Order of operations

The order of operations tells us which operations (e.g. addition, multiplication, powers) to do first when finding the value of an expression.

Abbreviations

There are lots of abbreviations to remember the order of operations. The most common ones are:

• BIDMAS (Brackets, Indices, division and multiplication, Addition and subtraction)
• BODMAS (Brackets, Orders, division and multiplication, Addition and subtraction)
• PEMDAS (Parentheses, Exponents, multiplication and division, Addition) - this is more commonly used in the USA.

In this page, we’ll use BIDMAS.

The order

Whenever we evaluate an expression, we should do it in this order:

1. Brackets: Anything inside brackets (parentheses) should be done first.
2. Indices: We then do any powers or roots (e.g. squares, square roots).
3. division and multiplication:
4. Addition and subtraction

Note: When we have multiple operations of the same rank (e.g. both division and multiplication), we do them from left to right.

Examples

Example: Evaluate 3 + 4 \times 2

• First, we do the multiplication: 4 \times 2 = 8.
• Then, we do the addition: 3 + 8 = 11.
• Answer: 11.

Example: Evaluate (2 + 3)^2

• First, we do the brackets: 2 + 3 = 5.
• Then, we do the indices: 5^2 = 25.
• Answer: 25.

Example: Evaluate 10 - 4 \div 2 + 3 \times 2

• First, we do the division: 4 \div 2 = 2.
• Then, we do the multiplication: 3 \times 2 = 6.
• Next, we do the subtraction: 10 - 2 = 8.
• Finally, we do the addition: 8 + 6 = 14.
• Answer: 14.

Example: Evaluate 5 + (6 - 2)^2 \div 2

• First, we do the brackets: 6 - 2 = 4.
• Then, we do the indices: 4^2 = 16.
• Next, we do the division: 16 \div 2 = 8.
• Finally, we do the addition: 5 + 8 = 13.
• Answer: 13.

Example: Evaluate 8 \div 2(2 + 2)

• First, we do the brackets: 2 + 2 = 4.
• Then, we do the division: 8 \div 2 = 4.
• Next, we do the multiplication: 4 \times 4 = 16.
• Answer: 16.

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