What will come in place of the question mark (?) in the following equation if '+' and '$\times$' are interchanged and '-' and '$\div$' are interchanged?
$5 \div 9 - 3 \times 4 + 6 = ?$
Understanding the Operator Interchange
The problem presents an equation and asks for the result after specific operator substitutions. The original equation is:
We are given two rules for interchanging operators:
- The addition symbol '+' should be replaced by the multiplication symbol '$\times$'.
- The subtraction symbol '-' should be replaced by the division symbol '$\div$'.
The reverse interchanges are implied: '$\times$' becomes '+' and '$\div$' becomes '-'.
Applying the Operator Interchanges
Let's rewrite the equation by applying these interchange rules systematically:
- The first operator '$\div$' becomes '-'.
- The second operator '-' becomes '$\div$'.
- The third operator '$\times$' becomes '+'.
- The fourth operator '+' becomes '$\times$'.
Applying these substitutions to the original equation:
After applying the interchanges, the new equation becomes:
Solving the Modified Equation
To find the value of the question mark, we solve the new equation $5 - 9 \div 3 + 4 \times 6$ using the standard order of operations (often remembered by the acronym BODMAS/PEMDAS):
- Division and Multiplication (from left to right):
- First, calculate the division: $9 \div 3 = 3$.
- The equation is now: $5 - 3 + 4 \times 6$.
- Next, calculate the multiplication: $4 \times 6 = 24$.
- The equation becomes: $5 - 3 + 24$.
- Addition and Subtraction (from left to right):
- Perform the subtraction: $5 - 3 = 2$.
- The equation is now: $2 + 24$.
- Finally, perform the addition: $2 + 24 = 26$.
Final Result
Following the operator interchanges and the order of operations, the calculation yields 26.
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?
$152 + 8 \times 16 \div 9 - 4 = 309$
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 = ?
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?
$56 \div 28 - 72 + 18 \times 6 = 60$
Important Questions from Bodmas Rule
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
What will come in place of the question mark ‘?’ in the following question?
(44 of 15) – [(450 × 240 ÷ 60 – 40) ÷ 80 × 25 + 50] – 10 = ?Simplify: 92 - 18 ( 9 + 36 ÷ 3 × 12 - 27 × 3) + 51
Simplify the following expression.
\(\rm \frac{3}{5}\ of\ \left\{\left(48\div\overline{36\div9}\times\frac{1}{6}\right)+\frac{1}{3}\right\}=?\)
