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
- What will come in the place of the question mark (?) in the following equation, if '+' and '−' are interchanged and '×' and '÷' are interchanged?
65 × 5 − 19 ÷ 3 + 25 = ? - What will come in place of the question mark (?) in the following equation if '×' and '+' are interchanged and '−' and '÷' are interchanged?
32 ÷ 2 × 72 − 9 + 5 = ? - If '+' means '$\div$', '$-$' means '$\times$', '$\div$' means '+' and '$\times$' means '$-$', then find the value of $2 - 1 \times 4 \div 4 + 2$?
Study the given pattern carefully and select the numbers from among the options that can replace the question marks (?).
- If $\nabla$ stands for operation "adding the first number to thrice the second number", then the value of $(4 \nabla 5) \nabla 6$ will be:
Study the given pattern carefully and select the number from among the given option that can replace the question mark (?).
- If '+' means 'division', '-' means 'addition', '$\times$' means 'subtraction' and '$\div$' means 'multiplication', then what will be the value of the following expression?
$\frac{[ \{ (20 \times 18) - (9 \div 3) \} + (5 - 2) ]}{1}$ - What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
25 − 9 × 3 + 4 ÷ 2 = ? - What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
12 ÷ 6 + 28 × 4 − 11 = ? - If '+' means 'subtraction', '$\div$' means 'addition', '$-$' means 'multiplication' and '$\times$' means 'division', then what is the value of $15 \div (5 + 8)$?
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
