Value Bars)$

Vertical Lines
("Absolute Value" Bars)

$Math - Angle Brackets$

Angle Brackets

$Nested Groupings (nested Brackets)$

Nested Groupings
("nested Brackets" ...
... Parentheses,
inside Parentheses")

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

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.

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

$Parentheses - Example 1$

short explanation . . .

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

3 ( 15 + 5 )

"P" - The parentheses are the math symbols which represent the innermost bracket grouping. There are no additional bracket groupings to evaluate inside the parentheses.

"E" - no exponents to evaluate inside the parentheses.

"M" - no multiplication to evaluate inside the parentheses.

"D" - no division to evaluate inside the parentheses.

"A" - ( 15+5 )

( 20 )

"S" - no subtraction to evaluate inside the parentheses.

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

3 ✕ 20

"P" - There are no additional expressions within parentheses.

"E" - no exponents to evaluate.

"M" - 3 ✕ 20

"D" - no division to evaluate.

"A" - no addition to evaluate.

"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

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

$Parentheses - Example 2$

short explanation . . .

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

3 / ( 15 + 5 )

"P" - The parentheses are the math symbols which represent the innermost bracket grouping. There are no additional bracket groupings to evaluate inside the parentheses.

"E" - no exponents to evaluate inside the parentheses.

"M" - no multiplication to evaluate inside the parentheses.

"D" - no division to evaluate inside the parentheses.

"A" - ( 15+5 )

( 20 )

"S" - no subtraction to evaluate inside the parentheses.

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

3 / 20

"P" - There are no additional expressions within parentheses.

"E" - no exponents to evaluate.

"M" - no multiplication to evaluate.

"D" - 3 / 20

"A" - no addition to evaluate.

"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) = $Final Answer - Parentheses - Example 2$

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

$Parentheses - Example 3$

short explanation . . .

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

$Parentheses - Example 3$

"P" - The parentheses are the math symbols which represent the innermost bracket grouping. There are no additional bracket groupings to evaluate inside the parentheses.

"E" - ( 15 + 5² )

( 15 + 25 )

"M" - no multiplication to evaluate inside the parentheses.

"D" - no division to evaluate inside the parentheses.

"A" - ( 15 + 25 )

( 40 )

"S" - no subtraction to evaluate inside the parentheses.

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

3 ✕ 40

"P" - There are no additional expressions within parentheses.

"E" - no exponents to evaluate.

"M" - 3 ✕ 40

120

"D" - no division to evaluate.

"A" - no addition to evaluate.

"S" - no subtraction to evaluate.

FINAL ANSWER: 3( 15 + 5² ) = $Final Answer - Parentheses - Example 3$

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)"

$Math - Parentheses Symbols (also called Round Brackets)$

+1 Solving-Math-Problems

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

+1 Solving-Math-Problems

- 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)"

$Math - Parentheses Symbols (also called Round Brackets)$