BODMAS Rule Explained: Order of Operations Made Easy

Get two people to solve 6 + 3 × 2 without agreeing on a method first, and you’ll get two different answers. One says 18. One says 12. Only one is right — and the reason comes down to a single rule most of us learned in school and half-remember as adults: BODMAS.

BODMAS rule is the order of operations used to solve any expression with more than one arithmetic operation: Brackets, Orders, Division, Multiplication, Addition, Subtraction — solved in that sequence so everyone reaches the same, correct answer, whether the expression appears in a textbook, a calculator, or a spreadsheet formula.

If you’ve ever gotten a “trick” math problem wrong on social media, chances are BODMAS — or its cousin PEMDAS — was the reason. Here’s how to never get one wrong again.

What Is the BODMAS Rule?

BODMAS is an acronym. Each letter stands for a category of operation, and the order of the letters is the order you’re supposed to work through an expression:

• B – Brackets
• O – Orders (powers and roots, like squares, cubes, and square roots)
• D – Division
• M – Multiplication
• A – Addition
• S – Subtraction

The rule exists because arithmetic on its own is ambiguous. 6 + 3 × 2 genuinely could mean “add 6 and 3, then multiply by 2” (18) or “multiply 3 and 2, then add 6” (12). Without a fixed convention, every textbook, calculator, and computer program could return a different answer to the same sum. BODMAS removes that ambiguity. It’s the same reason traffic exists on one side of the road — not because it’s the only workable choice, but because everyone needs to agree on the same one.

You’ll mostly meet BODMAS in UK, Indian, and Australian classrooms. In the US, the same idea is taught as PEMDAS. More on that shortly.

The BODMAS Rule, Step by Step

Here’s the order you follow, every time, without exception:

1. Brackets first. Solve everything inside (), [], or {} before touching anything outside them. If brackets are nested, start with the innermost one.
2. Orders next. Resolve powers (like 3²) and roots (like √9).
3. Division and Multiplication — left to right. These two sit at the same level of priority. You don’t always do division before multiplication; you do whichever one appears first as you read the expression left to right.
4. Addition and Subtraction — left to right. Same logic. These are equal-priority operations, resolved in the order they appear, not by which letter comes first in the acronym.

That last point trips up more students than anything else in this rule, so it’s worth repeating: BODMAS is not a strict letter-by-letter sequence. D doesn’t always beat M, and A doesn’t always beat S. Think of it as four tiers of priority — brackets, then orders, then multiply/divide as one tier, then add/subtract as one tier — not six separate steps.

Quick Takeaway

Brackets → Orders → (Divide/Multiply, left to right) → (Add/Subtract, left to right). Four tiers, not six rigid steps.

Worked Examples

Let’s build from simple to genuinely tricky.

Example 1 — Basic mix 3 + 5 × 2 Multiplication before addition: 5 × 2 = 10, then 3 + 10 = 13.

Example 2 — Brackets change everything (3 + 5) × 2 Brackets first: 3 + 5 = 8, then 8 × 2 = 16. Same numbers as Example 1, different answer, purely because of where the brackets sit. This is the cleanest way to demonstrate why the rule matters at all.

Example 3 — Division and multiplication, left to right 20 ÷ 4 × 2 Not 20 ÷ (4 × 2). Work left to right: 20 ÷ 4 = 5, then 5 × 2 = 10.

Example 4 — Orders (powers) 2 + 3² Powers before addition: 3² = 9, then 2 + 9 = 11.

Example 5 — Nested brackets and powers together 6 + 3 × [8 − (5 + 1)²] ÷ 2

1. Innermost bracket: 5 + 1 = 6
2. Apply the order (power): 6² = 36
3. Finish the square bracket: 8 − 36 = −28
4. Multiply: 3 × (−28) = −84
5. Divide: −84 ÷ 2 = −42
6. Add: 6 + (−42) = −36

That last example is exactly the kind of multi-layer expression that shows up in exams — and exactly the kind most guides skip in favor of easy one-step examples. If you can follow it, you’ve genuinely got BODMAS.

BODMAS vs PEMDAS vs BIDMAS vs GEMDAS

Here’s something that confuses a lot of people online: BODMAS, PEMDAS, BIDMAS, and GEMDAS are not competing rules. They’re regional vocabulary for the identical mathematical convention.

Acronym	Full Form	Mostly Used In
BODMAS	Brackets, Orders, Division, Multiplication, Addition, Subtraction	UK, India, Australia
PEMDAS	Parentheses, Exponents, Multiplication, Division, Addition, Subtraction	USA
BIDMAS	Brackets, Indices, Division, Multiplication, Addition, Subtraction	UK (alternative)
GEMDAS	Grouping, Exponents, Multiplication, Division, Addition, Subtraction	Canada

“Brackets” and “Parentheses” refer to the same symbols. “Orders,” “Indices,” and “Exponents” all mean powers and roots. And even though PEMDAS lists multiplication before division while BODMAS lists division before multiplication, the actual math doesn’t change — both are still resolved left to right as one combined tier, so a problem worked correctly under either acronym gives the same answer. If your textbook uses a different acronym than your teacher just said out loud, you haven’t been taught two different rules. You’ve been taught one rule in two dialects.

Common Mistakes Students Make with BODMAS

Most errors in BODMAS problems come from a handful of repeat offenders:

• Treating BODMAS as a strict six-step order. As covered above, division doesn’t automatically outrank multiplication, and addition doesn’t automatically outrank subtraction. Solve those pairs left to right instead.
• Mishandling negative numbers. 1 − 3 + 4 should be read as (1 − 3) + 4 = −2 + 4 = 2, worked left to right. A common wrong answer comes from grouping the numbers incorrectly, e.g., treating it as 1 − (3 + 4) = 1 − 7 = −6.
• Losing track of multiple brackets. When an expression has several sets of brackets, resolve the innermost pair first and work outward, one layer at a time, rather than trying to simplify everything at once.
• Forgetting powers apply before multiplication. In 2 + 3², students sometimes multiply 2 × 3 before squaring, instead of resolving the power first.
• Rushing left-to-right order. In 20 ÷ 4 × 2, calculating 4 × 2 first before dividing gives the wrong answer of 2, instead of the correct 10.

If you keep making the same mistake, it’s usually one of these five, not a gap in your understanding of the rule itself.

BODMAS with Negative Numbers, Fractions, and Decimals

BODMAS doesn’t change shape just because the numbers get messier — the same four tiers apply.

With negative numbers: treat a subtraction sign followed by a negative as addition — 5 − (−3) = 5 + 3 = 8. Solve inside the brackets first, exactly as with positive numbers.

With fractions: a fraction bar acts like an invisible bracket. In (1/2 + 1/4) × 4, resolve the bracketed fraction sum first, then multiply.

With decimals: the process is unchanged — 0.5 + 2 × 1.5 still means multiply first (2 × 1.5 = 3), then add (0.5 + 3 = 3.5). Decimals don’t get special treatment; they follow the same order any whole number would.

BODMAS in Algebra

BODMAS isn’t just an arithmetic drill — it’s the backbone of simplifying algebraic expressions too. Take a(b + c) = ab + ac: this is the distributive law, and it exists precisely because brackets must be resolved (or expanded) before anything else touches the terms inside them. When you’re simplifying something like 4 + 2(x + 3), you either expand the bracket first (2x + 6) or, if x has a known value, solve inside the bracket first — either way, the bracket takes priority. Every time you factor, expand, or simplify an algebraic expression in secondary-school maths, you’re applying BODMAS logic, even if no one calls it that in the moment.

Practice Questions

Try these before checking the answers below.

1. 4 + 3 × 8
2. (6 + 2) × 3 − 4
3. 18 ÷ 3 × 2
4. 5² − 10 ÷ 2
5. 2 × (3 + 4)² ÷ 7
6. 12 − (4 + 2) ÷ 3
7. 3 + [10 − (2 + 3)] × 2
8. (1/2 + 1/2) × 6 − 1

Answers: 1) 28 2) 20 3) 12 4) 20 5) 14 6) 10 7) 13 8) 5

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FAQ Section

Q1. What is the full form of BODMAS? BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction — the fixed sequence used to resolve expressions with multiple operations correctly.

Q2. Does multiplication always come before division in BODMAS? No. Division and multiplication have equal priority. You solve them in the order they appear, working left to right through the expression, not by letter order.

Q3. What is the difference between BODMAS and PEMDAS? Nothing mathematically. They’re regional names for the same rule — BODMAS is used in the UK, India, and Australia; PEMDAS is used in the US. “Brackets” equals “Parentheses,” and “Orders” equals “Exponents.”

Q4. Why do we need the BODMAS rule? Without an agreed order of operations, the same expression could produce different answers depending on who solves it. BODMAS guarantees everyone — students, teachers, calculators — reaches one consistent, correct result.

Q5. How do you handle brackets inside brackets? Start with the innermost bracket and work outward, resolving one layer completely before moving to the next, until every bracket has been simplified.

Q6. Is BIDMAS the same as BODMAS? Yes. BIDMAS swaps “Orders” for “Indices,” but both refer to powers and roots. The rule and the order of steps are identical.

Q7. Can BODMAS be used with negative numbers? Yes. The same four-tier order applies — resolve brackets first, then work left to right through the remaining operations, treating negative signs carefully (e.g., subtracting a negative becomes addition).

Q8. What’s the most common mistake students make with BODMAS? Treating it as six rigid, sequential steps rather than four priority tiers — specifically, assuming division must happen before multiplication, or addition before subtraction, when both pairs are actually solved left to right.