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BODMAS Questions – Step-by-Step Guide with Solved Examples

By Shailendra Singh

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Updated on 15 May 2025, 17:39 IST

Introduction to BODMAS

BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. It is a rule that determines the order in which mathematical operations should be carried out to simplify expressions correctly.

Understanding BODMAS is crucial for solving math problems accurately, especially in exams and real-world applications where precision is key.

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Understanding the BODMAS Rule

The BODMAS rule helps prioritize operations when faced with mathematical expressions that involve multiple steps. Below is a breakdown of each component of the rule:

Brackets (B)

Brackets are always solved first in any expression. Whether they are parentheses () or square brackets [], any operation inside the brackets is performed first.

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Orders (O)

Orders refer to powers and roots (exponentiation). Operations like squaring numbers, square roots, or other exponential calculations are performed next.

Division (D) and Multiplication (M)

Division and multiplication come after brackets and orders. These operations are handled from left to right, meaning you solve whichever comes first as you move from left to right across the equation.

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Addition (A) and Subtraction (S)

Finally, addition and subtraction are carried out last, also following the left to right rule. This is the simplest part of the operation, where you simply add or subtract numbers in sequence.

How to Solve BODMAS Problems

Step-by-Step Process

  • Step 1: Identify and solve operations inside brackets first.
  • Step 2: Apply orders (powers and roots).
  • Step 3: Perform division and multiplication from left to right.
  • Step 4: Perform addition and subtraction from left to right.

Example 1: Simple Expression

Consider the expression:

8 + (3 × 5) - 2

Step 1: Solve inside the brackets first: 
(3 × 5 = 15)

Step 2: Replace the bracketed part with the result: 
8 + 15 - 2

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Step 3: Now, solve from left to right: 
8 + 15 = 23 
23 - 2 = 21

Final Answer: 21

Example 2: Multi-step Equation

Consider the expression:

6 + 3 × (5 + 2)² ÷ 7

Step 1: Solve the bracket first: 
(5 + 2 = 7)

Step 2: Square the result (as per orders): 
7² = 49

Step 3: Now solve the rest of the expression: 
6 + 3 × 49 ÷ 7

Step 4: Perform division and multiplication from left to right: 
49 ÷ 7 = 7 
3 × 7 = 21

Step 5: Finally, perform addition: 
6 + 21 = 27

Final Answer: 27

Types of BODMAS Questions

BODMAS questions can vary depending on the complexity and the operations involved. Here are some common types:

Basic Arithmetic Questions

These questions involve simple operations such as addition, subtraction, multiplication, and division. Example: 
What is 7 + 3 × 4?

Algebraic Expressions

These problems use variables and often involve terms with exponents, fractions, and polynomials. Example: 
Simplify: 2x + (5 - x) × 3

Fractional Operations

These questions involve fractions and the application of BODMAS to simplify them. Example: 
What is (3/4) × (8/5) + 2?

Exponential Problems

These problems deal with powers and roots. Example: 
What is 2³ + 5 × (4²)?

Common Mistakes When Solving BODMAS Problems

Many students make common mistakes while solving BODMAS problems, often due to skipping steps or not following the order of operations strictly. Here are a few mistakes to watch out for:

  • Ignoring the order of precedence: For example, performing addition before multiplication or forgetting to apply powers.
  • Failing to simplify expressions inside brackets before moving on to other operations.
  • Misinterpreting the operations when multiple operations are involved.

BODMAS Practice Questions

Here are a few practice problems for you to solve:

  1. Simplify: 6 + 2 × (3 + 5)
  2. Evaluate: (7 + 5) × 3² - 4
  3. Solve: 8 × (2 + 3) ÷ 5 + 7

BODMAS Quiz

Engage yourself with a BODMAS quiz to test your understanding of the rule:

  • Question 1: What comes first in the BODMAS rule? a) Multiplication b) Addition c) Brackets d) Subtraction (Correct Answer: c) Brackets
  • Question 2: Simplify: 6 × (3 + 2) ÷ 5 (Correct Answer: 6)

Conclusion and Resources

BODMAS is an essential skill for solving mathematical problems correctly and efficiently. By practicing the rule and avoiding common mistakes, you can handle complex arithmetic and algebraic problems with ease. Be sure to practice regularly with different types of BODMAS questions to improve your problem-solving skills.

For further resources, explore:

  • BODMAS worksheets and practice questions for various grade levels.
  • Interactive BODMAS quizzes available online.
  • Downloadable PDFs of solved examples and problems to reinforce your understanding.

FAQs about Bodmas Questions

What is the BODMAS rule?

The BODMAS rule is a set of guidelines used to determine the correct order of operations when solving mathematical expressions. It stands for Brackets, Orders (Powers and Roots), Division and Multiplication, Addition and Subtraction. According to the order of operations, you must follow this sequence:

  1. Brackets (Parentheses first)
  2. Orders (Exponents or powers, like square roots or exponentiation)
  3. Division and Multiplication (from left to right)
  4. Addition and Subtraction (from left to right)

The rule ensures accurate and consistent results when solving arithmetic operations and expressions.

How do I apply the BODMAS rule in arithmetic problems?

To apply the BODMAS rule in arithmetic problems, follow these steps:

  1. Step 1: Solve inside the brackets (Parentheses) first.
  2. Step 2: Apply any orders (exponentiation or square roots) next.
  3. Step 3: Perform division and multiplication, working from left to right.
  4. Step 4: Finally, do the addition and subtraction, again from left to right.

For example, to solve 6 + (3 × 4) - 2, you would:

  • First, solve inside the brackets: 3 × 4 = 12
  • Then the expression becomes 6 + 12 - 2, and you solve from left to right: 6 + 12 = 18, and 18 - 2 = 16.

How do I solve BODMAS problems with exponents or powers?

To solve BODMAS problems involving powers or exponentiation, such as 2³ or √16, you should:

  1. Simplify exponents or roots (e.g., 2³ = 8 or √16 = 4).
  2. Follow the standard BODMAS rule and continue solving using division, multiplication, and addition/subtraction as needed.

For example, to solve (3 + 2)² × 4, you:

  • Solve inside the brackets first: 3 + 2 = 5
  • Then apply exponentiation: 5² = 25
  • Finally, perform multiplication: 25 × 4 = 100

Can you provide some BODMAS practice questions for Class 6?

Here are some practice BODMAS questions for Class 6 to help you understand the rule:

  1. Solve: 6 + 2 × (3 + 5)
  2. Simplify: (8 + 4) ÷ 4 × 3
  3. Evaluate: (7 + 3) × (5 - 2)

These questions involve basic arithmetic operations and will help reinforce the concept of solving BODMAS problems.

How do I simplify complex BODMAS expressions?

To simplify complex calculations using the BODMAS rule, follow these steps:

  1. Solve the operations inside brackets first.
  2. Apply powers and square roots (orders) next.
  3. Perform division and multiplication in order from left to right.
  4. Lastly, perform addition and subtraction from left to right.

It is important to approach the expression step by step, ensuring that you follow the correct operations order.

 

What is the difference between BODMAS and PEMDAS?

The main difference between BODMAS and PEMDAS lies in the terminology:

  • BODMAS stands for Brackets, Orders (Powers and Roots), Division, Multiplication, Addition, and Subtraction.
  • PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Both rules are essentially the same, but the term PEMDAS is more commonly used in the US, while BODMAS is more commonly used in the UK and other parts of the world. The order of precedence in both rules remains identical.

What are the different types of BODMAS questions?

BODMAS questions can vary in complexity. Some common types include:

  • Basic Arithmetic Operations: These questions involve simple operations like addition, subtraction, multiplication, and division.
    Example: Solve 7 + 3 × 4.
  • Algebraic Expressions: Involves solving equations with variables and operations.
    Example: Simplify 2x + (5 - x) × 3.
  • Fraction Operations: These questions involve simplifying expressions with fractions.
    Example: Simplify (3/4) × (8/5) + 2.
  • Exponential Expressions: Questions that involve powers or exponentiation.
    Example: Simplify 2³ + 5 × (4²).
  • Multi-step Equations: These involve more complex mathematical problems that require multiple operations.
    Example: 6 + 3 × (5 + 2)² ÷ 7.

What are some common mistakes in BODMAS problems?

When solving BODMAS problems, students often make these mistakes:

  • Ignoring the order of operations, such as performing addition before multiplication.
  • Misapplying parentheses and not solving inside them first.
  • Skipping steps in multi-step equations, which can lead to incorrect answers.
  • Incorrectly handling exponents or fractional operations.

To avoid these errors, always follow the BODMAS rule carefully and solve the problem step by step.

How do I approach BODMAS questions with mixed operations?

For mixed operations, where multiple types of operations appear in a single expression, follow these guidelines:

  1. Identify and solve operations inside brackets first.
  2. Solve any exponents (like powers or square roots).
  3. Perform division and multiplication from left to right.
  4. Finally, perform addition and subtraction from left to right.

For example, in the expression 6 × (2 + 3) ÷ 2 + 4, you would:

  • First, solve the bracket: 2 + 3 = 5.
  • Then, perform multiplication and division from left to right: 6 × 5 = 30, then 30 ÷ 2 = 15.
  • Finally, perform addition: 15 + 4 = 19.

Where can I find BODMAS questions with answers PDF?

You can find BODMAS questions with answers PDF on several educational websites and platforms, including:

  • BODMAS worksheets on online educational resources.
  • Math practice PDFs that contain BODMAS questions for Class 6, Class 5, Class 7, etc.
  • You can also download BODMAS quizzes and step-by-step solutions from Infinity Learn.

These resources will help you practice BODMAS problems with detailed solutions and explanations.

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