What Is BIDMAS? Definition, Rules & Examples

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Updated: Dec 15, 2024

Lesson

Mathematical calculations require a standardized order of operations to ensure consistency and accuracy. This is where BIDMAS comes in. The BIDMAS order of operations provides a clear framework for solving mathematical problems.

BIDMAS helps in eliminating ambiguity and ensuring that all mathematical problems arrive at the same solution.

What Is BIDMAS?

BIDMAS is a mnemonic that helps remember the order in which mathematical operations should be performed to ensure accurate results.

This table provides a breakdown of BIDMAS, the acronym used to remember the order of operations in mathematics:

Letter	Operation	Explanation
B	Brackets	Solve anything inside parentheses or brackets first.
I	Indices	Calculate powers or exponents (like squares, cubes, etc.).
D	Division	Perform division from left to right.
M	Multiplication	Perform multiplication from left to right.
A	Addition	Perform addition from left to right.
S	Subtraction	Perform subtraction from left to right.

The BIDMAS rule ensures that we perform operations in a consistent and structured order. In cases where division and multiplication or addition and subtraction appear together, they are performed from left to right, as they appear in the expression.

This table represents the Order of Operations (BIDMAS) used to solve mathematical expressions correctly and consistently. Here's how each operation is prioritized:

Order of Operations Table (BIDMAS)

Position of Operation	Priority of Operation	BIDMAS	Mathematical Symbol
1	1	Brackets	( )
2	2	Indices	xⁿ
3	3	Division	÷
4	3	Multiplication	×
5	4	Addition	+
6	4	Subtraction	-

For example: 3 + 2 x (5 - 3)²

Brackets (B): Solve inside the parentheses first.
5 − 3 = 2
Now the expression becomes:
3 + 2 × 2²
Indices (I): Solve the exponent next.
2²= 4
Now the expression becomes
3 + 2 x 4
Division/Multiplication (DM): Perform multiplication next (left to right).
2 X 4 = 8
Now the expression becomes:
3 + 8
Addition/Subtraction (AS): Perform addition last.
3 + 8 = 11

Final answer = 11

It establishes the order in which mathematical operations should be performed in an expression to obtain a consistent and correct result.

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Year 7 - BIDMAS

How to Operate BIDMAS

This is how we should follow the order of operations sequentially to solve mathematical expressions accurately.

Brackets: Simplify any expressions within brackets or parentheses first.

Example: 6 + (3 × 2) = 6 + 6 = 12

Indices (Orders/Exponents): Calculate any powers or exponents next.

Example: 5 + 2² = 5 + 4 = 9

Division and Multiplication: Perform division and multiplication operations from left to right.

Example: 10 ÷ 2 × 3 = 5 × 3 = 15

Addition and Subtraction: Perform addition and subtraction operations from left to right.

Example: 8 - 3 + 5 = 5 + 5 = 10

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Number - Year 8 - BIDMAS

BIDMAS Rules

There are certain rules that need to be followed while operating mathematical problems using BIDMAS

Equal Importance: Division and multiplication hold equal priority, as do addition and subtraction. Perform these operations from left to right.
Nested Brackets: When dealing with nested brackets (brackets within brackets), work from the innermost set of brackets outwards.
Implicit Multiplication: Understand that terms written together, like 3a or xy, imply multiplication.
Fraction Bars: Treat the numerator and denominator of a fraction as if they are enclosed in brackets, simplifying each separately before dividing.

Exponents and Roots: Indices encompass both exponents and roots (e.g., square roots, cube roots). Simplify these before moving to multiplication and division.

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Year 7y - BIDMAS

Comparison of BIDMAS , BODMAS and PEMDAS

BIDMAS, BODMAS, and PEMDAS are acronyms representing the order of mathematical operations. Despite slight variations in terminology, they all convey the same fundamental principles for calculating expressions accurately.

Acronym	Operation	Example	Explanation
BIDMAS/BODMAS	Brackets	(3+2)×4	Solve (3+ 2) = 5, then 5 × 4= 20.
	Indices/Orders	23+4	Solve 23 = 8, then 8 + 4 = 12.
	Division/Multiplication	8÷4×2	Left to right: 8 ÷ 4 = 2, then 2 × 2 = 4.
	Addition/Subtraction	5+3−2	Left to right: 5 + 3 = 8, then 8 − 2 = 6.
PEMDAS	Parentheses	Same as Brackets	Parentheses = Brackets, same operations as BIDMAS/BODMAS.
	Exponents	Same as Indices	Exponents = Indices in BIDMAS.

Key Mathematical Clarifications:

Division and Multiplication:
- In all three, these operations are equal in priority and solved left to right.
- Example:
  8 ÷ 4 × 2 → Solve 8 ÷ 4 = 2 then 2 × 2= 4
Addition and Subtraction:
- Similarly, these are solved left to right, with no inherent priority.
- Example:
  10 − 3 + 5 → Solve 10 − 3 = 7, then 7 + 5 = 12
Brackets/Parentheses:
- Operations inside brackets/parentheses are solved first.
- Example:
  (2 + 3) × 4 → Solve 2 + 3 = 5, then 5 × 4 = 20
Exponents/Indices/Orders:
- Powers or exponents are solved after brackets but before multiplication/division.
- Example:
  2 × 3² → Solve 3²= 9 then 2 × 9 = 18

The differences in naming (BIDMAS, BODMAS, PEMDAS) do not affect the mathematical calculations, as the underlying principles remain identical. The focus should always be on following the priority and solving from left to right for operations of the same level.

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