How to Solve Expressions Using the BODMAS Rule: Step-by-Step Guide
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 – Definition, Order and Examples
1. What is the BODMAS rule in Maths?
The BODMAS rule, or order of operations, dictates the sequence for solving mathematical expressions. It stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction. Following BODMAS ensures accurate calculations by prioritizing operations in the correct order.
2. How do you solve an expression using BODMAS step-by-step?
Solving expressions using BODMAS involves these steps:
• **Brackets:** Solve any expressions within brackets first.
• **Orders:** Calculate powers and roots.
• **Division and Multiplication:** Perform these operations from left to right.
• **Addition and Subtraction:** Perform these operations from left to right.
Always work from left to right within each priority level.
3. Is BODMAS the same as PEMDAS? What is the difference?
BODMAS and PEMDAS are essentially the same; they represent the same order of operations. The difference lies in the acronyms: BODMAS is commonly used in the UK and other parts of the world, while PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is more common in the US. Both acronyms represent the same mathematical principles.
4. When is the BODMAS rule not applicable?
The BODMAS rule doesn't apply when dealing with certain advanced mathematical concepts, such as matrix operations or calculus. It primarily focuses on arithmetic expressions. In those cases, specific rules and conventions for that operation set are applied.
5. What are some common mistakes students make when using BODMAS?
Common BODMAS errors include:
• Incorrectly prioritizing operations—not following the order of operations.
• Misinterpreting the meaning of brackets, leading to wrong calculations.
• Inconsistent application of left-to-right rule when faced with similar operations (e.g., multiplication and division).
6. Are there any examples with answers for BODMAS rule problems?
Yes. Here's an example: 10 + 5 × 2 – 4 ÷ 2 = ?
Following BODMAS:
1. Multiplication: 5 × 2 = 10
2. Division: 4 ÷ 2 = 2
3. Addition: 10 + 10 = 20
4. Subtraction: 20 – 2 = 18
Therefore, the answer is 18.
7. How does the order of multiplication and division (or addition and subtraction) impact the result?
Multiplication and division (and addition and subtraction) have equal priority within the BODMAS rule. When both appear in an expression, work from left to right to determine the correct answer. Changing the order will generally result in a different answer.
8. Why is understanding the BODMAS rule important?
BODMAS is crucial for accurate calculations in mathematics and science. It ensures consistent results and avoids errors. It's fundamental in various subjects, laying the groundwork for further mathematical concepts and problem-solving.
9. How can I improve my speed and accuracy in solving BODMAS problems?
Practice is key! Solve numerous expressions, progressively increasing complexity. Focus on understanding the order of operations, and use visual aids to help you memorize BODMAS. Regular practice will enhance your calculation speed and accuracy.
10. What resources are available for practicing BODMAS problems?
Many online resources offer practice problems and worksheets on BODMAS. Textbooks, educational websites, and online tutoring platforms provide various exercises with solutions. Consistent practice with these resources will build confidence and proficiency.
11. How does BODMAS apply to algebraic expressions?
The BODMAS rule applies to algebraic expressions in the same way it applies to numerical expressions. Follow the order of operations (brackets, orders, division, multiplication, addition, subtraction) to simplify the expression and solve for the unknown variables.
12. What are some tips for remembering the BODMAS rule?
Use mnemonics (like the acronym itself) and visual aids to memorize the order of operations. Practice regularly to reinforce your understanding. Create flashcards or use online interactive tools to test yourself and identify areas needing more attention.
