If A denotes '+', B denotes '×', C denotes '-’, and D denotes '÷', then what will be the value of the following expression? 124 C 5 B 23 A 56 D 8 = ?
16
Evaluating a Numerical Expression with Operator Substitution
The problem asks us to find the value of a given expression where letters represent standard mathematical operators. We need to substitute the letters with their corresponding operators and then evaluate the resulting mathematical expression following the correct order of operations.
Understanding the Operator Mapping
We are given the following mapping:
- A denotes '+' (Addition)
- B denotes '×' (Multiplication)
- C denotes '-' (Subtraction)
- D denotes '÷' (Division)
Substituting Operators in the Expression
The given expression is:
124 C 5 B 23 A 56 D 8
Replacing the letters with the operators they denote, we get:
124 - 5 × 23 + 56 ÷ 8
Or, using standard mathematical symbols:
\(124 - 5 \times 23 + 56 \div 8\)
Applying the Order of Operations (BODMAS/PEMDAS)
To evaluate this expression, we must follow the standard order of operations. The BODMAS/PEMDAS rule dictates the sequence:
- Brackets / Parentheses
- Orders (Powers and Square Roots) / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate the expression step-by-step:
Step 1: Perform Division
First, we perform the division:
\(56 \div 8 = 7\)
The expression now becomes:
\(124 - 5 \times 23 + 7\)
Step 2: Perform Multiplication
Next, we perform the multiplication:
\(5 \times 23 = 115\)
The expression now becomes:
\(124 - 115 + 7\)
Step 3: Perform Addition and Subtraction (from left to right)
Finally, we perform addition and subtraction from left to right:
First, subtraction:
\(124 - 115 = 9\)
The expression now becomes:
\(9 + 7\)
Then, addition:
\(9 + 7 = 16\)
Final Value of the Expression
The value of the expression 124 C 5 B 23 A 56 D 8 is 16.
Revision Table: Operator Mapping
| Letter | Denotes | Operator |
|---|---|---|
| A | + | Addition |
| B | × | Multiplication |
| C | - | Subtraction |
| D | ÷ | Division |
Additional Information: Understanding BODMAS/PEMDAS
The BODMAS (or PEMDAS) rule is a mnemonic used to remember the correct order of operations in mathematical expressions. It ensures that everyone evaluating the same expression arrives at the same unique answer. Ignoring this order can lead to incorrect results. For example, in \(124 - 115 + 7\), if we added first \(115+7=122\) and then subtracted \(124-122=2\), we would get 2, which is different from the correct answer 16. Addition and Subtraction (and similarly, Multiplication and Division) have equal priority and should be performed from left to right in the expression.
Similar Questions
If '+' means 'divided by', '-' means 'add', '×' means 'minus' and '÷' means 'multiplied by', then what will be the value of the following expression:
[{(18 × 16) - (5 ÷ 2)} + (5 - 1)] ÷ 1
Which two numbers from amongst the given options should be interchanged to make the given equation correct?
126 ÷ 23 – 138 ÷ ( 5 × 4 – 6) + 4 = 1
Which of the following interchange of signs would make the given equation correct?
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Which two symbols from amongst the given options should be interchanged to make the given equation correct?
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Which two numbers from amongst the given options should be interchanged to make the given equation correct?
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In the given question, the statement is followed by two conclusions. Which of the two conclusions is/are true?
Statement: B = T < E ≤ G > F = H > Q
Conclusions:
I. G > Q
II. G > B
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
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In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If ‘A’ denotes ‘+’, ‘B’ denotes ‘×’, ‘C’ denotes ‘–’ and ‘D’ denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
