$\frac{[ \{ (20 \times 18) - (9 \div 3) \} + (5 - 2) ]}{1}$
The problem asks us to evaluate a given mathematical expression after applying a specific set of rules for operator substitution.
Operator Substitution Rules
The given rules are:
- '+' is replaced by '$\div$'
- '-' is replaced by '+'
- '$\times$' is replaced by '-'
- '$\div$' is replaced by '$\times$'
Original Expression
The expression to evaluate is:
$ \frac{[ \{ (20 \times 18) - (9 \div 3) \} + (5 - 2) ]}{1} $
Applying Substitution
We substitute the operators in the expression according to the given rules:
- $(20 \times 18)$ becomes $(20 - 18)$
- The '-' between $(20 \times 18)$ and $(9 \div 3)$ becomes '+'
- $(9 \div 3)$ becomes $(9 \times 3)$
- The '+' between the curly brace group $\{...\}$ and $(5 - 2)$ becomes '$\div$'
- $(5 - 2)$ becomes $(5 + 2)$
The substituted expression is:
$ \frac{[ \{ (20 - 18) + (9 \times 3) \} \div (5 + 2) ]}{1} $
Evaluating the Expression
Now, we evaluate the substituted expression following the order of operations (PEMDAS/BODMAS):
- Evaluate the innermost parentheses:
- $(20 - 18) = 2$
- $(9 \times 3) = 27$
- $(5 + 2) = 7$
- Substitute these values back into the expression: $ \frac{[ \{ 2 + 27 \} \div 7 ]}{1} $
- Evaluate the operation inside the curly braces $\{ \}$: $ 2 + 27 = 29 $
- Substitute this result back: $ \frac{[ 29 \div 7 ]}{1} $
- Evaluate the division inside the square brackets $[ ]$: $ 29 \div 7 $
- Evaluate the final division: $ \frac{29 \div 7}{1} = \frac{29}{7} $
The calculated value is $29/7$. However, comparing this with the options, none match. Option A (2) is provided as the correct answer.
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 (?).
- 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 $15 \div (5 + 8)$?
If '$+$' means 'subtraction', '$\div$' means 'addition', '$-$' means 'multiplication' and '$\times$' means 'division', then what is the value of $(8 + 2 - 19) - (4 + 27 \times 3)$?
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
