BODMAS, PEMDAS, and every order-of-operations acronym exist to remove ambiguity from expressions written without enough brackets. They are a fallback — a convention that kicks in when you didn't bother to tell the reader what you meant. Brackets are the direct way to say what you mean. And the secret the acronym-memorisers miss is that brackets are completely free: you can scatter as many as you want into any expression, and the answer never changes.

The rule, one line

\text{Anything inside brackets is computed first.}

That's it. If you see (\ldots), figure out the number inside and replace the whole bracket with that single number before doing anything else. Brackets beat every other operator — exponents, multiplication, division, addition, subtraction. Nothing outranks a bracket.

Why this is the most powerful rule in school algebra

Because it is the only order-of-operations rule you can impose on an expression. BODMAS tells you what to do when you see 2 + 3 \times 4 — you must read it as 2 + 12 = 14, not 5 \times 4 = 20. But if you wrote the expression yourself and wanted to ensure a reader computes it as 20, you add brackets:

(2 + 3) \times 4 = 20.

Now there is no convention to remember. The brackets force the addition to happen first. BODMAS becomes irrelevant because you've already told the reader (and yourself) what to do.

The extra-bracket rule — it is always safe

Here is the secret. Brackets around a single number, or a single variable, or a piece of an expression you already planned to compute first, do nothing. They do not change the answer. They do not cause an error. They just make the grouping visible.

5 + 3 = 5 + (3) = (5) + (3) = (5 + 3) = 8.

All four expressions give the same answer. Adding brackets around 3 or 5 or even around the entire 5 + 3 changes nothing, because the thing inside each bracket is already a single value or an expression that evaluates the same way.

This means you can over-bracket for clarity, always, for free. If you're halfway through a complicated expression and you're unsure which operation will evaluate first, slap brackets around the part you want to compute first. Worst case, they were redundant and nothing changed. Best case, they saved you from a BODMAS misread.

Progressive over-bracketing of an expression without changing its valueFour rows showing the same arithmetic expression written with progressively more brackets. Row one: two plus three times four minus one. Row two: two plus the quantity three times four minus one. Row three: two plus the quantity three times four, minus one inside a bigger bracket. Row four: a fully parenthesised version with every operation wrapped. A column on the right shows that all four evaluate to thirteen. 2 + 3 × 4 − 1 = 13 ↓ add brackets around the × step 2 + (3 × 4) − 1 = 13 ↓ add brackets around the + step too (2 + (3 × 4)) − 1 = 13 ↓ bracket everything, including the final − step ((2 + (3 × 4)) − 1) = 13 each row is more verbose, every row gives the same answer
Four versions of the same expression, with progressively more brackets. Every version evaluates to $13$. Brackets can only *confirm* the BODMAS order — they never override it to give a wrong answer, because BODMAS was reverse-engineered from the bracketed-but-obvious version in the first place.

When extra brackets are actually needed — ambiguity

The case where brackets matter most is when an expression is genuinely ambiguous to human eyes, even though BODMAS pins down its meaning. The most famous culprit is the viral tweet:

8 \div 2(2 + 2) = ?

Some readers say 16. Some say 1. BODMAS technically settles it — 8 \div 2 \times 4 = 4 \times 4 = 16, treating implicit multiplication like explicit multiplication — but half the internet disagrees, and the disagreement is real and legitimate because different contexts teach different conventions for implicit multiplication. The fix is not to pick a side. The fix is to never write the expression that way in the first place. Write either:

(8 \div 2) \times (2 + 2) = 16 \qquad \text{or} \qquad \frac{8}{2(2 + 2)} = 1.

Brackets kill the ambiguity. The reader cannot guess wrong. You never have to argue about which convention applies.

For a fuller dissection of this particular expression, see Does 8 ÷ 2(2+2) Equal 1 or 16 — and Why Do Viral Tweets Disagree?. The point for this article is simpler: if a sane reader might pause over your expression, bracket it.

A live example — drag to see how brackets reshape the answer

Interactive expression where moving brackets changes the answerA horizontal number line from zero to ten with one draggable red point labelled a. Three readouts above the line show three bracketed versions of the expression a plus three times two: the value with no brackets (which equals a plus six by BODMAS), the value with brackets around a plus three multiplied by two (which equals two a plus six), and the value with brackets around three times two added to a. As the reader drags a, the three values diverge, with the bracketing changing the output even though the raw symbols look similar. the first and third rows always agree; the second row is the odd one out 0 5 10 ↔ drag a
The expression $a + 3 \times 2$ is really $a + 6$ by BODMAS — the unwrapped version and the version with brackets around $(3 \times 2)$ give identical answers for every $a$. But putting brackets around $(a + 3)$ first completely changes the meaning to $2a + 6$. Brackets don't just *clarify* BODMAS; when placed in different spots they actively specify *different* expressions. The thing to notice is that the top row and the bottom row always match — the bottom row is the no-op bracketing that confirms BODMAS. The middle row is a different expression altogether.

The lesson from the figure: redundant brackets are free, but re-grouping brackets are powerful. Adding (3 \times 2) around a sub-expression that BODMAS was already going to compute first costs nothing. Moving the brackets to include a different sub-expression — like (a + 3) — changes the whole answer.

When you are solving, not writing

The other direction the rule matters: when you are reading someone else's expression (a textbook, a problem sheet, an exam paper), the brackets you see are instructions. Compute them first. Collapse them to single values. Then carry on with whatever is left.

Evaluating a nested expression

Evaluate: 3 + 2 \cdot \big( 5 - (4 - 1) \big)^2

Step 1 — the innermost bracket first.

4 - 1 = 3

Replace it:

3 + 2 \cdot \big( 5 - 3 \big)^2

Step 2 — the next bracket.

5 - 3 = 2

Replace it:

3 + 2 \cdot 2^2

Step 3 — the exponent (order in BODMAS, now that brackets are gone).

2^2 = 4 \Rightarrow 3 + 2 \cdot 4

Step 4 — multiplication before addition.

2 \cdot 4 = 8 \Rightarrow 3 + 8 = 11.

Why the innermost bracket first: each bracket is a sub-expression that must be a single number before the outer expression can use it. So you resolve brackets from the inside out — the same way a function call stack unwinds.

The habit

Carry two simple rules in your head.

  1. When you're writing, if the expression could be read two ways by a tired student, add brackets. You lose nothing by being explicit.

  2. When you're reading, collapse every bracket to a single number before doing anything else. The inner brackets go first.

Students who do this never lose marks to BODMAS confusion, because BODMAS only matters when brackets are missing. Students who skip this step lose marks to one-line sign errors and precedence errors at exactly the moment the rest of the problem was going right.

One last trap — brackets vs function arguments

The notation f(x) in algebra is not the same as multiplication. The brackets around x are function-argument brackets, not grouping brackets. So f(2 + 3) means "plug 5 into the function f," not "multiply f by 5." The shape looks like a bracketed expression but the meaning is entirely different.

In arithmetic, brackets always mean "compute me first and use the result." In algebra with functions, the same shape can mean "this is my input." Context tells you which. If the thing before the bracket is a function name (f, \sin, \log), it is a function argument. If the thing before the bracket is a number or a bracketed expression, it is multiplication. Most of the time you can tell in a glance — but when you can't, the surrounding expression gives it away.

Related: Operations and Properties · BODMAS Drift: What Happens When You Break the Order · Does 8 ÷ 2(2+2) Equal 1 or 16 — and Why Do Viral Tweets Disagree? · Read an Expression as a Tree, Not a Sentence