Solving Mathematical Expressions with Operator Interchange

The question asks us to find the value of the given expression after interchanging specific mathematical operators. We need to apply the given interchange rules and then evaluate the new expression following the order of operations (BODMAS/PEMDAS).

Understanding the Operator Interchange Rules

The rules for interchanging operators are:

• The operator '+' is interchanged with '÷'. This means wherever '+' appears, it becomes '÷', and wherever '÷' appears, it becomes '+'.
• The operator '-' is interchanged with '×'. This means wherever '-' appears, it becomes '×', and wherever '×' appears, it becomes '-'.

Applying the Interchange Rules to the Expression

The original expression is:

\(25 \times 6 - 4 \div 18 + 9\)

Applying the interchange rules:

• '×' becomes '-'
• '-' becomes '×'
• '÷' becomes '+'
• '+' becomes '÷'

The new expression after interchanging the operators is:

\(25 - 6 \times 4 + 18 \div 9\)

Evaluating the New Expression using Order of Operations (BODMAS/PEMDAS)

We need to evaluate the new expression \(25 - 6 \times 4 + 18 \div 9\) following the BODMAS or PEMDAS rule, which dictates the order of operations:

• B/P: Brackets/Parentheses
• O/E: Orders/Exponents
• D/M: Division and Multiplication (from left to right)
• A/S: Addition and Subtraction (from left to right)

Let's evaluate the expression step-by-step:

1. Division: Perform the division operation first.

   \(18 \div 9 = 2\)

   The expression becomes: \(25 - 6 \times 4 + 2\)

2. Multiplication: Perform the multiplication operation next.

   \(6 \times 4 = 24\)

   The expression becomes: \(25 - 24 + 2\)

3. Subtraction and Addition: Perform addition and subtraction from left to right.

   First, subtraction: \(25 - 24 = 1\)

   The expression becomes: \(1 + 2\)

   Finally, addition: \(1 + 2 = 3\)

So, the value of the expression after interchanging the operators is 3.

Result Summary

Therefore, the value that comes in place of the question mark is 3.

Revision Table: Operator Interchange & BODMAS

Additional Information: Solving Expression Questions

Questions involving operator interchange require careful attention to detail. Always write down the new expression clearly after applying the interchange rules. Then, strictly follow the order of operations to avoid errors. Remember that division and multiplication have the same priority and should be performed from left to right as they appear. Similarly, addition and subtraction have the same priority and are performed from left to right.

Practicing different variations of these problems helps in quickly applying the rules and performing calculations accurately under exam conditions.