Type 6÷2(1+2) into two different calculators and you can get two different, defensible answers: 9 and 1. That is not a bug in either machine. It comes down to one small habit, writing a multiplication sign as nothing at all, and whether the calculator in your hand gives that missing sign extra weight. Below is both readings worked step by step, what real calculators actually show with their sources, why the same argument keeps going viral under new numbers, and how to write the expression so nobody can argue about it again.
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So, is 6÷2(1+2) equal to 1 or 9?
Both. Read strictly left to right, the order most schools teach, 6÷2(1+2) equals 9. Treat the multiplication sign you left out before (1+2) as binding tighter than division, the rule several handheld calculators use, and it equals 1. Neither reading is a mistake; the expression itself is written ambiguously.
- Left to right, equal rank for × and ÷ (the order most schools teach): 9.
- The missing multiplication sign binds first (the rule several handheld calculators use): 1.
Which one is "right" depends entirely on which of those two rules your calculator, teacher or textbook follows, and that is the actual, checkable fact worth knowing rather than picking a side.
The case for 9: read it strictly left to right
Parentheses first: (1+2) = 3, so the expression becomes 6÷2(3). In the order most schools teach, PEMDAS in the United States, BODMAS or BIDMAS elsewhere, multiplication and division sit at the same rank, and operations at the same rank run left to right. Read that way, the division comes before the leftover multiplication: 6÷2(3) = 6÷2×3 = 3×3 = 9.
This is also how most general purpose software reads it. A typical expression parser gives an omitted multiplication sign no special priority over division; it just inserts the sign and keeps evaluating left to right. Write the sign in yourself and there is nothing left to argue about: 6÷2×(1+2) = 9.
The case for 1: when the missing sign binds first
Some calculators, and some algebra habits, treat the multiplication you left out as more than cosmetic. Write 2x instead of 2×x and most people read the 2 and the x as one glued unit before anything divides it. Several handheld scientific calculators apply that same habit to 2(1+2): the missing sign attaches the 2 to the bracket first, so (1+2) resolves to 3, then 2(3) resolves to 6 as a single step, and only then does 6÷2(1+2) become 6÷6.
On this reading, the parentheses were never just grouping 1+2. They were grouping 2(1+2) as a whole against everything to their left, which is why the same handheld calculators that do this return 1 rather than 9: 6÷2(1+2) = 1.
Why do calculators give different answers to 6÷2(1+2)?
Because their manuals say so, in writing. Handheld calculators publish a calculation priority sequence, an ordered list of which operation type is evaluated first when two operations tie for attention, and manufacturers have never agreed on where a multiplication sign that was left out belongs in that list. Here is the documented behaviour, model by model.
| Calculator | Answer to 6÷2(1+2) | Source |
|---|---|---|
| Casio fx-991ES PLUS, fx-570ES PLUS, fx-9910NG PLUS (handheld) | 1 | Casio, fx-115ES PLUS / fx-991ES PLUS User's Guide |
| Casio fx-991CW, fx-570CW ClassWiz (current handheld) | 1 | Casio support site, Calculation Priority Sequence |
| TI-82 (older, discontinued) | 1 | Texas Instruments, Calculators and Order of Operations |
| TI-83 family onward, including the TI-84 Plus | 9 | Texas Instruments, Solution 11773 |
| Google search bar, Wolfram Alpha | 9 | Plus Magazine, The PEMDAS Paradox |
Plus Magazine points out that Wolfram Alpha reads 6÷2(1+2), a bracket around plain numbers, as 9, but reads 6÷2x, a bracket free term with a letter in it, as 3x, grouping the 2 and the x first. The same missing sign gets treated two different ways depending on what sits next to it, on the same tool.
If your own calculator is not on that list, do not assume. Type 6÷2(1+2) into it once and read the display; that is the only way to know for certain, and it is the one thing every source above agrees on: check your own model rather than trust a rule of thumb from a forum post. For more on why this particular expression is a poor way to judge whether a calculator is trustworthy, see the one test with no right answer.
Why the same argument keeps going viral
The argument is older than any tweet. Mathematical historian Florian Cajori recorded the same disagreement over the order of ÷ and × almost a century ago, and Oliver Knill, writing a short note on the subject for a Harvard course, points out there has still never been a worldwide standard for it. What changed is the audience. In March 2013, 6÷2(1+2) itself spread across Facebook, widely enough that a national outlet ran an explainer on it. In July 2019, a near identical shape, 8÷2(2+2), was posted on Twitter and within days Steven Strogatz was explaining it in the New York Times.
Neither round settled anything, because there was nothing to settle. Two different, internally consistent conventions produce two different, correct answers, and no international body has picked one. See what a calculator that ranks the missing sign first returns for the 2019 version: 8÷2(2+2) = 1.
How to write 6÷2(1+2) so nobody can misread it
You almost never need to write it the ambiguous way. If you mean multiply, then divide, group the left side first: (6÷2)(1+2) = 9, which is unambiguous under any convention, because the brackets fix that grouping before anything else happens. If you mean divide by the whole bracketed term, group the other way instead: 6÷(2(1+2)), which is unambiguous and equals 1 under any convention, because the outer bracket fixes the entire denominator.
A multiplication sign left out next to a division symbol is one of the few places plain arithmetic notation genuinely breaks down. An extra pair of brackets costs a moment of typing and removes the argument completely.
What WideMath does with it
WideMath treats a multiplication sign that has been left out as binding tighter than division, so typing the expression above returns 1. This matches the calculation priority sequence printed in the Casio fx-991ES PLUS manual, where a multiplication with the sign left out is ranked above explicit multiplication and division. Write the sign in yourself, or add brackets to say exactly what you mean, and WideMath follows your grouping exactly, the same as any calculator should.
If you are still getting comfortable with the keypad itself, start with how to use a scientific calculator. And if you are wondering why a small team in Nepal cares this much about one ambiguous expression, that is more or less why we built WideMath in the first place: we would rather fix a disagreement in our own tool than leave it for you to discover mid exam.
Try it yourself
Type any version, with or without brackets, and see exactly how WideMath reads it.
Open the calculator with 6÷2(1+2) loaded →Questions people ask
Is 6÷2(1+2) equal to 1 or 9?
Both, depending on which convention you use. Read strictly left to right, the order most schools teach, it equals 9. Treat the multiplication sign left out before (1+2) as binding first, the convention several handheld calculators use, and it equals 1. The expression is genuinely ambiguous, so the honest answer names both and explains why.
What is implied multiplication, and why does it change the answer?
Implied multiplication, also called multiplication by juxtaposition, is writing 2(3) instead of 2 times 3 with the sign shown. Everyone agrees it means multiply. The disagreement is about priority: some calculators evaluate it at the same rank as division, left to right, while others rank it above division, so it happens first even next to a division sign.
Is 8÷2(2+2) the same problem as 6÷2(1+2)?
Yes, the same shape with different numbers. 8÷2(2+2) was posted on Twitter on 28 July 2019 and was explained in the New York Times days later. It splits the same way: 16 read strictly left to right, or 1 if the missing multiplication sign binds to the bracket first.
Why do calculators give different answers to the same expression?
Because manufacturers never agreed on one shared rule for a multiplication sign that has been left out. It is documented, not random. Casio's manuals since the fx-991ES PLUS rank implied multiplication above division. Texas Instruments moved the TI-83 and later models, including the TI-84 Plus, to strict left to right evaluation instead. Both are internally consistent; they simply chose differently.
How do I write 6÷2(1+2) so there is only one possible answer?
Add a bracket around the part you mean to keep together. (6÷2)(1+2) is unambiguous and equals 9 under any convention. 6÷(2(1+2)) is unambiguous and equals 1 under any convention. Either version is only slightly longer than the original and settles the question completely.
Is PEMDAS or BODMAS the correct order of operations?
They describe the same order. PEMDAS and BODMAS, or BIDMAS, are regional acronyms, not competing rules. The letters group multiplication with division, and addition with subtraction, to show each pair shares a rank rather than fixing a strict sequence. Neither acronym says what to do about a multiplication sign that was left out, which is exactly where 6÷2(1+2) lives.
Sources
Every external claim above, in the order it appears.
- Casio's documented calculation priority sequence (handheld). fx-115ES PLUS / fx-991ES PLUS User's Guide (PDF, Casio), the source for the priority 7 ranking of a multiplication with the sign left out, above priority 10 explicit multiplication and division.
- Casio's current ClassWiz manual. Calculation Priority Sequence, fx-991CW+ UK support page (Casio), confirming the same ranking on the current handheld line.
- Texas Instruments on implied multiplication. Calculators and Order of Operations (TI bulletin, 28 July 2023) and Solution 11773, Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators (TI knowledge base), the source for the TI-82 versus TI-83 and later split.
- The academic case for genuine ambiguity. Oliver Knill, Harvard, Ambiguous PEMDAS (PDF, 28 February 2021), and David Linkletter, The PEMDAS Paradox, Plus Magazine (17 June 2019).
- The 2013 Facebook round. Tara Haelle, What Is the Answer to That Stupid Math Problem on Facebook? (12 March 2013).
- The 2019 Twitter round. Steven Strogatz, The Math Equation That Tried to Stump the Internet, first published in The New York Times, 2 August 2019.