BODMAS is an acronym used to remember the order of operations in mathematics. It stands for:

**Brackets****Orders** (i.e., powers and roots, such as squares and square roots)**Division****Multiplication****Addition****Subtraction**

The BODMAS rule ensures that expressions are evaluated correctly by following these steps in the given order:

1. Brackets: Solve anything inside brackets first. This includes parentheses \(()\), square brackets \([]\), and curly brackets \(\{\}\).

2. Orders: Evaluate exponents or roots, such as \(a^2\) or \(\sqrt{b}\).

3. Division and Multiplication: Perform division and multiplication from left to right as they appear. Note that division and multiplication are of equal precedence; perform them sequentially.

4. Addition and Subtraction: Perform addition and subtraction from left to right as they appear. Like division and multiplication, addition and subtraction are of equal precedence; perform them sequentially.

Example 1: Simple Calculation

Expression:

\[ 6 + 3 \times 2 \]

Solution:

1. No Brackets

2. No Orders

3. Perform Multiplication: \(3 \times 2 = 6\)

4. Addition: \(6 + 6 = 12\)

Result: \(12\)

Expression:

\[ (4 + 5) \times 2 \]

Solution:

1. Brackets First: \(4 + 5 = 9\)

2. No Orders

3. No Division/Multiplication in Brackets

4. Multiplication: \(9 \times 2 = 18\)

Result: \(18\)

Expression:

\[ 3 + 2^2 \times 5 \]

Solution:

1. No Brackets

2. Orders First: \(2^2 = 4\)

3. Perform Multiplication: \(4 \times 5 = 20\)

4. Addition: \(3 + 20 = 23\)

Result: \(23\)

Expression:

\[ 8 + (6 \times 5^2 – 3) \div 3 \]

Solution:

1. **Brackets** First: Solve inside brackets**Orders**: \(5^2 = 25\)**Multiplication**: \(6 \times 25 = 150\)**Subtraction**: \(150 – 3 = 147\)

So, the expression inside the brackets is \(147\)

2. **Division**: \(147 \div 3 = 49\)

3. **Addition**: \(8 + 49 = 57\)

Result: \(57\)

Expression:

\[ \frac{8 + (3 \times (2 + 4^2))}{2} \]

Solution:

1. Brackets First: Solve inside the innermost brackets

Orders: \(4^2 = 16\)

Addition Inside Brackets: \(2 + 16 = 18\)

Multiplication: \(3 \times 18 = 54\)

2. Outer Brackets: \(8 + 54 = 62\)

3. Division: \(\frac{62}{2} = 31\)

Result: \(31\)

By following the BODMAS rule, you ensure that mathematical expressions are evaluated correctly and consistently.

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