BODMAS Explained (NSW) -Quick Summary:
The BODMAS rule helps students solve maths expressions in the correct order. It stands for
Brackets, Orders, Division, Multiplication, Addition and Subtraction.
This guide includes step-by-step rules, worked examples, common mistakes, and practice tips aligned to the NSW curriculum.
Introduction to the BODMAS Rule
Many students lose marks in maths not because they don’t know the operations, but because they perform them in the wrong order.
The BODMAS rule helps students solve mathematical expressions correctly by following a clear and consistent sequence.
BODMAS stands for:
- B – Brackets
- O – Orders (powers and square roots)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
By following this order, students avoid confusion and get the correct answer consistently. BODMAS is taught as part of the NSW Mathematics curriculum and appears regularly in school assessments, NAPLAN, OC, and Selective preparation.
Related: NSW Mathematics syllabus support
Why the BODMAS Rule is Important?
Mathematical expressions often contain more than one operation. Without a clear order, the same question could produce different answers.
BODMAS ensures everyone solves the expression the same way.
Example: Solve 6 + 2 × 3
- Multiply first: 2 × 3 = 6
- Add next: 6 + 6 = 12
Students use BODMAS throughout primary and high school maths, including algebra, fractions, equations, and word problems. It’s a foundational skill for exam accuracy.
The BODMAS Rule: Step-by-Step Guide
Follow these steps in order:
1) Brackets
Solve calculations inside brackets first. If there are multiple brackets, start with the innermost one.
Example: (5 + 3) × 2 → 5 + 3 = 8 → 8 × 2 = 16
2) Orders (Indices, Powers and Roots)
Next, solve powers (squares/cubes), square roots, and other indices.
Example: 4² = 16
3) Division and Multiplication (Left to Right)
Division and multiplication have equal priority. Solve them from left to right as they appear.
Example: 9 ÷ 3 × 3 → 9 ÷ 3 = 3 → 3 × 3 = 9
4) Addition and Subtraction (Left to Right)
Finally, solve addition and subtraction from left to right.
Example: 16 + 4 − 5 → 16 + 4 = 20 → 20 − 5 = 15
BODMAS Summary Table
| Step | Operation |
|---|---|
| 1 | Brackets |
| 2 | Orders (powers/roots) |
| 3 | Division and Multiplication (left to right) |
| 4 | Addition and Subtraction (left to right) |
Worked Examples (BODMAS Step-by-Step)
Example 1: 9 ÷ 3 × 3
- Division first: 9 ÷ 3 = 3
- Then multiply: 3 × 3 = 9
Example 2: 8 × 2 + 3
- Multiply first: 8 × 2 = 16
- Then add: 16 + 3 = 19
Example 3: 8 × (2 + 3)
- Brackets first: 2 + 3 = 5
- Then multiply: 8 × 5 = 40
Example 4 (Advanced): 4² × 24 ÷ (9 + 3) + 4 − 5
- Brackets: 9 + 3 = 12 → expression becomes 4² × 24 ÷ 12 + 4 − 5
- Orders: 4² = 16 → expression becomes 16 × 24 ÷ 12 + 4 − 5
- Multiply/divide (left to right): 16 × 24 = 384, then 384 ÷ 12 = 32 → expression becomes 32 + 4 − 5
- Add/subtract (left to right): 32 + 4 = 36, then 36 − 5 = 31
Common Mistakes Students Make
Mistake 1: Solving Left to Right Only
Example: 8 + 4 × 2
Wrong: 8 + 4 = 12 → 12 × 2 = 24
Correct: 4 × 2 = 8 → 8 + 8 = 16
Mistake 2: Ignoring Brackets
Brackets must be solved first. Ignoring brackets can completely change the answer, especially in harder problems.
Mistake 3: Skipping Orders (Squares/Roots)
Students sometimes forget to simplify powers and roots before moving to multiplication or division.
Mistake 4: Rushing in Exams
Many errors happen due to speed rather than understanding. Practising mixed-operation questions helps students apply BODMAS automatically.
How BODMAS is Taught in NSW Schools?
BODMAS is introduced in upper primary and reinforced throughout high school. Teachers use clear step-by-step strategies, practice worksheets, and exam-style questions to build accuracy.
External reference:
NSW Education Standards Authority (NESA)
BODMAS in Exams (NAPLAN, OC and Selective)
BODMAS-style questions appear in many NSW assessments, including NAPLAN and selective preparation. Students who apply the correct order
avoid losing marks on otherwise straightforward questions.
Real-Life Applications of BODMAS
Outside school, BODMAS helps with multi-step calculations such as discounts, budgeting, and formulas. In later years, it becomes essential for algebra, science, and financial maths.
BODMAS vs PEMDAS and BIDMAS
Different countries use different names for the same order of operations:
| System | Meaning |
|---|---|
| BODMAS | Brackets, Orders, Division/Multiplication, Addition/Subtraction |
| PEMDAS | Parentheses, Exponents, Multiplication/Division, Addition/Subtraction |
| BIDMAS | Brackets, Indices, Division/Multiplication, Addition/Subtraction |
In Australia, the standard term used is BODMAS.
Practice Tips to Build Confidence
- Solve mixed-operation questions regularly
- Write each step clearly (avoid mental shortcuts)
- Check your work from left to right for ×/÷ and +/− steps
- Practise exam-style questions to improve speed and accuracy
Need Help with BODMAS?
If your child keeps making order mistakes, gets stuck on multi-step expressions, or loses marks in tests, personalised guidance can help.
At Aussie Math Tutor NSW, we help students understand BODMAS step-by-step, improve accuracy, and build confidence.
- One-on-one tutoring for NSW students (Year 3–10)
- Support for school exams, NAPLAN, OC and Selective preparation
- Online and face-to-face tutoring options
- We proudly serve Sydney suburbs including Telopea, Dundas, Carlingford, Parramatta, Rydalmere, North Rocks, Ermington, Dundas Valley, and Eastwood
Next step: Book a FREE assessment
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Frequently Asked Questions about BODMAS
What does BODMAS stand for?
BODMAS stands for Brackets, Orders (like powers or roots), Division, Multiplication, Addition, and Subtraction. Basically, it’s just the order we follow to solve maths problems properly!
When is BODMAS taught in NSW schools?
In NSW, kids usually get introduced to BODMAS around Year 5, when they start learning how to tackle the order of operations in maths.
Why do we use BODMAS in maths?
We use BODMAS in maths so everyone solves things in the same order and gets the right answer. Without it, people would do sums in different ways and end up with different results—BODMAS keeps it all consistent.
What happens if I don’t follow BODMAS?
If you don’t follow BODMAS, you’ll likely end up with the wrong answer because the order matters. Without it, you might add or multiply in the wrong sequence, and different people would get different results from the same problem. It’s all about keeping things consistent.
What is the order of operations rule used in Australia, and is it different from PEMDAS or BIDMAS in other countries?
In Australia, we use BODMAS, which stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It’s basically the same as BIDMAS (where “Orders” are called “Indices”) and PEMDAS (where “Brackets” are called “Parentheses”). They all follow the same order of operations, just with different names.
What is the order of operations rule used in NSW Schools?
Because NSW follows the Australian curriculum, students here learn BODMAS—just like the rest of Australia. It’s our standard order of operations for solving maths problems consistently.
What is the order of operations rule used in Selective Exams?
In Selective Exams, students use the BODMAS rule—Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It ensures that all multi-step maths problems are solved in the correct order, just as students are taught in NSW schools.
How can I remember the BODMAS rule easily?
A simple way to remember BODMAS is to break it down into its parts: Brackets first, then Orders (like powers), followed by Division and Multiplication (left to right), and finally Addition and Subtraction (left to right). With practice, you’ll get used to the order, and many people simply remember the acronym as a handy guide.
Are there any tricks to avoid mistakes when using BODMAS?
To avoid mistakes, always work step by step and write each stage down. Start with brackets first, then handle any powers or roots before dividing or multiplying from left to right, and finally add or subtract in order. Double-check each step before moving on, and if the expression seems tricky, take your time—rushing leads to most errors!
