Every few years a post goes viral with the expression 8 \div 2(2+2) and a poll: 1 or 16? Half the internet is sure the answer is 1. The other half is sure it is 16. Each side mocks the other for not knowing BODMAS. This is one of those rare cases where both sides are right, and the fight is really about something they never learned the name for.

State the misconception

The misconception: the expression has a single, unambiguous arithmetic answer, and anyone who disagrees with you has failed at BODMAS.

Why it's tempting: you were taught BODMAS as a strict rule. "Brackets, Orders, Division, Multiplication, Addition, Subtraction — do it in that order, end of story." If BODMAS is a complete algorithm, then the expression must have exactly one correct reading, and the other camp must be wrong.

The counter-example

Here is the trap: BODMAS is not a complete algorithm. It is silent on a specific case — what to do with implicit multiplication, the missing "\times" sign between 2 and (2+2). Different reading conventions fill that silence differently. The same symbols genuinely have two readings.

Reading A: strict left-to-right BODMAS, \times and \div tied. Treat implicit multiplication as identical in precedence to \times. Then divisions and multiplications are equal-weight and evaluated left-to-right.

8 \div 2(2+2) \;=\; 8 \div 2 \times (2+2) \;=\; 8 \div 2 \times 4 \;=\; 4 \times 4 \;=\; 16

Why: with the juxtaposition 2(2+2) read as 2 \times (2+2) at the same level as \div, left-to-right puts the division first: 8 \div 2 = 4, then 4 \times 4 = 16.

Reading B: implicit multiplication binds tighter than \div. This is the convention of many physics textbooks, many calculators (Casio fx-series especially), and much of scientific writing. Juxtaposition 2(2+2) is a single product unit, evaluated before the surrounding \div.

8 \div 2(2+2) \;=\; 8 \div [2 \times (2+2)] \;=\; 8 \div [2 \times 4] \;=\; 8 \div 8 \;=\; 1

Why: under this convention, 2(2+2) is treated as one compound factor — the way 2x is treated as a single thing in 8 \div 2x. The division is applied to the whole unit.

Both readings are self-consistent. Both are taught, in different places. The expression 8 \div 2(2+2) is genuinely ambiguous notation.

The correct mental model

The correct framing is not "which camp is right?" — it is "good notation does not create this ambiguity in the first place."

In practice, professional mathematicians never write 8 \div 2(2+2). They write either

\frac{8}{2(2+2)} \;=\; 1 \qquad \text{or} \qquad \frac{8}{2}(2+2) \;=\; 16

using a fraction bar, which scopes its denominator visually. The ambiguity exists only because the inline division symbol \div has no such scope. On paper it is obvious where the denominator ends; in a text field, you cannot see the bar, so the reader has to guess.

This is why inline division viral posts are designed to split readers: the typography itself is withholding information. The poll isn't testing arithmetic; it's testing whose convention each reader grew up with.

The same expression under two bracketing conventions gives different answersThe expression eight divided by two times the quantity two plus two is shown at the top. Below it, two reading paths fork. The left path labelled reading A adds brackets around eight divided by two first, then multiplies by four to get sixteen. The right path labelled reading B adds brackets around two times the quantity two plus two first, then divides eight by eight to get one. A note at the bottom says good notation avoids this by using a fraction bar. 8 ÷ 2(2+2) Reading A: (8 ÷ 2) × (2+2) = 4 × 4 = 16 Reading B: 8 ÷ [2 × (2+2)] = 8 ÷ 8 = 1 Good notation uses a fraction bar to pick a side.
Two readings of the same five symbols. Neither is "wrong arithmetic." The tweet forces a choice that the $\div$ sign was never designed to adjudicate — which is why every serious mathematical text uses a fraction bar instead of $\div$ for any expression with more than one operation in sight.

Why the juxtaposition convention exists

Reading B — implicit multiplication binds tighter than \div — isn't arbitrary. It makes common algebraic notation work. Consider the expression \dfrac{1}{2x}. If you rewrote it as 1 \div 2x on a single line, everyone would read it as \dfrac{1}{2x}, not as \dfrac{1}{2} \cdot x. The juxtaposition 2x is understood as a single block. That's the same rule applied in 8 \div 2(2+2) under reading B.

If you forced strict left-to-right with \div (reading A), you would have to read 1 \div 2x as \dfrac{x}{2}, which is nobody's expectation. So reading B is in wide use because it matches how algebraic expressions are written by hand.

Reading A, meanwhile, is in wide use among calculators and spreadsheets, which don't recognise juxtaposition at all — they treat every \div and \times at equal precedence.

What the exam-room answer should be

If you see something like this in an exam, two principles help:

  1. In Indian school syllabi (ICSE, CBSE, state boards), reading A is the taught convention — BODMAS treats juxtaposition as multiplication at the same level, with left-to-right tie-breaking. The exam-expected answer to 8 \div 2(2+2) would be 16. Confirm with your teacher if in doubt.
  2. In any serious mathematical writing of your own, don't use \div at all for expressions with more than one operation. Use a fraction bar. It forces you to pick one side and makes the expression unambiguous.

Your goal as a problem-solver is not to win the tweet war. It is to write and read expressions so no one has to argue about them in the first place.

A quick table of similar traps

A few other inline expressions viral posts love to exploit:

Expression Reading A (strict BODMAS) Reading B (juxtaposition tight)
6 \div 2(1+2) (6 \div 2) \times 3 = 9 6 \div (2 \times 3) = 1
48 \div 2(9+3) 24 \times 12 = 288 48 \div 24 = 2
12 \div 4(4-1) 3 \times 3 = 9 12 \div 12 = 1

Same structural ambiguity every time: a lone \div sign, followed by a coefficient-and-bracket juxtaposition. If you catch yourself seeing one of these in a quiz, the right move is to mentally rewrite it with a fraction bar on the version the question-setter almost certainly meant, and answer that.

The real takeaway

The reason viral tweets about 8 \div 2(2+2) never get resolved is that there is nothing to resolve. The expression is badly written. BODMAS is not wrong; it just doesn't cover the juxtaposition case. Two reasonable conventions fill the gap, and each social-media camp has internalised a different one. The tweet spreads because it feels like an argument about arithmetic, when it is really an argument about typography.

If you want to be the person who stops arguing on these posts: write the expression on paper as a fraction, ask the poster which version they meant, and move on with your life. The fact that the question has no single answer is the answer.

Related: Operations and Properties · BODMAS Drift: What Happens When You Break the Order · Algebraic Expressions · Fractions and Decimals