“Please Excuse My Dear Aunt Sally” (PEMDAS math mnemonic)

“My Dear Aunt Sally” (MDAS) is a math mnemonic for the order operations: Multiplication-Division-Addition-Subtraction. “My Dear Aunt Sally” has been cited in print since at least 1935.
   
“Please Excuse My Dear Aunt Sally” (PEMDAS), a mnemonic for Parentheses-Exponents-Multiplication-Division-Addition-Subtraction, has been cited in print since at least the 1980s.
     
   
Wikipedia: Order of operations
Mnemonics
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to “Please Excuse My Dear Aunt Sally”, with the first letter of each word creating the acronym PEMDAS. Canada and New Zealand use BEDMAS, standing for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Most common in the UK and Australia are BODMAS meaning “B"rackets, “O"f or “O"rder, “D"ivision, “M"ultiplication, “A"ddition and “S"ubtraction in Nigeria and some other West African countries and BIDMAS. In some English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponents may be called either Indices, Powers or Orders, which have the same precedence as Roots or Radicals. Since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BOMDAS. The original order of operations in some countries was BODMAS, which stands for Brackets, Orders or pOwers, Division, Multiplication, Addition, Subtraction. The O is sometimes associated with Of. This mnemonic was common until exponentials were added into the mnemonic.
 
Newspapers.com
9 October 1935, The Vidette-Messenger (Valparaiso, IN), “Library Center School Notes,” pg. 5, col. 3:
Does Mr. Ulrick really have a ‘my dear Aunt Sally’ or was he putting his advanced algebra class on a level with a former eighth grade arithmetic class by suggesting that they remember her?
 
10 December 1942, The McIntosh County Democrat (Checotah, OK),  “The Very Latest” by Helen Norwood, pg. 7, col. 3:
Wonder why Wanda Norwood goes around saying, “My dear aunt Sally.”  Could it be that she wants to make good on her Math. Miss Harrison told her it stood for “Multiply, divide, add and subtract.”
     
15 October 1955, Mason City (IA) Cub-Gazette, “Cub Quips,” pg. 6, col. 6:
LAMONT CONSTABLE’s intermediate algebra classes have been hearing about a relative that Constable refers to as “My Dear Aunt Sally.” THe first letter of each word stands for multiplication, division, addition and subtraction—the order in which students do complex problems.
 
5 October 1958, Minneapolis (MN) Sunday Tribune, “Semantics Are Pedantic, and Math Is Still Wrath” by Hoff, sec. 7, pg. 1:
“My Dear Aunt Sally” (Multiplication Division Addition Subtraction). This is a way to remember that all multiplications and divisions must be done in the order indicated before the additions and subtractions.
 
6 March 1976, Morning Star (Rockford, IL), “Test Yourself” by Dr. Gary Gray (Gannett News Service), Saturday Magazine, pg. 10, cols. 3-4:
What does the phrase “Please remember my dear Aunt Sally” represent?
These are the order of operations in mathematics—powers, roots, multiplication, division, addition, subtraction.
 
OCLC WorldCat record
Please, My Dear Aunt Sally
Author: Richard W Shoemaker
Edition/Format: Article Article : English
Publication: The Arithmetic Teacher, v27 n9 (19800501): 34-35
Database: JSTOR Mathematics & Statistics Collection
 
28 April 1985, Newsday (Long Island, NY), “Learning Line: The use of tricks to jog the memory” by Meredith Young, pt. 2, pg. 87, col. 1:
Beginning algebra students like “Please Excuse My Dear Aunt Sally” because it helps them remember the correct order to use when solving equations that contain several operations. (Work within parenthesis must be done first, followed by exponents, then multiplication and division, and finally addition and subtraction.)
 
OCLC WorldCat record
The return of “My Dear Aunt Sally”
Author: M L Keedy
Edition/Format: Article Article : English
Publication: The Mathematics Teacher, v79 n5 (19860501): 323-324
Database: JSTOR Arts & Sciences X Collection
 
Newspapers.com
30 September 1988, Kansas City (MO) Times, “His mnemonics are a phonic tonic to recall it all” by Don Wade, pg. B-5, col. 6:
And granted, Please Excuse My Dear Aunt Sally seems helpful in remembering the sequence of mathematical operations—Parentheses, Exponentiation, Multiplication, Division, Addition and Subtraction.
   
Google Groups: alt.callahans
A few of my favorite words
Charles Olson
4/20/92
(...)
“Please Pity My Dear Aunt Sally: Parens Powers Mult Div Add Subtract; order of
precedence in elementary arithmetic.
 
OCLC WorldCat record
Writing a PEMDAS Story.
Author: Vadim Golembo
Edition/Format: Article Article : English
Publication: Mathematics Teaching in the Middle School, v5 n9 p574-79 May 2000
Database: ERIC The ERIC database is an initiative of the U.S. Department of Education.
Summary:
Presents a project that asks students to relate mathematical operations to real-world situations, communicate mathematical concepts in writing, share their ideas with their peers, and exercise their creativity. (ASK)
 
Education Week—Teacher
Please Excuse My Dear Aunt Sally (PEMDAS)—Forever!
By David Ginsburg on January 1, 2011 10:21 PM
You don’t have to be a math whiz to know that 4 - 2 + 1 equals 3. Yet I was working with several students recently who said it equals 1. And it wasn’t their fault. Nor was it their teacher’s fault. Nope, the blame in this case and in countless similar cases I’ve encountered over the years rested squarely with the fictitious Aunt Sally of “Please excuse my dear Aunt Sally” (or PEMDAS: parentheses, exponents, multiplication, division, addition, subtraction) fame—the acronym intended to help students remember the order of operations.
 
The problem with PEMDAS is that it excludes the “from left to right” requirement for multiplication and division (#3 below) and addition and subtraction (#4 below). Students, as a result, think multiplication always precedes division and addition always precedes subtraction. This explains why students in the above example said 4 - 2 + 1 equals 1 rather than 3 (i.e., they simplified 2 + 1 first rather than 4 - 2).
     
OCLC WorldCat record
Reflecting on PEMDAS
Author: Kyungsoon Jeon
Publisher: National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: .(JavaScript must be enabled to view this email address); Web site: http://www.nctm.org/publications/
Edition/Format: Article Article : English
Publication: Teaching Children Mathematics, v18 n6 p370-377 Feb 2012
Database: ERIC The ERIC database is an initiative of the U.S. Department of Education.
Other Databases: British Library Serials
Summary:
When the author asked her preservice elementary teachers what “order of operations” is and why it is important for children to learn, they recited “PEMDAS” or “Please Excuse My Dear Aunt Sally” but typically became silent when questioned about the importance of the order of operations. Reys and Fennell once suggested that the mathematics component of preservice elementary education must be examined if real change is to occur at the elementary school level (2003, p. 278). In an attempt to bring such change to the classrooms, in this article the author examines what students understand about the order of operations and offers some helpful hints to correct their misunderstanding. She shares three stories about PEMDAS that she has collected while instructing classes of preservice elementary school teachers of mathematics. (Contains 2 tables.)
 
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Ivana Olson
‏@hazeymarie
@fanoonman Order of Operations in math. PEMDAS. Please Excuse My Dear Aunt Sally. Parentheses, Exponents, Multiply, Divide, Add, Subtract.
6:21 PM - 24 Dec 2016 from Phoenix, AZ