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? 426 A 3 D 12 C 105 B 1 = ?
235
Understanding Operator Substitution Problems
This type of question involves substituting given letters with specific mathematical operators and then solving the resulting equation following the standard order of operations.
Mapping Letters to Operators
We are given the following mapping:
- 'A' stands for '\(\div\)' (Division)
- 'B' stands for '\(\times\)' (Multiplication)
- 'C' stands for '+' (Addition)
- 'D' stands for '-' (Subtraction)
The Original Equation
The equation provided is:
426 A 3 D 12 C 105 B 1 = ?
Substituting Operators into the Equation
Now, we replace each letter in the equation with its corresponding mathematical operator based on the given mapping:
The equation becomes: \(426 \div 3 - 12 + 105 \times 1 = ?\)
Solving the Equation Using BODMAS/PEMDAS Rule
To solve this mathematical expression, we must follow the order of operations, commonly known as BODMAS or PEMDAS.
- Brackets (Parentheses)
- Orders (Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Step-by-Step Calculation:
First, perform the Division and Multiplication operations from left to right:
Perform the division:
\(426 \div 3 = 142\)
The equation is now: \(142 - 12 + 105 \times 1\)
Perform the multiplication:
\(105 \times 1 = 105\)
The equation is now: \(142 - 12 + 105\)
Next, perform the Addition and Subtraction operations from left to right:
Perform the subtraction:
\(142 - 12 = 130\)
The equation is now: \(130 + 105\)
Perform the addition:
\(130 + 105 = 235\)
Final Result of the Equation
After performing all the operations in the correct order, the value of the expression is 235.
| Step | Operation | Calculation | Equation Progress |
|---|---|---|---|
| 1 | Substitution | A=\(\div\), D=-, C=+, B=\(\times\) | \(426 \div 3 - 12 + 105 \times 1\) |
| 2 | Division | \(426 \div 3 = 142\) | \(142 - 12 + 105 \times 1\) |
| 3 | Multiplication | \(105 \times 1 = 105\) | \(142 - 12 + 105\) |
| 4 | Subtraction | \(142 - 12 = 130\) | \(130 + 105\) |
| 5 | Addition | \(130 + 105 = 235\) | \(235\) |
The value that comes in place of the question mark '?' is 235.
Revision Table: Key Concepts
| Concept | Description | Importance in Problem |
|---|---|---|
| Operator Substitution | Replacing symbols (like letters) with standard mathematical operators. | Essential first step to convert the letter equation into a solvable math problem. |
| Order of Operations (BODMAS/PEMDAS) | A rule defining the sequence for performing mathematical operations (Brackets, Orders, Division/Multiplication, Addition/Subtraction). | Crucial for solving the resulting mathematical expression correctly. Failing to follow this leads to an incorrect answer. |
Additional Information: BODMAS/PEMDAS Explained
The BODMAS (or PEMDAS) rule is a fundamental concept in mathematics to ensure that everyone gets the same answer when evaluating an expression. Here's a bit more detail:
- BODMAS: Brackets, Of (or Orders/Exponents), Division, Multiplication, Addition, Subtraction.
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Both mnemonics represent the same order. Division and Multiplication have equal priority and are performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have equal priority and are performed from left to right.
In our problem, after substitution, we had division and multiplication. We performed division first because it appeared to the left of multiplication. Then we had subtraction and addition. We performed subtraction first because it appeared to the left of addition.
Important Questions from Bodmas Rule
The value of 90 ÷ 20 of 6 × [11 ÷ 4 of {3 × 2 - (3 - 8)}] ÷ (9 ÷ 3 × 2) is:
The value of 1800 ÷ 20 × {(12 - 6) + (24 - 12)} is:
The value of 20 ÷ 5 of 8 × [9 ÷ 6 × (6 - 3)] - (10 ÷ 2 of 20) is:
The value of \(\left( {18 \div 2\;of\frac{1}{4}} \right)\; \times \;\left( {\frac{2}{3} \div \frac{3}{4}\; \times \;\frac{5}{8}} \right) \div \left( {\frac{2}{3} \div \frac{3}{4}of\frac{3}{4}} \right)\) is:
The value of 18 ÷ [26 - {25 - (15 - 5) ÷ 2}] of 12 + 2 - 2 ÷ 4 × 16 is:
