What will come in place of the question mark (?) in the following equation if '+' and '÷' are interchanged and '-' and '×' are interchanged? 25 × 6 - 4 ÷ 18 + 9 = ?
3
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:
- Division: Perform the division operation first.
\(18 \div 9 = 2\)
The expression becomes: \(25 - 6 \times 4 + 2\)
- Multiplication: Perform the multiplication operation next.
\(6 \times 4 = 24\)
The expression becomes: \(25 - 24 + 2\)
- 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
| Original Expression | Operator Changes | New Expression | Evaluated Value |
|---|---|---|---|
| \(25 \times 6 - 4 \div 18 + 9\) | \(+ \leftrightarrow \div\), \(-\leftrightarrow \times\) | \(25 - 6 \times 4 + 18 \div 9\) | 3 |
Therefore, the value that comes in place of the question mark is 3.
Revision Table: Operator Interchange & BODMAS
| Concept | Description | Example (from this problem) |
|---|---|---|
| Operator Interchange | Replacing one mathematical operator with another based on given rules. | '+' becomes '÷', '×' becomes '-' etc. |
| BODMAS/PEMDAS | Rule for the order of operations: Brackets/Parentheses, Orders/Exponents, Division/Multiplication (L to R), Addition/Subtraction (L to R). | Division (18 ÷ 9), then Multiplication (6 × 4), then Subtraction (25 - 24), then Addition (1 + 2). |
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.
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
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In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If A denotes ‘+’, B denotes ‘×’, C denotes ‘-’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
34 A 15 B 3 C 11 B 2 A (51 D 17) = ?
