If + = \(\times\), - = /, \(\times\) = +, / = -; then,
what is \((5+2)* 3-4/2\)?
Operator Substitution Calculation
This problem requires us to solve a mathematical expression by replacing the standard arithmetic symbols with new ones according to a given set of rules. After substitution, we will evaluate the expression using the standard order of operations.
Symbol Replacement Rules
The provided mapping for the operators is:
- \(+\) is replaced by \(×\)
- \(-\) is replaced by \(/\)
- \(×\) is replaced by \(+\)
- \(/\) is replaced by \(-\)
The expression to evaluate is \((5 + 2) * 3 - 4 / 2\). We interpret the symbol '\(*\)' as multiplication (\(×\)), as is common practice in such problems.
Expression Evaluation Steps
First, we apply the symbol substitutions to the original expression:
Original Expression: \((5 + 2) * 3 - 4 / 2\)
Step-by-step substitution:
- Replace \(+\) with \(×\): The expression becomes \((5 × 2) * 3 - 4 / 2\).
- Replace the multiplication symbol \(*\) (which represents \(×\)) with \(+\): The expression becomes \((5 × 2) + 3 - 4 / 2\).
- Replace \(-\) with \(/\): The expression becomes \((5 × 2) + 3 / 4 / 2\).
- Replace \(/\) with \(-\): The expression becomes \((5 × 2) + 3 / 4 - 2\).
Thus, the transformed expression is \((5 × 2) + 3 / 4 - 2\).
Result Calculation with BODMAS
Now, we calculate the value of the transformed expression \((5 × 2) + 3 / 4 - 2\) using the BODMAS/PEMDAS order of operations:
- Parentheses: Evaluate the operation inside the parentheses first. Using LaTeX, the calculation is \(5 \times 2 = 10\). The expression becomes: \(10 + 3 / 4 - 2\).
- Division: Next, perform the division operation. Using LaTeX, the calculation is \(3 / 4 = 0.75\). The expression becomes: \(10 + 0.75 - 2\).
- Addition: Perform the addition. Using LaTeX, the calculation is \(10 + 0.75 = 10.75\). The expression becomes: \(10.75 - 2\).
- Subtraction: Finally, perform the subtraction. Using LaTeX, the calculation is \(10.75 - 2 = 8.75\).
The final result is \(8.75\).
Similar Questions
- If 5#3=8 and 7#2=9, then what is the value of 9#4?
If + means -, $\div$ means +, - means $\times$, and $\times$ means $\div$ then,
what is $18 \div 6 - 2 + 8$?If+means -,$\div$means+ , - means $\times$, and $\times$means $\div$, then, what is $30 - 5 + 10 \div 5$?
What will come in place of the question mark (?) in the following equation?
100 ÷ 10 – 7 + 2 × 6 = ?- If += -, - *, *= /, / = +; then,
what is 6+ (4*2)-3/1? If + means -, ÷ means +, - means ×, and × means ÷, then what is the value of the following expression?
15 - 4 ÷ 6 + 12 = ?
- If += *,- +, = -, /=/; then,
what is (3+4)* 2-1/5?
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.)
