If '+' means '÷', '-' means '+', 'x' means ' - ' and '÷' means 'x', what will be the value of the following expression?
[{(49×12)-(6÷2)}+(4-3)]÷5
Understanding the Operator Substitution
The problem asks us to evaluate a mathematical expression, but with a twist: the standard arithmetic operators (+, -, ×, ÷) have been redefined.
Here are the given operator substitutions:
- '+' represents '÷'
- '-' represents '+'
- '×' represents '-'
- '÷' represents '×'
The original expression is: [{(49×12)-(6÷2)}+(4-3)]÷5
Applying the Operator Substitutions
We need to replace each operator in the original expression with its new meaning according to the rules provided.
- Replace '
×' with '-': The term(49×12)becomes(49 - 12). - Replace '
÷' with '×': The term(6÷2)becomes(6 × 2). - Replace '
-' with '+': The term(4-3)becomes(4 + 3). - Replace the '
-' sign (between the first two terms inside the curly braces) with '+'. - Replace the '
+' sign (between the curly braces and the last term inside the square brackets) with '÷'. - Replace the final '
÷' sign outside the square brackets with '×'.
After applying all these substitutions, the expression transforms into:
[ {(49 - 12) + (6 × 2)} ÷ (4 + 3) ] × 5
Step-by-Step Evaluation
Now, we evaluate the transformed expression using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
- Evaluate innermost parentheses:
(49 - 12) = 37(6 × 2) = 12(4 + 3) = 7
- Substitute these results back into the expression:
[ {37 + 12} ÷ 7 ] × 5 - Evaluate the expression inside the curly braces:
{37 + 12} = 49 - Substitute this result back:
[ 49 ÷ 7 ] × 5 - Evaluate the expression inside the square brackets:
49 ÷ 7 = 7 - Substitute this result back:
7 × 5 - Perform the final calculation:
7 × 5 = 35
Therefore, the value of the given expression after applying the operator substitutions is 35.
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.)
