PEMDAS and BODMAS are exactly the same rule packaged in different regional acronyms. The common misconception that multiplication always comes before division in PEMDAS, or that division always comes before multiplication in BODMAS, is fundamentally incorrect.
Both acronyms serve as memory aids for the standard order of operations, and they treat multiplication and division as equal priorities, just as they treat addition and subtraction as equal priorities. When operators of the same priority appear together, you must solve them by working strictly from left to right.
Here is a breakdown of how these two acronyms align:
The Order Hierarchy
- P / B: Parentheses / Brackets
- E / O: Exponents / Orders (such as indices, roots, or powers)
- MD / DM: Multiplication and Division (equal priority, solved left-to-right)
- AS: Addition and Subtraction (equal priority, solved left-to-right)
Visualizing the Priority Tiers
Because formatting the rules as a linear string of letters causes confusion, it is much more accurate to view them in four horizontal tiers of mathematical hierarchy:
Why the “Left-to-Right” Rule Matters
Without the left-to-right rule, a simple mathematical expression could yield two different answers depending on which acronym you use. Consider the expression:
- The Incorrect Way (Rigid PEMDAS): If you blindly follow the letters, you might multiply 3 times 2 first to get 6, and then calculate 12 / 6 = 2.
- The Incorrect Way (Rigid BODMAS): If you blindly follow the letters of a different expression like 12 times 3 / 2, a rigid division-first interpretation would skew the math similarly.
- The Correct Way (Left-to-Right): Because division and multiplication sit on the exact same priority tier, you evaluate the expression from left to right. First, calculate 12 / 3 = 4. Then, multiply 4 times 2 = 8.
The correct mathematical result is 8, no matter which acronym you grew up learning in school. The exact same logic applies to addition and subtraction: 10 – 5 + 2 must be solved left-to-right 5 + 2 = 7, not by adding first 10 – 7 = 3.
PEMDAS and BODMAS are not competing systems of mathematics; they are just different regional names for the same global standard. Whether you say “Parentheses” or “Brackets”, or “Exponents” or “Orders”, the mathematical execution remains identical. They are equal partners on shared tiers, governed entirely by the direction of the page.
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