If $'\div'$ stands for 'subtraction', '$\times$' stands for 'division', '$+$' stands for 'multiplication' and '-' stands for 'addition', then which of the following equations is correct?
The question asks us to evaluate several equations after reinterpreting the mathematical symbols according to a given mapping.
Symbol Mapping
First, let's establish the new meaning for each symbol:
- $' \div '$ means subtraction ($'-'$)
- $' \times '$ means division ($'/'$)
- $'+'$ means multiplication ($'*'$)
- $'-'$ means addition ($'+'$)
Evaluating Equations
Now, we substitute these meanings into each option and solve using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Division and Multiplication from left to right, Addition and Subtraction from left to right).
Option 1: $12 \div 4 - 7 \times 2 + 3 = 4$
- Substitute symbols: $12 - 4 + 7 / 2 * 3$
- Evaluate: $12 - 4 + 3.5 * 3$
- Evaluate multiplication: $12 - 4 + 10.5$
- Evaluate addition/subtraction: $8 + 10.5 = 18.5$
- Check: $18.5 \neq 4$. This option is incorrect.
Option 2: $8 \div 4 + 2 - 6 \times 2 = 4$
- Substitute symbols: $8 - 4 * 2 + 6 / 2$
- Evaluate division and multiplication: $8 - 8 + 3$
- Evaluate addition/subtraction: $0 + 3 = 3$
- Check: $3 \neq 4$. This option is incorrect.
Option 3: $8 \div 4 + 2 - 6 \times 2 = 5$
- Substitute symbols: $8 - 4 * 2 + 6 / 2$
- Evaluate division and multiplication: $8 - 8 + 3$
- Evaluate addition/subtraction: $0 + 3 = 3$
- Check: $3 \neq 5$. This option is incorrect.
Option 4: $12 \times 4 - 7 \div 2 + 3 = 4$
- Substitute symbols: $12 / 4 + 7 - 2 * 3$
- Evaluate division and multiplication: $3 + 7 - 6$
- Evaluate addition/subtraction: $10 - 6 = 4$
- Check: $4 = 4$. This option is correct.
Conclusion
After applying the given symbol substitutions and evaluating according to the order of operations, only the fourth equation holds true.
Similar Questions
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Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
