What is BODMAS?
BODMAS is a mnemonic that represents the correct sequence of operations for solving mathematical expressions. BODMAS stands for Brackets, Orders (powers), Division, Multiplication, Addition, and Subtraction. The BODMAS rule ensures every math expression produces one correct answer by defining which operation to perform first.
Without the BODMAS rule, the expression 3 + 4 × 2 could give 14 (wrong) or 11 (correct). The BODMAS calculator tool applies this sequence automatically to solve math expressions and provide a step-by-step solution.
What is BIDMAS and PEMDAS?
BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction. BIDMAS is the same order of operations as BODMAS — the only difference is the word "Indices" replaces "Orders." The words “Indices” and “Orders” refer to powers in these mnemonics.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. PEMDAS is the order of operations standard used in the United States. The difference between PEMDAS, BIDMAS, and BODMAS is regional naming — not mathematical logic. All three systems produce identical results for every arithmetic expression.
BODMAS Full Form
The six letters of BODMAS represent the following steps and operations:
How to Solve Math Expressions Using the BODMAS Rule
To solve a math expression using the BODMAS rule, follow these 4 steps in order:
- Solve all brackets present in the math expression -- start with the innermost bracket first.
- Evaluate the powers and roots in the expression.
- Perform division and multiplication operations from left to right.
- Perform addition and subtraction operations from left to right.
Perform multiplication and division from left to right, then addition and subtraction from left to right. The operations in each pair have equal priority. The calculator shows each step.
The BODMAS Rule and Order of Operations
BODMAS is a mnemonic for the order of operations, rather than a formula. Begin with the innermost brackets and apply the same priorities within each group.
- Priority 1: Brackets -- ( ), { }, [ ]
- Priority 2: Powers and roots
- Priority 3: Division and Multiplication -- left to right
- Priority 4: Addition and Subtraction -- left to right
Division does not always come before multiplication. In the BODMAS rule, Division/Multiplication and Addition/Subtraction are "paired" groups with equal priority. Solve them in the order they appear from left to right.
Practical BODMAS Example
Follow this practical math problem to see the same BODMAS order applied from the original expression to the final answer:
Expression becomes: 12 * 3 + 2 - 4^2 + 18 / 3
Expression becomes: 12 * 3 + 2 - 16 + 18 / 3
12 * 3 = 36, then 18 / 3 = 6
Expression becomes: 36 + 2 - 16 + 6
36 + 2 = 38, then 38 - 16 = 22, then 22 + 6 = 28