If 'A' stands for '$\div $', 'B' stands for 'x', 'C' stands for '+' and 'D' stands for '-', then what will come in place of the question mark (?) in the following equation? 33 A 3 C 4 B 2 D 4 A 2 = ?
Decoding the Equation: Symbol Substitution
This question involves decoding a mathematical equation where letters represent specific mathematical operators. We need to substitute these letters with their corresponding symbols and then solve the equation using the standard order of operations (BODMAS/PEMDAS).
1. Symbol Substitution
First, let's list the given code:
- 'A' represents division ($\div$)
- 'B' represents multiplication (x)
- 'C' represents addition (+)
- 'D' represents subtraction (-)
Now, substitute these symbols into the given equation:
$33 A 3 C 4 B 2 D 4 A 2$ becomes $33 ÷ 3 + 4 x 2 - 4 ÷ 2$
2. Applying Order of Operations (BODMAS/PEMDAS)
The BODMAS rule dictates the sequence of operations:
- Brackets
- Orders (powers/roots)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's apply this to our substituted equation: $33 ÷ 3 + 4 x 2 - 4 ÷ 2$
Step 1: Divisions and Multiplications (Left to Right)
Perform the division and multiplication operations as they appear from left to right.
- First division: $33 ÷ 3 = 11$
- Next, multiplication: $4 x 2 = 8$
- Last division: $4 ÷ 2 = 2$
The equation now looks like this:
$11 + 8 - 2$
Step 2: Addition and Subtraction (Left to Right)
Now, perform the addition and subtraction operations from left to right.
- First, addition: $11 + 8 = 19$
- Next, subtraction: $19 - 2 = 17$
3. Final Result
Therefore, the value of the expression after decoding and applying the order of operations is 17.
The question asks for the value that comes in place of the question mark (?). Based on our calculation, the result is 17.
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?
$(0.008\div?) + (0.006 \div 0.03) + (0.008 \div 0.04) =0.5$
