COURSE: JUST 3900INTRODUCTORY STATISTICS

FOR CRIMINAL JUSTICEBoot camp: Order of Operations

Peer Tutor SlidesInstructor:

Mr. Ethan W. Cooper, Lead Tutor© 2013 - - PLEASE DO NOT CITE, QUOTE, OR REPRODUCE WITHOUT THE

WRITTEN PERMISSION OF THE AUTHOR. FOR PERMISSION OR QUESTIONS, PLEASE EMAIL MR. COOPER AT THE FOLLWING: coopere07@students.ecu.edu

Order of Operations

Many equations only contain one mathematical equation. Example:

However, most of the equations in JUST 3900 contain two or more operations. Example:

In such equations it is important to perform the operations in the proper order. Simply working from left to right will not yield the correct answer.

LEFT TO RIGHT: WRONG!!!

ORDER OF OPERATIONS: CORRECT!!!

Order of Operations

Operations should be performed in the proper order and can be remembered by the following acronym: Please Excuse My Dear Silly Aunt Sally (PEMDSAS)

Please (P) Parentheses Excuse (E) Exponents My (M) Multiplication Dear (D) Division Silly (S) Summation Aunt (A) Addition Sally (S) Subtraction

This operation was not taught in high school.

Order of Operations: Then and Now

High School Please () Excuse X2

My Dear (*) (÷) Aunt Sally (+) (-)

JUST 3900 Please () Excuse X2

My Dear (*) (÷) Silly Ʃ Aunt Sally (+) (-)

Order of Operations

Left to Right Order of Operations

Order of Operations: Parentheses

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Any operations set off by parentheses should be done

first.

Sometimes there are multiple operations within a set off parentheses. In these cases, we still follow the proper order. Exponents

Multiplication

Addition

Order of Operations: Parentheses

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Often times, you’ll come across equations written like

this:

In such cases, we must solve the numerator, first and the denominator, second.

It’s as if it were written:

We do what’s in parentheses,first, working from left to right.

Order of Operations: Exponents

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) After performing all operations written in parentheses,

we move on to exponents:

Order of Operations: Exponents

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) When there are multiple exponents within an equation,

complete them in order from left to right before moving on to the next operation:

Order of Operations: Exponents

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) There are times when a set of parentheses are raised to

the nth power. In these cases, perform the operations in parentheses first, working from left to right:

Order of Operations: Multiplication and Division

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) After parentheses and exponents, multiplication and

division are performed, in order, from left to right:

Here, we multiply, first.

Order of Operations: Multiplication and Division

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Another example:

Remember two things:1) Multiplication and division should be done after parentheses and exponents.2) Multiplication and division should be done, in order, from left to right.

This time we divide, first.

Order of Operations: Multiplication and Division

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Put it all together:

Order of Operations:Summation

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Summation is an operation not usually covered in high

school algebra classes, but it will be important to know for JUST 3900.

Summation involves summing a set of numbers. Because we’re using data sets in statistics, summation will become an important operation. Values for X: 1, 2, 3, 4, 5

Order of Operations:Summation

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Using the same set of numbers:

Order of Operations:Summation

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) And again….

Order of Operations: Addition and Subtraction

Please Excuse My Dear Silly Aunt Sally (PEMDSAS) Just like multiplication and division, addition and

subtraction are performed in order from left to right.

Or

Order of Operations

Let’s put it all together and solve the following equation: