BODMAS Rule in Mathematics

Introduction

The BODMAS rule is a fundamental principle in mathematics used to solve expressions with multiple operations. It defines the correct order in which operations should be carried out to ensure accurate results. In this blog, we will break down the BODMAS rule and explain each component in detail.

What is the BODMAS Rule?

The BODMAS rule helps us determine the order in which mathematical operations must be performed in an expression. The acronym BODMAS stands for:

• Brackets
• Orders (Powers or Exponents)
• Division
• Multiplication
• Addition
• Subtraction

Using the BODMAS rule ensures that all operations are performed in the correct order, resulting in accurate answers.

Explanation of Each Component

Let’s break down each part of the BODMAS rule:

1. Brackets (B)

Operations inside the brackets should always be performed first. Brackets include parentheses ( ), square brackets [ ], and curly braces { }. For example, in the expression:

Example: 2 × (3 + 5) = 2 × 8 = 16

Here, we solve the operation inside the parentheses first (3 + 5), then perform the multiplication.

2. Orders (O)

Orders refer to exponents (powers) or roots (square roots, cube roots, etc.). After solving the brackets, you move on to the orders. For example:

Example: 2³ = 8

In this example, the exponent 3 means that 2 is multiplied by itself three times (2 × 2 × 2 = 8).

3. Division and Multiplication (D and M)

After solving any brackets and exponents, division and multiplication are performed from left to right as they appear in the expression. Both operations have the same priority, so whichever comes first from the left should be solved first. For example:

Example: 8 ÷ 2 × 4 = 4 × 4 = 16

4. Addition and Subtraction (A and S)

Finally, after performing all division and multiplication operations, addition and subtraction are carried out from left to right. Again, both operations have the same priority, so you solve whichever comes first. For example:

Example: 10 – 3 + 2 = 7 + 2 = 9

Step-by-Step Example

Let’s solve a complex expression using the BODMAS rule:

Example: 6 + 2 × (5² – 1) ÷ 2

1. Step 1: Solve the bracket first: 5² – 1 = 25 – 1 = 24.
2. Step 2: The expression becomes: 6 + 2 × 24 ÷ 2.
3. Step 3: Perform the division and multiplication: 2 × 24 ÷ 2 = 48 ÷ 2 = 24.
4. Step 4: Now, perform the addition: 6 + 24 = 30.

Answer: The final result is 30.

Importance of the BODMAS Rule

The BODMAS rule ensures that mathematical expressions are solved correctly and consistently. Without this rule, different people might solve the same problem in different ways, leading to varying results. By following BODMAS, we can avoid confusion and make sure that everyone arrives at the same solution.

Common Mistakes to Avoid

While using the BODMAS rule, students sometimes make mistakes such as:

• Skipping the brackets and solving other parts first.
• Not following the left-to-right rule for division and multiplication.
• Performing addition before multiplication or division.

By following the rule strictly and practicing with examples, these mistakes can be easily avoided.

Conclusion

Understanding the BODMAS rule is essential for solving complex mathematical expressions. Whether you’re a student or someone working with numbers, mastering this rule will help you tackle any problem with ease and accuracy.