# BODMAS: Simplifying Mathematical Operations with Examples and Sums

Mathematics is a fascinating subject that involves solving complex equations and performing various operations. One crucial concept that lays the foundation for mathematical calculations is BODMAS, an acronym that stands for Brackets, Orders (exponents and roots), Division and Multiplication, and Addition and Subtraction. Understanding BODMAS is essential for solving equations accurately and efficiently. In this article, we will delve into the world of BODMAS, providing clear explanations, examples, and practice sums to help you master this fundamental principle.

## 1. What is BODMAS?

BODMAS is a mnemonic device used to remember the order of operations in mathematics. It ensures that mathematical expressions are evaluated consistently and accurately. Each letter in the acronym represents a specific operation.

• B: Brackets: Operations enclosed in brackets must be performed first. Brackets include parentheses (), square brackets [], and curly braces {}.
• O: Orders: After simplifying expressions within brackets, the next step is to evaluate any exponents or powers. This involves raising a number to a given power or calculating the root of a number.
• D: Division and Multiplication: Once the brackets and orders are resolved, division and multiplication operations are performed from left to right.
• M: Multiplication: After division, any remaining multiplication operations are carried out.
• A: Addition and Subtraction: Finally, addition and subtraction are performed from left to right.

## 2. Examples of BODMAS

To better grasp the concept of BODMAS, let's explore some examples:

### Example 1:

Evaluate the expression: 6 + 4 × 2.
According to BODMAS, we must perform the multiplication before addition:
6 + 4 × 2 = 6 + 8 = 14.

### Example 2:

Evaluate the expression: 10 - 4 ÷ 2 + 3.
10 - 4 ÷ 2 + 3 = 10 - 2 + 3 = 8 + 3 = 11.

### Example 3:

Evaluate the expression: (5 + 2) × 3 - 6 ÷ 2.
First, we solve the expression within the brackets:
(5 + 2) × 3 - 6 ÷ 2 = 7 × 3 - 6 ÷ 2.
Next, we perform the multiplication:
7 × 3 - 6 ÷ 2 = 21 - 6 ÷ 2.
Finally, we perform the division and subtraction:
21 - 6 ÷ 2 = 21 - 3 = 18.

## 3. BODMAS with Complex Expressions

BODMAS becomes especially useful when dealing with more complex expressions. Let's consider the following example:

### Example 4:

Evaluate the expression: 3 × (4 + 2) ÷ (5 - 1) + 2 × 3.

Using BODMAS, we first solve the brackets:
3 × (4 + 2) ÷ (5 - 1) + 2 × 3 = 3 × 6 ÷ 4 + 2 × 3.

Next, we perform the multiplication:
3 × 6 ÷ 4 + 2 × 3 = 18 ÷ 4 + 2 × 3.

Then, we perform the division:
18 ÷ 4 + 2 × 3 = 4.5 + 2 × 3.

Finally, we perform the remaining multiplication and addition:
4.5 + 2 × 3 = 10.5.

## 4. Importance of BODMAS

Understanding BODMAS is crucial for solving mathematical problems accurately and avoiding confusion or ambiguity. It provides a standardized order of operations that ensures consistent results across different calculations. Without BODMAS, mathematicians and scientists would face difficulties when dealing with complex equations.

Furthermore, BODMAS is essential for simplifying equations and expressions, allowing us to break down complex problems into manageable steps. This simplification aids in efficient problem-solving, reducing the chances of errors and facilitating better comprehension of mathematical concepts.

## 5. Practice Sums

To solidify your understanding of BODMAS, here are some practice sums:

1. 12 ÷ (3 + 1) × 5 - 2
2. (8 - 3) × 2 + 4 ÷ (6 - 3)
3. 15 - 3 × (6 ÷ 2) + 4

Remember to follow the order of operations outlined by BODMAS while solving these problems. Take your time, and once you have calculated the answers, verify them against the solutions provided below:

1. 12 ÷ (3 + 1) × 5 - 2 = 3 × 5 - 2 = 15 - 2 = 13
2. (8 - 3) × 2 + 4 ÷ (6 - 3) = 5 × 2 + 4 ÷ 3 = 10 + 1.33 ≈ 11.33
3. 15 - 3 × (6 ÷ 2) + 4 = 15 - 3 × 3 + 4 = 15 - 9 + 4 = 10

## Final Words

BODMAS is a fundamental concept that simplifies mathematical operations and ensures consistent and accurate calculations. By understanding the order of operations and following BODMAS, you can solve complex equations with confidence.

Embrace this valuable tool, practice diligently, and watch your mathematical prowess soar as you conquer more challenging equations and calculations.