Please Excuse My Dear Aunt Sally — What Did She Get Wrong?

Please Excuse My Dear Aunt Sally: order of operations, explained the way she never did. For over a century she's gotten away with something, and nobody's ever asked her to explain herself. Today, that changes!

Same equation. Two "correct" answers. Only one still holds up.

Every few months a division-and-parentheses equation like 8÷2(2+2) goes viral because two real conventions solve it differently. Type any equation in that shape below and watch both methods play out, side by side.

You were taught math has no gray areas. This equation is proof that even professional mathematicians have gone public with opposite answers.

It's not that one side forgot how to do arithmetic. It's that the equation, as written, hands you two different valid instructions — and no one told you notation could do that.

Try it — use the form A÷B(C+D) or A÷B(C−D)
Try the pattern number÷number(expression) — e.g. 8÷2(2+2)
Two ways to read the same symbols:

Older convention

A number touching parentheses is treated as one glued-together unit, multiplied out before any division.
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Modern convention — PEMDAS / BODMAS

Multiplication and division sit at the same level. After parentheses, work strictly left to right.
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Even the experts whose job is to settle this won't call it a simple mistake. In an interview about this exact kind of equation, the American Mathematical Society's own public awareness officer described the expression as genuinely ambiguous, and noted that mathematicians work hard to write rules as precisely as possible specifically because everyday notation doesn't always manage it.
American Mathematical Society, public comment on viral order-of-operations equations
Here's the part that should really bother you: punch the same equation into two different calculators and you can get two different answers. Some older calculator models treat a number glued to parentheses as one locked-together unit and multiply it first; newer ones follow strict left-to-right precedence. Same buttons, same equation, different machine, different number on the screen. If two calculators can't agree, the problem was never your math skills.

So which one is correct?

Textbooks, calculators, and math teachers today all follow the same rule: once you're inside parentheses, multiplication and division are equals — you go left to right, no exceptions for implied multiplication. That makes the modern answer the one you should trust. The older convention isn't "wrong" historically, it just isn't the rule being taught anymore, which is exactly why the two camps keep colliding online.

A word you'll never unhear the same way again

Meet Aunt Sally, math's most controversial relative

"Please Excuse My Dear Aunt Sally" has spent over a century getting kids to apologize for an old woman's behavior without ever explaining what she actually did. No one has ever met Aunt Sally. No one knows why she needs excusing. She simply arrives once a year in third grade, quietly implies that multiplication outranks division, and vanishes.

Here's the part that should really get people arguing: PEMDAS lists Multiplication before Division, which makes it look like a rule. It isn't. Multiplication and division are equals — you go left to right, no exceptions — but Aunt Sally has been letting an entire country believe otherwise since grade school and, frankly, getting away with it.

Aunt Sally Lie Detector — pick a claim she's made:
Order of operations at a glance: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. When an equation still looks unclear after that, the equation was written ambiguously — not you.

Algebra lessons