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Example Problems  Geometric Sequence
Example Problems  Arithmetic Sequence
Example Problems  Rationalize the Denominator
Example Problems  Quadratic Equations
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 Math Symbols  The Most Valuable and Important Grouping Symbols Used:
"Parentheses Symbols (Round Brackets)"
>
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.
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 nonnested 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.
Evaluate the following expression:
short explanation . . .
"PEMDAS" Order
(while reading the mathematical
expression left to right)
"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) =
step by step
solution
using PEMDAS
Order of
Operations . . .
evaluate the parentheses
none
none
none
none
add terms
none
none
multiply numbers
none
none
none
 FINAL ANSWER: 3(15+5) = 60
Evaluate the following expression:
short explanation . . .
"PEMDAS" Order
(while reading the mathematical
expression left to right)
"P" (15+5)
(20)
"E"
 no exponents to evaluate
"M"
 no multiplication to evaluate
"D"
"A"
 no addition to evaluate outside of
the original parentheses
"S"
 no subtraction to evaluate
FINAL ANSWER: 3/(15+5) =
step by step
solution
using PEMDAS
Order of
Operations . . .
evaluate the parentheses
none
none
none
none
add terms
none
none
none
division
none
none
 FINAL ANSWER: 3/(15+5) =
Evaluate the following expression:
short explanation . . .
"PEMDAS" Order
(while reading the mathematical
expression left to right)
"P"
"E"
 no exponents to evaluate outside of
the original parentheses
"M"
"D"
 no division to evaluate
"A"
 no addition to evaluate outside of
the original parentheses
"S"
 no subtraction to evaluate
FINAL ANSWER: =
step by step
solution
using PEMDAS
Order of
Operations . . .

