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 = ?
Solving the Equation with Interchanged Operators
The problem asks us to find the value of the expression after swapping specific mathematical operators. We need to carefully follow the steps of operator interchange and then apply the correct order of operations (BODMAS/PEMDAS).
Operator Interchanges
The given equation is:
16 ÷ 6 + 12 × 3 – 6 = ?
The rules for interchanging operators are:
+is interchanged with–×is interchanged with÷
Applying these interchanges to the original equation:
16 ÷ 6becomes16 × 6+ 12becomes– 12× 3becomes÷ 3– 6becomes+ 6
The new equation after interchanging the operators is:
16 × 6 – 12 ÷ 3 + 6 = ?
Applying Order of Operations (BODMAS/PEMDAS)
To solve the new equation 16 × 6 – 12 ÷ 3 + 6, we follow the BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
- Multiplication and Division (from left to right):
- First, perform the multiplication:
16 × 6 = 96 - Next, perform the division:
12 ÷ 3 = 4
- First, perform the multiplication:
- Substitute the results back into the equation:
The equation now becomes:
96 – 4 + 6 = ? - Addition and Subtraction (from left to right):
- First, perform the subtraction:
96 – 4 = 92 - Then, perform the addition:
92 + 6 = 98
- First, perform the subtraction:
Final Result
Therefore, the value that comes in place of the question mark (?) after interchanging the operators is 98.
Similar Questions
Which two signs should be interchanged to make the given equation correct?
$36+8 \times 184-23\div10 = 90$Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
Important Questions from Bodmas Rule
The value of 30 ÷ 6 × 5 of (2 + 3) - 12(3 × 2) is equal to:
solve the following:
523 + 523 × 523 ÷ 523
The value of 96 - 4 of (18 - 13) + 4 × 7 is:
Find the value of 45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6.
The value of \(\frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7}{8} - \frac{5}{4}} \right)} \right] - \frac{4}{5}\) is:
