PEMDAS is an example of a mnemonic device, specifically a type of acronym designed to help you remember information. In this case, it serves as a memory aid for the order of operations in mathematics: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. You may also know it through its companion phrase, “Please Excuse My Dear Aunt Sally,” which is a second mnemonic layered on top of the acronym itself.
How a Mnemonic Device Works
A mnemonic device is any technique that helps you encode and recall information more easily. Mnemonics come in many forms: acronyms (like PEMDAS or NASA), rhymes (“i before e, except after c”), visual imagery, or phrases where each word’s first letter maps to something you need to remember. The underlying idea is that your brain holds onto patterns, rhymes, and familiar words more readily than abstract rules.
PEMDAS uses two mnemonic strategies at once. The acronym itself compresses six mathematical operations into a single pronounceable word. The sentence “Please Excuse My Dear Aunt Sally” then turns that acronym into a vivid, easy-to-recall phrase. Both layers serve the same goal: giving you a quick mental shortcut so you don’t have to memorize the raw rule from scratch every time.
What PEMDAS Actually Represents
The mathematical convention behind PEMDAS is the order of operations, a set of rules that dictate the sequence for evaluating an expression. Without a universal order, the same expression could produce different answers depending on which operation you performed first. The hierarchy works like this:
- Parentheses (or any grouping symbol) are resolved first.
- Exponents come next.
- Multiplication and Division are handled together, working left to right.
- Addition and Subtraction are handled together, also left to right.
That left-to-right rule is important, and it’s the spot where the mnemonic can actually mislead people. Because PEMDAS lists multiplication before division and addition before subtraction, many students assume multiplication always comes first. It doesn’t. Multiplication and division share equal priority, and so do addition and subtraction. You simply work through whichever appears first as you read the expression from left to right.
For example, in the expression 8 ÷ 4 × 2, you work left to right: 8 ÷ 4 = 2, then 2 × 2 = 4. If you mistakenly did the multiplication first (4 × 2 = 8, then 8 ÷ 8 = 1), you’d get the wrong answer.
International Versions of the Same Mnemonic
PEMDAS is primarily used in the United States and France, but other countries teach the same mathematical convention with different acronyms. In the United Kingdom, students learn BIDMAS or BODMAS (Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction). Canadian students often use BEDMAS or GEMDAS. Despite the different letters, every version encodes the same underlying rule. The math doesn’t change across borders, only the memory trick does.
Why Some Educators Prefer Alternatives
Because PEMDAS can create the false impression that multiplication outranks division, some math teachers have started using alternative mnemonics that make the equal-priority pairing more obvious. One popular replacement is GEMS, which stands for Grouping, Exponents, Multiply/Divide, Subtract/Add. By collapsing multiplication and division into a single letter, GEMS makes it harder to misread the hierarchy. The “G” for Grouping is also broader than “P” for Parentheses, since it covers brackets, fraction bars, and any other symbols that group terms together.
Another variant, GEMA (Grouping, Exponents, Multiplicative, Additive), takes the same approach and uses category names instead of listing individual operations. Both alternatives teach the identical math. They just package it in a way that reduces the most common misunderstanding students develop from PEMDAS.
Other Well-Known Mnemonic Devices
PEMDAS belongs to a large family of academic mnemonics you’ve probably encountered before. “ROY G. BIV” helps you remember the colors of the visible light spectrum. “Every Good Boy Does Fine” maps the lines of the treble clef in music. “My Very Educated Mother Just Served Us Nachos” captures the order of the planets. In each case, the mnemonic converts a list or sequence that would otherwise require rote memorization into something your brain can grab onto quickly. PEMDAS is simply the math world’s version of the same trick.