You have probably seen a viral tweet with an expression like 6 \div 2(1 + 2) and a comments section split exactly in half — one camp saying 1, the other saying 9. The fight looks like it is about arithmetic. It isn't. It is about which order you agreed to read the symbols in. This satellite lets you pick the order and watch the answer drift, so you can see for yourself which readings are conventional and which are wrong.

The drift figure

Below, the expression 24 \div 4 + 2 \times 3^2 is evaluated under three different rules. The correct BODMAS answer is on the left. The other two are common student mistakes. Drag the selector to see each answer.

A slider that cycles through three evaluation orders of the same arithmetic expressionAn interactive figure with a three-position slider. Each position shows the same expression twenty-four divided by four plus two times three squared evaluated under a different rule: standard BODMAS, strict left-to-right, and multiplication before division. A readout box above shows the chosen rule's name and the resulting value. The values differ: eighteen, sixty-six, and eighteen respectively. 24 ÷ 4 + 2 × 3² BODMAS strict left-to-right M before D ↔ drag to change rule
The slider selects an evaluation rule. Only the leftmost position — BODMAS — matches the answer your calculator gives. The other two are rules people invent when they forget the convention.

Three readings, three answers. The difference between them is not arithmetic — every individual +, -, \times, \div was computed correctly. The difference is which computation was done first.

What each rule does

BODMAS (the correct one). Read from left to right, but jump ahead when you hit a higher-priority operation. 3^2 gets evaluated first because it is the exponent. Then 24 \div 4 and 2 \times 9 are done left-to-right at the same level. Finally the addition.

24 \div 4 + 2 \times 3^2 \to 24 \div 4 + 2 \times 9 \to 6 + 18 = 24

Why: BODMAS puts exponents above multiplication and division, which are above addition and subtraction. Within each tier, left-to-right.

Strict left-to-right. This is the rule a child invents if no one has told them about operator precedence: "just compute each operation as you read it."

24 \div 4 = 6 \to 6 + 2 = 8 \to 8 \times 3 = 24 \to 24^2 = 576

That gives 576 — wildly wrong. A milder variant skips the exponent step and gives 66. Either way, it ignores the fact that multiplication and division bind tighter than addition.

Multiplication before division. This is the rule a student invents if they read "BODMAS" as a strict priority list: B, O, D, M, A, S. They think M comes after D, so division goes first. Or they think M comes before A, so multiplication outranks everything below. In this expression it happens to give the same answer as BODMAS (24), but in an expression like 24 \div 4 \times 2 the two rules diverge: BODMAS says 12, "M-before-D" says 3.

Where the viral tweet comes from

The infamous 8 \div 2(2 + 2) drift happens because "implicit multiplication" — writing 2(2+2) without a \times sign — is interpreted by some people as binding tighter than the surrounding \div. Under that interpretation, the expression is 8 \div (2 \times 4) = 1. Under strict BODMAS with no special rule for juxtaposition, it is (8 \div 2) \times 4 = 16. Neither is "wrong" arithmetic — they are answering two different questions, and the expression is genuinely ambiguous.

The lesson is not which camp is correct. The lesson is: whenever you write arithmetic for someone else to read, add enough brackets so the reader can't drift. Write (8 \div 2)(2 + 2) or \dfrac{8}{2(2 + 2)} — whichever you meant. Ambiguity is a writing problem, not an arithmetic problem.

BODMAS is a convention, not a theorem

You can see this more clearly now. None of the three rules above is forced by the structure of the real numbers. They are three different reading conventions. BODMAS is the one mathematicians agreed to, because:

The convention exists to make written mathematics compact. You can override it with brackets any time you need to. You cannot override it with a strong opinion on a tweet.

Spot-check yourself

Before you trust your mental answer on an expression with mixed operations, run through this checklist:

  1. Are there brackets? Do everything inside them first, treating the bracketed sub-expression as atomic.
  2. Are there exponents or roots? Apply them next, one at a time, treating the base as atomic.
  3. Multiplications and divisions? Do them left-to-right in the order they appear. Do not promote one above the other.
  4. Additions and subtractions? Same: left-to-right in the order they appear.

If you ever hesitate between two readings of your own work, add brackets. The calculator does not guess.

Related: Operations and Properties · Algebraic Expressions · Exponents and Powers · Real Numbers and Their Properties