BODMAS Explained: Order of Operations with Examples

If someone asks you to work out 3 + 4 × 2, you might be tempted to do 3 + 4 first to get 7, then multiply by 2 to get 14. But the correct answer is 11. The reason comes down to the order of operations, and in Australia we use the acronym BODMAS to remember it.

What does BODMAS stand for?

Letter	Stands for	Examples
B	Brackets	(3 + 4), [2 × 5]
O	Orders (powers and roots)	5², √9
D	Division	12 / 4
M	Multiplication	3 × 5
A	Addition	7 + 2
S	Subtraction	10 - 3

BODMAS tells you the order in which to perform operations when a calculation has more than one. Brackets first, then orders, then division and multiplication (left to right), and finally addition and subtraction (left to right).

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Important: D and M are equal, A and S are equal

This is where many students get confused. BODMAS does not mean you always do division before multiplication. Division and multiplication have the same priority, and you work through them from left to right. The same applies to addition and subtraction.

Example: 12 / 3 × 2

Division and multiplication are equal priority, so go left to right:
12 / 3 = 4
4 × 2 = 8

If you did the multiplication first (3 × 2 = 6, then 12 / 6 = 2), you would get the wrong answer.

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Worked examples

Example 1: 3 + 4 × 2

1. No brackets. No orders.
2. Multiplication first: 4 × 2 = 8.
3. Then addition: 3 + 8 = 11.

Answer: 11 (not 14)

Example 2: (5 + 3) × 2

1. Brackets first: 5 + 3 = 8.
2. Then multiplication: 8 × 2 = 16.

Answer: 16. The brackets change the order and give a different result from 5 + 3 × 2, which would be 11.

Example 3: 20 - 3² + 1

1. No brackets.
2. Orders: 3² = 9.
3. Left to right for addition and subtraction: 20 - 9 = 11, then 11 + 1 = 12.

Answer: 12

Example 4: 2 × (10 - 4)² / 3

1. Brackets first: 10 - 4 = 6.
2. Orders: 6² = 36.
3. Left to right for multiplication and division: 2 × 36 = 72, then 72 / 3 = 24.

Answer: 24

Example 5: 8 + 12 / (2 + 2)

1. Brackets first: 2 + 2 = 4.
2. Division: 12 / 4 = 3.
3. Addition: 8 + 3 = 11.

Answer: 11

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Nested brackets

Sometimes brackets appear inside other brackets. Work from the inside out.

Example: 2 × [3 + (4 × 2)]

1. Innermost brackets: 4 × 2 = 8.
2. Outer brackets: 3 + 8 = 11.
3. Multiplication: 2 × 11 = 22.

Answer: 22

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Common mistakes

• Going strictly left to right and ignoring BODMAS. The expression 5 + 2 × 3 equals 11, not 21. Multiplication is done before addition.
• Thinking D always comes before M. They are equal. Work left to right when you have both.
• Forgetting that "orders" includes square roots. √16 + 2 = 4 + 2 = 6. Evaluate the root first.
• Skipping steps. Writing out each step is not a waste of time. It is how you avoid errors. Even strong students make mistakes when they try to do too many steps in their head.

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BODMAS vs PEMDAS vs BIDMAS

You might see different acronyms depending on where a resource comes from. PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is common in American textbooks. BIDMAS replaces "Orders" with "Indices." They all describe exactly the same rules. In Australia, BODMAS and BIDMAS are the most common.

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Practice tip

The best way to master BODMAS is to write out every step on a separate line. Do not try to do the whole calculation at once. Evaluate one operation at a time, rewriting the expression after each step. Once you are confident with simple expressions, increase the complexity.

imSteyn covers order of operations in the Year 7 curriculum and revisits it as expressions get more complex in later years. It gives you problems to solve and guides you through any mistakes, rather than just showing the answer. If you want to sharpen your BODMAS skills with guided practice, try it free.

Getting BODMAS right matters because every area of maths that follows, from algebra to trigonometry, assumes you can evaluate expressions correctly. It is a small investment in understanding that pays off in every topic you study from here on.