If '$+$' means 'subtraction', '$\div$' means 'addition', '$-$' means 'multiplication' and '$\times$' means 'division', then what is the value of $(8 + 2 - 19) - (4 + 27 \times 3)$?
Symbol Substitution Logic
The problem requires substituting mathematical symbols based on a given code and then evaluating the expression using the standard order of operations (BODMAS/PEMDAS).
Symbol Mapping
First, let's establish the new meaning for each symbol as defined:
- '$+$' is replaced by '$-$' (subtraction).
- '$\div$' is replaced by '$+$' (addition).
- '$-$' is replaced by '$\times$' (multiplication).
- '$\times$' is replaced by '$\div$' (division).
Rewriting the Expression
The original expression is: $(8 + 2 - 19) - (4 + 27 \times 3)$
Now, apply the symbol substitutions to the entire expression:
- The '+' inside the first parenthesis becomes '-'.
- The '-' inside the first parenthesis becomes '$\times$'.
- The main '-' operator connecting the two parentheses becomes '$\times$'.
- The '+' inside the second parenthesis becomes '-'.
- The '$\times$' inside the second parenthesis becomes '$\div$'.
The transformed expression is: $(8 - 2 \times 19) \times (4 - 27 \div 3)$
Step-by-Step Evaluation
Evaluate the expression using the order of operations (Parentheses/Brackets, Orders/Exponents, Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right)).
- Solve the first parenthesis: $(8 - 2 \times 19)$
- Perform multiplication first: $2 \times 19 = 38$.
- Perform subtraction: $8 - 38 = -30$.
- Solve the second parenthesis: $(4 - 27 \div 3)$
- Perform division first: $27 \div 3 = 9$.
- Perform subtraction: $4 - 9 = -5$.
- Perform the final operation: The expression is now $(-30) \times (-5)$.
- Multiply the results: $(-30) \times (-5) = 150$.
Final Result
The value of the expression after applying the symbol substitutions and evaluating according to the order of operations is 150.
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?
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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?
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Important Questions from Mathematical Operations
Which two numbers (not digits) should be interchanged to make the given equation correct?
21 × 8 – 18 + (64 ÷ 2) + 32 = 64
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs?
9 × 1 ÷ 3 + 8 – 7 = 12 ÷ 3 + 2 × 33 – 13
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
