What will come in place of the question mark (?) in the following equation if '+' and '-' are interchanged and 'x' and '$\div$' are interchanged?
$8 \times 2 \div 16 = ?$
Understanding the Equation Problem
The question asks us to find the value of the expression $8 \times 2 \div 16$ after performing specific interchanges between mathematical operators. The rules given are:
- '+' and '-' are interchanged.
- 'x' and '$\div$' are interchanged.
Interchanging Operators
Let's apply the given interchange rules to the original equation:
Original equation: $8 \times 2 \div 16 = ?$
According to the rules:
- The multiplication symbol 'x' needs to be replaced with the division symbol '$\div$'.
- The division symbol '$\div$' needs to be replaced with the multiplication symbol 'x'.
Applying these replacements, the equation transforms into:
$8 \div 2 \times 16 = ?$
Calculation After Operator Interchange
Now, we need to solve the new equation $8 \div 2 \times 16$. We follow the standard order of operations (PEMDAS/BODMAS), which states that multiplication and division should be performed from left to right.
- First, perform the division: $8 \div 2$.
$8 \div 2 = 4$ - Next, perform the multiplication using the result from the previous step: $4 \times 16$.
$4 \times 16 = 64$
Therefore, the value of the expression after the operator interchanges is 64.
Final Result
The question mark in the equation $8 \times 2 \div 16 = ?$ will be replaced by 64 after interchanging the operators as specified.
Important Questions from Simplification (Notes)
- In the Delhi zoo, there are some ducks and rabbits. If the heads are counted there are 160, while the legs are 450. What will be number of ducks in the zoo ?
Identify the number that will replace the question mark in the second equation based on the relationship represented in the first equation.
Simplify: $\frac{\sqrt{16x^4 - 72x^2y^2 + 81y^4}}{\sqrt{4x^2 - 12xy + 9y^2}} - (2x - 3y)$, given that $2x > 3y$.
- Simplify:
$\frac{2}{5} \text{ of } \left(\left(\frac{3}{4} \div 0.25\right) + \frac{1}{2}\right) - \frac{1}{3}$ What value should come in the place of question mark (?) in the following equation?
$(0.008\div?) + (0.006 \div 0.03) + (0.008 \div 0.04) =0.5$
