What Is the BODMAS Rule Formula and How to Solve Expressions Using It
The concept of BODMAS rule plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing how to use the BODMAS rule helps students solve expressions correctly and avoids calculation errors in Maths, whether they’re learning basics or preparing for competitive exams.
What Is BODMAS Rule?
The BODMAS rule is a standard order of operations in Maths to solve expressions with more than one operator. The full form of BODMAS is: Brackets, Orders (powers, roots), Division, Multiplication, Addition, and Subtraction. You’ll find this concept applied in areas such as order of operations, simplification, and algebra.
Key Formula for BODMAS Rule
Here’s the standard formula order for solving expressions using the BODMAS rule:
| Letter | Represents | Operation | Examples |
|---|---|---|---|
| B | Brackets | ( ), { }, [ ] | (4 + 5), 3{2+1} |
| O | Orders | Powers, Indices, Roots | 23, √9 |
| D | Division | ÷ or / | 18 ÷ 3 |
| M | Multiplication | × or * | 7 × 2 |
| A | Addition | + | 11 + 8 |
| S | Subtraction | - | 10 - 3 |
Step-by-Step Illustration (BODMAS Example)
- Solve: (3 + 4) × 5 + 6 − 2
2. Multiplication: 7 × 5 = 35
3. Addition: 35 + 6 = 41
4. Subtraction: 41 − 2 = 39
Quick Reference: BODMAS vs PEMDAS
| BODMAS (India/UK) | PEMDAS (US/International) | Difference |
|---|---|---|
| Brackets, Orders, Division, Multiplication, Addition, Subtraction | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction | Brackets vs Parentheses, Orders vs Exponents |
Both rules have the same operation order logic, just different acronyms. If you understand BODMAS, you’ll easily understand PEMDAS! Explore details in the PEMDAS topic here.
Speed Trick or Vedic Shortcut for BODMAS
A handy trick is to scan the expression for brackets and solve them first. For very long sums, underline each operation in the BODMAS order to stay organized. In competitive exams, using BODMAS from left to right after each operator saves precious time and avoids “careless mistakes.”
Example: If an expression has both multiplication and division, solve them in order from left to right — not multiplication always first!
Try These Yourself
- Solve: 8 + 9 ÷ 9 + 5 × 2 − 7 using BODMAS.
- Simplify: [25 – 3 (6 + 1)] ÷ 4 + 9.
- Find the result: 17 − 24 ÷ 6 × 4 + 8 with the correct order of operations.
- Solve: 3 + 24 × (15 ÷ 3) following BODMAS.
Frequent Errors and Misunderstandings
- Forgetting to solve brackets first before other operations.
- Multiplying before dividing, even when division comes earlier left-to-right.
- Adding before multiplying or dividing.
- Solving from right to left instead of left to right.
- Missing “Orders” (squares, cubes, roots) in the sequence.
Relation to Other Concepts
The BODMAS rule connects closely with arithmetic operations and algebraic expressions. Mastering BODMAS helps you solve simplification problems, fractions, and equations with several steps. It also ties in with the simplification techniques used in higher classes.
Classroom Tip
A quick way to remember BODMAS is to say the word out loud, or use a visual mnemonic: “Big Orange Dragons Make Awesome Snacks.” Vedantu’s teachers use color coding and BODMAS ladders during live sessions and worksheets — you can create one yourself to aid memory!
BODMAS Practice Worksheet & Calculator Tool
Practice makes perfect! Download free worksheets with BODMAS sums, or try an online BODMAS calculator to check your answers instantly. Regular practice boosts your accuracy and confidence for all school and Olympiad-style exams.
We explored BODMAS rule—from definition, operation order, examples and mistakes, to shortcuts and classroom tricks. With practice and proper understanding, you will never make mistakes in the order of operations. Continue practicing with Vedantu to become confident in Maths using BODMAS!
Related Topics for Further Learning
FAQs on BODMAS Rule in Mathematics with Clear Explanation
1. What is the BODMAS rule in Maths?
The BODMAS rule is the order of operations used to solve mathematical expressions correctly. It stands for:
- B – Brackets
- O – Orders (powers and roots)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
2. Why is the BODMAS rule important?
The BODMAS rule is important because it prevents confusion and ensures everyone gets the same correct answer for a mathematical expression. Without an order of operations, expressions like 2 + 3 × 4 could give different results. By applying BODMAS, multiplication is done before addition, giving the correct answer 14 instead of 20.
3. How do you apply the BODMAS rule step by step?
To apply the BODMAS rule, solve the expression by following the correct order of operations.
- Step 1: Solve expressions inside brackets.
- Step 2: Solve orders (powers, roots).
- Step 3: Perform division and multiplication from left to right.
- Step 4: Perform addition and subtraction from left to right.
4. Can you give an example of BODMAS rule?
An example of the BODMAS rule is solving 8 + 2 × 3.
- Multiplication first: 2 × 3 = 6
- Then addition: 8 + 6 = 14
5. What does ‘O’ mean in BODMAS?
In BODMAS, ‘O’ stands for Orders, which means powers and roots. Orders include:
- Exponents like 3²
- Roots like √16
6. Is division done before multiplication in BODMAS?
In the BODMAS rule, division and multiplication are performed from left to right, whichever comes first. They have equal priority. For example, in 20 ÷ 5 × 2:
- 20 ÷ 5 = 4
- 4 × 2 = 8
7. What is the difference between BODMAS and PEMDAS?
The difference between BODMAS and PEMDAS is only in terminology, not in meaning. BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction, while PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Both follow the same order of operations and give identical results.
8. How do you solve brackets using BODMAS?
According to the BODMAS rule, brackets are solved first before any other operation. For example, in (5 + 3) × 2:
- Solve inside brackets: 5 + 3 = 8
- Then multiply: 8 × 2 = 16
9. What are common mistakes when using the BODMAS rule?
Common mistakes in using the BODMAS rule include ignoring the order of operations and not working left to right for multiplication and division.
- Adding before multiplying
- Ignoring brackets
- Solving multiplication before division without checking order
10. Does BODMAS apply to algebraic expressions?
Yes, the BODMAS rule applies to both numerical and algebraic expressions. For example, in 3 + 2x × 4:
- Multiply first: 2x × 4 = 8x
- Then add: 3 + 8x = 3 + 8x
