What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘ב are interchanged and also ‘−’ and ‘÷’ are interchanged? 4 + 8 ÷ 4 × 2 − 2 = ?
29
Evaluating Mathematical Expressions with Interchanged Operators
The question asks us to find the value of a given mathematical expression after interchanging certain operators. We are given the equation: \(4 + 8 \div 4 \times 2 - 2 = ?\)
The rules for interchanging operators are:
- '+' and '×' are interchanged.
- '−' and '÷' are interchanged.
Let's apply these changes to the original equation.
Applying the Operator Changes
The original equation is: \(4 + 8 \div 4 \times 2 - 2\)
Applying the changes:
- '+' becomes '×'
- '÷' becomes '−'
- '×' becomes '+'
- '−' becomes '÷'
So, the new equation becomes: \(4 \times 8 - 4 + 2 \div 2\)
Solving the New Equation using BODMAS/PEMDAS
Now we need to evaluate the new equation \(4 \times 8 - 4 + 2 \div 2\) using the order of operations (BODMAS/PEMDAS).
The order of operations is:
- Brackets / Parentheses
- Orders / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Step-by-Step Calculation
- First, perform the Division: \(2 \div 2 = 1\)
The equation becomes: \(4 \times 8 - 4 + 1\) - Next, perform the Multiplication: \(4 \times 8 = 32\)
The equation becomes: \(32 - 4 + 1\) - Now, perform Addition and Subtraction from left to right.
Subtraction: \(32 - 4 = 28\)
The equation becomes: \(28 + 1\) - Finally, perform the Addition: \(28 + 1 = 29\)
So, the value of the expression after interchanging the operators is 29.
Summary of Steps
| Original Equation | Operator Changes Applied | New Equation |
|---|---|---|
| \(4 + 8 \div 4 \times 2 - 2\) | \(+ \leftrightarrow \times\), \( - \leftrightarrow \div\) | \(4 \times 8 - 4 + 2 \div 2\) |
| Step | Operation | Calculation | Resulting Expression |
|---|---|---|---|
| 1 | Division | \(2 \div 2 = 1\) | \(4 \times 8 - 4 + 1\) |
| 2 | Multiplication | \(4 \times 8 = 32\) | \(32 - 4 + 1\) |
| 3 | Subtraction | \(32 - 4 = 28\) | \(28 + 1\) |
| 4 | Addition | \(28 + 1 = 29\) | \(29\) |
The final result of the expression after the operator interchange is 29.
Revision Table: Operator Interchanges
| Original Operator | Interchanged With |
|---|---|
| + | × |
| × | + |
| − | ÷ |
| ÷ | − |
Additional Information: Understanding BODMAS/PEMDAS in Mathematical Operations
The BODMAS or PEMDAS rule is a mnemonic used to remember the correct order for evaluating mathematical expressions. It ensures that everyone gets the same answer when solving a multi-step calculation.
- B/P: Brackets/Parentheses - Operations inside brackets are performed first.
- O/E: Orders/Exponents - Powers and roots are calculated next.
- DM: Division and Multiplication - These are performed from left to right.
- AS: Addition and Subtraction - These are performed from left to right.
When solving problems with interchanged operators, it is crucial to first rewrite the expression with the new operators and then apply the BODMAS/PEMDAS rule correctly to the new expression.
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 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
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) = ?
