How to Solve Questions Using the BODMAS Rule?
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 BODMAS Rule: Order of Operations in Mathematics
1. What is the BODMAS rule in maths?
The BODMAS rule, or order of operations, dictates the sequence for solving mathematical expressions with multiple operations. It stands for Brackets, Orders (powers/exponents), Division, Multiplication, Addition, and Subtraction. Following BODMAS ensures consistent and accurate results.
2. Why is the BODMAS rule important?
BODMAS ensures everyone solves complex expressions the same way, preventing calculation errors. It provides a standardized approach, vital for consistent results in mathematics and various applications.
3. What is the difference between BODMAS and PEMDAS?
BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) and PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) are essentially the same. They represent the same order of operations, but use different terminology for brackets/parentheses and orders/exponents.
4. How do I use the BODMAS rule step-by-step?
1. Solve expressions within brackets first.
2. Calculate orders (powers and roots).
3. Perform division and multiplication from left to right.
4. Perform addition and subtraction from left to right.
5. What are some common mistakes when using BODMAS?
Common errors include: Incorrectly prioritizing operations, neglecting the left-to-right rule for division/multiplication and addition/subtraction, and misinterpreting bracket precedence.
6. Can I use BODMAS for all mathematical expressions?
Yes, BODMAS applies to any arithmetic expression with more than one operation or brackets. It is crucial for accurate calculations in various mathematical contexts.
7. What if there are multiple brackets in an expression?
Solve the innermost brackets first, and then work outwards. Prioritize solving brackets in this order: ( ), { }, [ ].
8. What does 'O' (Orders) mean in BODMAS?
'O' represents Orders, which refers to exponents (powers) and roots. Evaluate these before performing other operations.
9. What happens if division and multiplication are in the same expression?
Perform division and multiplication operations from left to right, whichever comes first in the expression. They have equal precedence.
10. What happens if addition and subtraction are in the same expression?
Perform addition and subtraction operations from left to right, whichever appears first. They have equal precedence.
11. Are there any online tools to help me practice BODMAS?
Yes, many online calculators and educational websites offer BODMAS practice exercises and tools to check your answers. These resources can help you improve your understanding and skills.
12. How can I teach BODMAS to younger students effectively?
Use simple examples and visual aids. Break down the steps clearly. Start with simpler expressions, gradually increasing complexity. Make it fun and interactive to improve understanding and retention.
