Simplifying Mathematical Expressions using BODMAS

To solve the given mathematical expression, we need to follow the order of operations, often remembered by the acronym BODMAS or PEDMAS. This order helps us perform calculations in the correct sequence to arrive at the accurate result.

Understanding the Order of Operations (BODMAS)

BODMAS stands for:

• Brackets first (( ), { }, [ ])
• Orders (powers, square roots, etc.) / Of
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

The given expression is:

\(20 \div 5 \text{ of } 8 \times [9 \div 6 \times (6 - 3)] - (10 \div 2 \text{ of } 20)\)

Step-by-Step Simplification

Let's simplify the expression step by step according to the BODMAS rule.

1. Solve the Brackets:
   • Start with the innermost bracket: \((6 - 3) = 3\).
   • Next, simplify the terms involving 'of' inside the brackets: \(2 \text{ of } 20 = 2 \times 20 = 40\).
   The expression now becomes: \(20 \div 5 \text{ of } 8 \times [9 \div 6 \times 3] - (10 \div 40)\)
2. Solve 'of':
   • Simplify the term \(5 \text{ of } 8 = 5 \times 8 = 40\).
   The expression is now: \(20 \div 40 \times [9 \div 6 \times 3] - (10 \div 40)\)
3. Solve the remaining Brackets:
   • Simplify inside the square bracket \([9 \div 6 \times 3]\). Perform division and multiplication from left to right.
     • \(9 \div 6 = \frac{9}{6} = \frac{3}{2}\)
     • \(\frac{3}{2} \times 3 = \frac{9}{2}\)
   • Simplify inside the parentheses: \(10 \div 40 = \frac{10}{40} = \frac{1}{4}\).
   The expression simplifies to: \(20 \div 40 \times \frac{9}{2} - \frac{1}{4}\)
4. Perform Division and Multiplication (from left to right):
   • First, division: \(20 \div 40 = \frac{20}{40} = \frac{1}{2}\).
   • Next, multiplication: \(\frac{1}{2} \times \frac{9}{2} = \frac{1 \times 9}{2 \times 2} = \frac{9}{4}\).
   The expression becomes: \(\frac{9}{4} - \frac{1}{4}\)
5. Perform Subtraction:
   • Subtract the fractions: \(\frac{9}{4} - \frac{1}{4} = \frac{9 - 1}{4} = \frac{8}{4}\).
   • Simplify the result: \(\frac{8}{4} = 2\).

The final value of the expression is 2.

Verification with Options

Let's compare our result with the given options:

Our calculated value, 2, matches Option 2.

Revision Table: Key Steps in Solving the Expression

Additional Information on BODMAS and Operator Precedence

The BODMAS rule is crucial for solving expressions correctly. It establishes a hierarchy for different mathematical operations. When operations of the same level of precedence appear together (like division and multiplication, or addition and subtraction), they are performed from left to right.

The term 'of' in BODMAS acts as multiplication, but it is typically evaluated after brackets and before division and multiplication. For example, '5 of 8' means \(5 \times 8\). If an expression has both 'of' and regular multiplication/division, 'of' is usually handled first within its level.

Understanding operator precedence ensures consistency and accuracy in mathematical calculations, especially in complex expressions involving various operations and grouping symbols.