BODMAS Rule – Explained with Examples, Order of Operations & Common Mistakes

Mathematics is a universal language that follows a set of precise rules. One of the most important rules in arithmetic is the BODMAS rule, which tells us the correct sequence in which mathematical operations should be performed. Whether you’re solving simple numerical expressions or tackling complex algebraic problems, following the BODMAS rule ensures accurate and consistent results.

In this complete guide, we’ll explore the meaning, full form, importance, and practical application of the BODMAS rule, along with plenty of solved examples and common mistakes to avoid. By the end of this article, you’ll confidently solve any expression using the correct order of operations.

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What is the BODMAS Rule?

The BODMAS rule is a mathematical order of operations used to solve expressions that contain multiple operations such as brackets, exponents, multiplication, addition, etc. It helps ensure that every mathematician or student solves expressions the same way, regardless of location or context.

BODMAS stands for:

• B – Brackets ((), {}, [])

• O – Orders (powers and roots, like exponents or square roots)

• D – Division

• M – Multiplication

• A – Addition

• S – Subtraction

Tip: Always solve from left to right for operations of the same rank (like D and M, or A and S).

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Why is the BODMAS Rule Important?

Without BODMAS, people would interpret the same expression differently, leading to conflicting answers.

Example:
Solve:

$$8+4\times 2$$

• Without BODMAS: $(8+4)\times 2=12\times 2=24$ ❌

• With BODMAS: $4\times 2=8;8+8=16$ ✅

So the correct answer is 16.

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Detailed Explanation of Each BODMAS Component

1. Brackets (B)

Solve expressions inside brackets first. There are three types:

• ( ) – Parentheses

• { } – Braces

• [ ] – Square Brackets

Solve the innermost brackets first.

Example:

$$2+[3\times (4+1)]=2+[3\times 5]=2+15=17$$

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2. Orders (O)

These include:

• Exponents (powers): e.g., 32=93^2 = 932=9

• Roots (square root, cube root): e.g., 16=4\sqrt{16} = 416​=4

Example:

4+32=4+9=134 + 3^2 = 4 + 9 = 134+32=4+9=13

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3. Division and Multiplication (D & M)

These are of equal priority. Solve them from left to right.

Example:

$$16÷4\times 2=(4)\times 2=8$$

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4. Addition and Subtraction (A & S)

Also of equal priority. Solve them from left to right.

Example:

$$10-2+3=8+3=11$$

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BODMAS Rule – Step-by-Step Solved Examples

Example 1:

$$7+2\times (3+4)$$

Step 1: Solve brackets: $3+4=7$
Step 2: Multiply: $2\times 7=14$
Step 3: Add: $7+14=21$

✅ Final Answer: 21

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Example 2:

8+6÷328 + 6 ÷ 3^28+6÷32

Step 1: Orders: 32=93^2 = 932=9
Step 2: Division: $6÷9=0.666$
Step 3: Addition: $8+0.666\approx 8.666$

✅ Final Answer: 8.666

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Example 3:

$$(12-4)+6\times 2$$

Step 1: Brackets: $12-4=8$
Step 2: Multiplication: $6\times 2=12$
Step 3: Add: $8+12=20$

✅ Final Answer: 20

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Difference Between BODMAS and PEMDAS

In some countries like the US, PEMDAS is used instead of BODMAS.

Both follow the same logic — the difference is in terminology.

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Common Mistakes to Avoid

1. Ignoring brackets

   • Always solve the innermost brackets first.

2. Confusing the order of division and multiplication

   • Always go left to right.

3. Skipping exponents

   • Orders must be solved before any multiplication or division.

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Real-Life Applications of BODMAS Rule

• Finance: Calculating compound interest or taxes

• Coding: Writing math logic in programming languages

• Engineering: Formula simplification

• Daily Math: Calculating discounts, bills, measurements

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Practice Questions on BODMAS Rule

1. 10 + 6 ÷ 3 \times 2]

2. (5+3)2−4×2(5 + 3)^2 – 4 \times 2(5+3)2−4×2
3. $20-[2+3\times (4-1)]$
4. 8+23÷48 + 2^3 ÷ 48+23÷4
5. $30÷5\times 2-(3+1)$

Try solving them using the BODMAS rule. Scroll down for the answers.

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Answers to Practice Questions

1. $10+(6÷3\times 2)=10+4=14$

2. (8)2−4×2=64−8=56(8)^2 – 4 \times 2 = 64 – 8 = 56(8)2−4×2=64−8=56

3. $20-[2+3\times 3]=20-[2+9]=20-11=9$

4. $8+8÷4=8+2=10$

5. $30÷5\times 2=6\times 2=12;12-(3+1)=12-4=8$

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BODMAS in Programming

In most programming languages like Python, Java, and C++, expressions are solved using precedence rules similar to BODMAS.

Example (Python):

Always remember to use parentheses if you want to change the default order.

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Final Thoughts

The BODMAS rule is one of the most important foundational concepts in arithmetic. It tells us the exact order in which to perform mathematical operations to avoid confusion and errors. By mastering this rule, students can solve complex expressions with confidence and accuracy.