Why 8÷2(2+2) Has Two Correct Answers — The BODMAS Debate Explained

Every few months a deceptively simple arithmetic expression goes viral on Twitter, Facebook, and WhatsApp. Millions of people argue about it. Families fall out. Adults doubt their own education. The most famous version looks something like this:

Here's the thing most people don't know: both answers can be mathematically justified. This isn't a case where one side is simply wrong and the other is right. It's a case where the expression itself is ambiguously written — and the two different answers reflect two different, legitimately held conventions that are taught in different countries, institutions, and textbooks around the world.

Understanding why requires a short but genuinely fascinating dive into the history of mathematical notation, the difference between BODMAS and PEMDAS, and — most practically for Nigerian students — exactly which rule WAEC uses in its examinations.

WHAT BODMAS ACTUALLY MEANS

BODMAS is the acronym used across Nigeria, the UK, and most Commonwealth countries to remember the order of mathematical operations. Each letter tells you what to calculate first:

The most important — and most misunderstood — part of BODMAS is that D and M are not separate priority levels. Division and Multiplication share the same level of precedence. When both appear in an expression, you evaluate them strictly from left to right, whichever comes first. Similarly, A and S share the same priority, evaluated left to right.

WHY 8÷2(2+2) GETS TWO ANSWERS

Let's trace both solutions carefully so you can see exactly where the fork appears.

Everyone agrees on the first step: solve the bracket. 2+2 = 4. So the expression becomes 8 ÷ 2(4).

Now the expression has two operations remaining: a division symbol (÷) and implied multiplication (the 2 sitting right next to the bracket with no symbol between them). This is where the two camps diverge completely.

TEAM 16: THE STRICT LEFT-TO-RIGHT ARGUMENT

This method treats "2(4)" as exactly the same as "2 × 4" — just written without the multiplication sign. Under strict BODMAS left-to-right, the division comes first because it appears first reading left to right. This is what most calculators do, and it's what most teachers in Nigeria will tell you is correct.

TEAM 1: THE IMPLIED MULTIPLICATION ARGUMENT

This method argues that when a number is written directly adjacent to a bracket with no operator — like "2(4)" — it forms a single unit that should be resolved before anything else. Mathematicians call this "implicit multiplication" or "juxtaposition." In physics textbooks, engineering notation, and many higher-level mathematics texts, this convention is standard. The expression "a/bc" in a physics paper almost universally means "a ÷ (bc)", not "(a ÷ b) × c."

BODMAS vs PEMDAS vs BEDMAS — A WORLD MAP

The reason this argument cuts across borders is that different countries were taught genuinely different mnemonics with genuinely different emphasis:

Notice that PEMDAS puts M before D, while BODMAS puts D before M. This has fooled generations of students into thinking the order actually differs — but mathematically they all represent the same rule: multiplication and division are equal priority, evaluated left to right. The letter order in the acronym is just a convention for spelling a memorable word, not a true hierarchy.

WHAT NIGERIA'S WAEC EXPECTS YOU TO USE

For Nigerian students sitting WAEC, NECO, JAMB, or any secondary school examination, the practical answer is clear: use BODMAS strictly, treating division and multiplication as equal priority evaluated left to right. This is the convention taught in Nigerian secondary schools and tested in Nigerian examinations. Under this convention, 8÷2(2+2) = 16.

WAEC's examination papers are designed to avoid the kind of ambiguous notation that generates these internet debates. In a properly written WAEC question, the expression would be written with explicit brackets to make the intended grouping unambiguous: either 8÷(2×(2+2)) to get 1, or (8÷2)×(2+2) to get 16. When you see ambiguous notation in everyday life, it's almost always a problem with the way the question was written, not with the rules themselves.

HOW TO NEVER GET THESE WRONG AGAIN

The real lesson from the viral BODMAS debate isn't "which answer is right." It's this: ambiguous notation is bad mathematics. A mathematics professor at UC Davis put it best: the best practice, recommended since 1917 in the Mathematical Gazette, is to use brackets to eliminate all possible ambiguity. No self-respecting mathematician would write 8÷2(2+2) when they could write (8÷2)(2+2) or 8÷(2(2+2)) to make their meaning crystal clear.

As a student, when you write your own mathematical expressions in exams and coursework, use brackets generously. Not because you don't know the order of operations, but because clear communication is itself a mathematical virtue — and WAEC rewards it.

THE DEEPER LESSON

The viral BODMAS debate reveals something important about mathematics that most school teaching misses: mathematical notation is a human invention, and like all inventions, it has ambiguities, historical quirks, and regional variations. The "rules" of BODMAS are not cosmic laws handed down from nature — they are conventions agreed upon (imperfectly) by mathematicians over centuries to make written expressions unambiguous.

Understanding that mathematical rules are conventions, not dogma, is actually a sign of mathematical maturity. The students who find this article and genuinely understand both sides of the debate — not just the answer their textbook gives — are building exactly the kind of critical mathematical thinking that distinguishes high performers from rote learners.