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

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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"All Math Symbols"

Grouping Symbols (delimiters) - click description

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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 . . .

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.

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

Evaluate the following expression:

short explanation . . .

"PEMDAS" Order
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 )

20

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

"PEMDAS" Order
expression left to right)

3 20

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

"E" - no exponents to evaluate.

"M" - 3 20

60

"D" - no division to evaluate.

"A" - no addition to evaluate.

"S" - no subtraction to evaluate.

step by step solution using PEMDAS Order of Operations

evaluate the parentheses

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multiply numbers

- FINAL ANSWER: 3(15+5) = 60

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Evaluate the following expression:

short explanation . . .

"PEMDAS" Order
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 )

20

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

"PEMDAS" Order
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) =

step by step solution using PEMDAS Order of Operations

evaluate the parentheses

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division

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Evaluate the following expression:

short explanation . . .

"PEMDAS" Order
expression left to right)

"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 )

40

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

"PEMDAS" Order
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 ) =

step by step solution using PEMDAS Order of Operations

evaluate the parentheses

evaluate exponent

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multiplication

- FINAL ANSWER: 3/(15+52) = 120

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