BODMAS Rule Definition Steps Formula and Solved Examples
The concept of BODMAS Rule plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Following BODMAS helps ensure your answers to arithmetic expressions are always accurate, making it a must-know for students of all levels.
What Is BODMAS Rule?
The BODMAS Rule is a standard order of operations used in maths for solving expressions with multiple operations like addition, subtraction, multiplication, division, brackets, and powers (orders). BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. You’ll find this concept applied in areas such as arithmetic, algebra, and solving equations in both school exams and competitive tests.
Key Formula for BODMAS Rule
Here’s the BODMAS order you must always follow in any calculation:
| B | O | D | M | A | S |
|---|---|---|---|---|---|
| Brackets [ ( ) { } ] | Orders (Powers or Roots, e.g., 32, √4) | Division (÷) | Multiplication (×) | Addition (+) | Subtraction (−) |
Step-by-Step Illustration
Let’s use a real example to see how BODMAS works. Suppose you need to solve:
Example: 6 + 3 × [8 − (5 + 1)2] ÷ 2
1. Start with the innermost bracket: (5 + 1) = 62. Next, Orders: 62 = 36
3. Substitute back: [8 − 36] = -28
4. Now, finish the operations inside the square bracket:
3 × (-28) = -84
5. Division: -84 ÷ 2 = -42
6. Addition: 6 + (−42) = -36
Final Answer: -36
Easy Ways to Remember the BODMAS Rule
Remember BODMAS with this simple mnemonic: “Brilliant Order Does Maths Always Simple.” Or, just keep the BODMAS word in your mind whenever you see a complicated maths sum!
- Solve Brackets first, starting from the innermost one.
- Calculate Orders (like exponents or square roots).
- Do Division and Multiplication (from left to right, whichever comes first).
- Finish with Addition and Subtraction (again from left to right).
BODMAS vs PEMDAS (and Other Variants)
| BODMAS | PEMDAS | Used in |
|---|---|---|
| Brackets, Orders, Division, Multiplication, Addition, Subtraction | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction | BODMAS: India, UK, Australia PEMDAS: US, Canada |
BODMAS Rule Examples with Solutions
Solve these step-by-step using the BODMAS rule:
Q1. [18 - 2(5 + 1)] ÷ 3 + 7
1. (5 + 1) = 6
2. 2 × 6 = 12
3. 18 - 12 = 6
4. 6 ÷ 3 = 2
5. 2 + 7 = 9
Answer: 9
Q2. (1 + 20 - 16 ÷ 4²) ÷ {(5 - 3)2 + 12 ÷ 2}
1. 4² = 16
2. 16 ÷ 16 = 1
3. 1 + 20 - 1 = 20
4. (5 - 3) = 2, so 2² = 4
5. 12 ÷ 2 = 6
6. 4 + 6 = 10
7. 20 ÷ 10 = 2
Answer: 2
Download a worksheet for more practice!
Try These Yourself
- Simplify: 3 × (4 + 5) - 8
- Solve: 1800 ÷ 10{(12 − 6)+(24 − 12)}
- What is the value of: 5 + 2 × 32?
- Simplify: [50 - {3 × (9 + 7)}]
Common Errors and Misunderstandings
- Doing multiplication before division just because M comes after D. Always work left to right!
- Ignoring brackets or not solving the innermost bracket first.
- Thinking there’s a higher priority for addition over subtraction—actually, they are the same level.
- Calculator confusion: Basic calculators may not follow BODMAS unless you enter brackets correctly.
BODMAS for Kids: Simple Explanation
BODMAS tells you what to do first in a maths sum—like following a recipe! Remember: Brackets first, then Orders (like squares), then Division and Multiplication (left to right), and finish with Addition and Subtraction (left to right).
| Step | What to Do |
|---|---|
| 1 | Solve what's in brackets ( ) first. |
| 2 | Do powers/roots (Orders). |
| 3 | Do any ÷ and × (left to right). |
| 4 | Do + and − last (left to right). |
Quick Reference: BODMAS Chart
| Letter | Meaning |
|---|---|
| B | Brackets [ ( ) { } ] |
| O | Orders (Powers/Roots) |
| D | Division (÷) |
| M | Multiplication (×) |
| A | Addition (+) |
| S | Subtraction (−) |
Frequent Classroom Tip
A quick mnemonic teachers use: “Brackets Orders Division Multiplication Addition Subtraction”—write BODMAS vertically so you don’t forget the sequence. If you enjoy learning with visuals or handy tricks, Vedantu's live maths classes show you more ways to remember the rule and avoid mistakes.
Relation to Other Concepts
Learning the BODMAS Rule is important before moving on to topics like solving equations, rational expressions, or factorization. It also helps when working with fractions or in word problems that mix several operations together.
We explored BODMAS Rule—from definition, formula, stepwise examples, mistakes to avoid, and connections to algebra, numbers and more. Keep practicing with Vedantu’s worksheets and online classes to master arithmetic operations the right way!
Additional Practice & Related Tools
FAQs on What Is BODMAS in Maths Complete Guide
1. What is BODMAS in Maths?
BODMAS is a rule that tells us the correct order to solve mathematical expressions with multiple operations. It stands for:
- B – Brackets
- O – Orders (powers and roots)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
Using the BODMAS rule ensures that calculations are performed in the correct sequence to avoid wrong answers.
2. What does BODMAS stand for?
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It defines the order of operations in arithmetic expressions.
- Solve expressions inside brackets first.
- Then calculate orders (powers like 2³ or √9).
- Next perform division and multiplication from left to right.
- Finally do addition and subtraction from left to right.
3. Why is BODMAS important in Maths?
BODMAS is important because it ensures everyone gets the same correct answer for a mathematical expression. Without an order of operations, calculations could give different results.
- Example: 8 + 2 × 3
- Using BODMAS: 2 × 3 = 6, then 8 + 6 = 14
- If added first: (8 + 2) × 3 = 30 (incorrect)
This shows why the BODMAS rule is essential for accuracy.
4. How do you solve questions using BODMAS?
To solve questions using BODMAS, follow the order of operations step by step.
- Step 1: Solve inside brackets.
- Step 2: Evaluate orders (powers/roots).
- Step 3: Perform division and multiplication from left to right.
- Step 4: Perform addition and subtraction from left to right.
Example: 12 ÷ 3 + 2 × 4 → 12 ÷ 3 = 4, 2 × 4 = 8, then 4 + 8 = 12.
5. Can you give an example of BODMAS?
Yes, here is a simple BODMAS example: Solve 6 + (4 × 2).
- First solve brackets: 4 × 2 = 8
- Then add: 6 + 8 = 14
Since multiplication is inside brackets, it is done before addition according to the BODMAS rule.
6. What is the difference between BODMAS and PEMDAS?
BODMAS and PEMDAS both describe the same order of operations but use different terms.
- BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Both rules mean that multiplication and division are solved left to right, followed by addition and subtraction left to right.
7. Do you multiply or divide first in BODMAS?
In BODMAS, division and multiplication are performed from left to right, whichever comes first.
- Example: 20 ÷ 4 × 2
- First: 20 ÷ 4 = 5
- Then: 5 × 2 = 10
You do not always multiply before dividing; you follow the left-to-right rule.
8. Do you add or subtract first in BODMAS?
In BODMAS, addition and subtraction are done from left to right, whichever appears first.
- Example: 15 − 5 + 3
- First: 15 − 5 = 10
- Then: 10 + 3 = 13
You should not always add before subtracting; follow the left-to-right sequence.
9. What are common mistakes when using BODMAS?
A common mistake in using BODMAS is ignoring the correct order of operations.
- Adding before multiplying (e.g., 5 + 3 × 2).
- Forgetting to solve brackets first.
- Not following division and multiplication from left to right.
- Ignoring powers or roots under orders.
Carefully applying each step avoids calculation errors.
10. How do brackets affect BODMAS calculations?
In BODMAS, brackets are always solved first before any other operation.
- Example: (10 − 4) × 3
- First: 10 − 4 = 6
- Then: 6 × 3 = 18
Brackets group numbers together and change the normal order of operations, making them the highest priority in BODMAS.
