What will come in the place of the question mark (?) in the following equation, if '÷' and '-' are interchanged and 'x' and '+' are interchanged? [(48 - 2) ÷ 23] × 19 + 3 = ?
Understanding the Equation Problem
The question asks us to find the value of the expression [(48 - 2) ÷ 23] × 19 + 3 after interchanging specific mathematical operators. We need to replace the subtraction ('-') with division ('÷') and division ('÷') with subtraction ('-'). Similarly, we must replace multiplication ('×') with addition ('+') and addition ('+') with multiplication ('×').
Applying Operator Interchanges
Let's look at the original equation:
[(48 - 2) ÷ 23] × 19 + 3
The given interchanges are:
- '-' is interchanged with '÷'
- '×' is interchanged with '+'
Applying these rules to the original equation:
- The '-' inside the bracket becomes '÷'.
- The '÷' outside the bracket becomes '-'.
- The '×' becomes '+'.
- The '+' becomes '×'.
The equation after interchanging the symbols becomes:
[(48 ÷ 2) - 23] + 19 × 3
Step-by-Step Calculation
Now, we solve the new equation using the standard order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- Solve the expression inside the innermost part of the bracket:
First, perform the division within the parentheses:
(48 ÷ 2)Using LaTeX notation: \( 48 \div 2 = 24 \) - Continue with the expression inside the main bracket:
Now substitute the result back into the bracket:
[24 - 23]Perform the subtraction:24 - 23 = 1Using LaTeX notation: \( 24 - 23 = 1 \) - Rewrite the equation with the bracket value:
The equation now simplifies to:
1 + 19 × 3Using LaTeX notation: \( 1 + 19 \times 3 \) - Perform the multiplication:
According to the order of operations, multiplication comes before addition.
19 × 3Using LaTeX notation: \( 19 \times 3 = 57 \) - Perform the final addition:
Substitute the multiplication result back into the equation:
1 + 57Perform the addition:1 + 57 = 58Using LaTeX notation: \( 1 + 57 = 58 \)
Therefore, the value that comes in place of the question mark (?) is 58.
Similar Questions
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$56+ (11 \times 2) - (52 \div 4) + 16 = 76$What will come in the place of '?' in the following equation, if '+' and '-' are interchanged and also 'x' and '$\div$' are interchanged?
$13 \div 8-96 \times 6+17=?$Which two numbers (not digits of the numbers), from amongst the given options, should be interchanged to make the given equation correct?
$12 \times 9 + 27 \div 3 - 5 = 60$
- Which two signs should be interchanged to make the given equation correct?
$99 \div 33 - 6 + 48 \times 26 = 40$ 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?
36 B 17 D 59 C 224 A 7 = ?What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged?
16 ÷ 6 + 12 × 3 – 6 = ?Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$21 \times 5 - 35 + (42 \div 7) + 28 = 96$Which two signs need to be interchanged to make the following equation correct?
$56 \div 28 - 72 + 18 \times 6 = 60$- Which two signs should be interchanged to make the given equation correct?
$551 \div 19 - 16 \times 12 + 121 = 100$
Important Questions from Bodmas Rule
If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.
DIRECTIONS: What should come in place of the question mark (?) in the following question?
3800 - 22 × 1968 ÷ 48 = ? × 7
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
Evaluate: (13 × 8 - √81 × 6 + 1 ) ÷ (√49 + 72 - 18 × 2 + 19)
