Order of Operations

The order of operations is a set of rules that tells you which part of a calculation to do first. Without these rules, the same calculation could give different answers depending on the order you choose. The SET 11+ exam tests this topic directly and also relies on it indirectly in multi-step problems.

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The Rule: BODMAS (or BIDMAS)

The order of operations is remembered using the acronym BODMAS:

Letter	Stands for	Meaning
B	Brackets	Do anything inside brackets first
O	Orders	Powers (squares, cubes) and roots
D	Division	Do division and multiplication...
M	Multiplication	...from left to right (they are equal priority)
A	Addition	Do addition and subtraction...
S	Subtraction	...from left to right (they are equal priority)

Key Point: Division and Multiplication have the same priority — work from left to right. Addition and Subtraction also have the same priority — work from left to right.

Some people use BIDMAS instead, where the "I" stands for "Indices" (another word for powers). Both acronyms mean exactly the same thing.

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Worked Examples

Example 1: No brackets

Calculate 3 + 4 × 5.

Multiplication comes before addition:

4 × 5 = 20, then 3 + 20 = 23.

A common mistake is to add 3 + 4 first to get 7, then multiply by 5 to get 35. This is wrong because multiplication must be done before addition.

Example 2: With brackets

Calculate (3 + 4) × 5.

Brackets come first:

3 + 4 = 7, then 7 × 5 = 35.

Notice: The brackets change the answer completely — from 23 to 35. This is why BODMAS matters!

Example 3: Multiple operations

Calculate (7 + 3) × 2 - 4.

Step 1: Brackets: 7 + 3 = 10.

Step 2: Multiplication: 10 × 2 = 20.

Step 3: Subtraction: 20 - 4 = 16.

Example 4: With powers

Calculate 3² + 4 × 2.

Step 1: Orders (powers): 3² = 9.

Step 2: Multiplication: 4 × 2 = 8.

Step 3: Addition: 9 + 8 = 17.

Example 5: Division and brackets

Calculate 48 ÷ (2 × 4) + 3².

Step 1: Brackets: 2 × 4 = 8.

Step 2: Division: 48 ÷ 8 = 6.

Step 3: Orders: 3² = 9.

Step 4: Addition: 6 + 9 = 15.

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Common Mistakes

Mistake 1: Adding before multiplying