Calculating Mathematical Expressions using Order of Operations

To find the value of the expression \(14 \div \{(5 \text{ of } 2 – 3)\} \times 4(7 – 2)\), we need to follow the order of operations. The common acronyms for the order of operations are BODMAS or PEMDAS.

• B/P: Brackets or Parentheses (perform operations inside grouping symbols first)
• O/E: Order or Exponents (calculate powers and roots)
• D/M: Division and Multiplication (perform from left to right)
• A/S: Addition and Subtraction (perform from left to right)

Let's break down the given expression step-by-step:

The expression is: \(14 \div \{(5 \text{ of } 2 – 3)\} \times 4(7 – 2)\)

Step-by-Step Calculation

1. First, calculate the operations inside the parentheses and curly braces. We have two sets of grouping symbols: \((5 \text{ of } 2 – 3)\) and \((7 – 2)\).
2. Inside the first grouping symbol \((5 \text{ of } 2 – 3)\), we have 'of' and subtraction. 'Of' means multiplication. So, we calculate \(5 \text{ of } 2\).
   \(5 \text{ of } 2 = 5 \times 2 = 10\)
   Now, substitute this back into the curly braces: \(\{10 – 3\}\)
   Calculate the subtraction inside the curly braces: \(10 – 3 = 7\)
3. Inside the second grouping symbol \((7 – 2)\), calculate the subtraction:
   \(7 – 2 = 5\)
4. Now substitute the results back into the original expression:
   The expression becomes: \(14 \div \{7\} \times 4(5)\)
   Which simplifies to: \(14 \div 7 \times 4 \times 5\)
5. Next, perform Division and Multiplication from left to right.
   First, the division: \(14 \div 7\)
   \(14 \div 7 = 2\)
6. Substitute this result back:
   The expression is now: \(2 \times 4 \times 5\)
7. Finally, perform the multiplications from left to right:
   \(2 \times 4 = 8\)
   Then, \(8 \times 5\)
   \(8 \times 5 = 40\)

So, the value of the expression \(14 \div \{(5 \text{ of } 2 – 3)\} \times 4(7 – 2)\) is 40.

Let's quickly verify the steps with the BODMAS/PEMDAS order:

• B/P:
  • \((7 - 2) = 5\)
  • \((5 \text{ of } 2 - 3)\) -> \(5 \times 2 - 3\) -> \(10 - 3 = 7\)
• Expression is now \(14 \div 7 \times 4 \times 5\)
• O/E: None
• D/M: From left to right
  • \(14 \div 7 = 2\)
  • \(2 \times 4 = 8\)
  • \(8 \times 5 = 40\)
• A/S: None

The final result is 40.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information: 'Of' in Mathematics

The term 'of' in mathematics, especially in expressions involving fractions or percentages, signifies multiplication. In the context of BODMAS/PEMDAS, operations involving 'of' are usually performed after brackets but before regular multiplication and division.

• Example 1: \(5 \text{ of } 20\) means \(5 \times 20 = 100\).
• Example 2: \(1/2 \text{ of } 100\) means \(1/2 \times 100 = 50\).
• Example 3: \(20\% \text{ of } 50\) means \(0.20 \times 50 = 10\).

In the given question, \(5 \text{ of } 2\) was correctly interpreted as \(5 \times 2\), and this multiplication was performed within the curly braces before the subtraction within those same braces, following the order inside grouping symbols.

Understanding the correct order of operations is crucial for evaluating mathematical expressions accurately.