In a certain code language, '×' represents '+', '÷' represents '×', '-' represents '÷' and '+' represents '-'. Find out the answer to the following question.
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Understanding Coded Operators and Mathematical Evaluation
This problem involves a coded language where standard mathematical operators (×, ÷, -, +) are replaced by different operators. We are given an expression using the original operators and need to find its value after applying the code and performing the calculation according to the correct order of operations.
Decoding the Operators
The rules for decoding the operators are as follows:
- '×' represents '+'
- '÷' represents '×'
- '-' represents '÷'
- '+' represents '-'
Applying the Code to the Expression
The given expression is:
\(15 \times 4 \div 35 - 70 + 16\)
Now, we replace the original operators with their coded meanings:
- The '×' between 15 and 4 becomes '+'.
- The '÷' between 4 and 35 becomes '×'.
- The '-' between 35 and 70 becomes '÷'.
- The '+' between 70 and 16 becomes '-'.
The expression in the new code language is:
\(15 + 4 \times 35 \div 70 - 16\)
Evaluating the Expression Using Order of Operations (BODMAS/PEMDAS)
To find the value of the expression \(15 + 4 \times 35 \div 70 - 16\), we must follow the order of operations:
- Brackets (None in this expression)
- Orders (Powers, Square Roots, etc. - None in this expression)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate step by step:
Step 1: Perform Multiplication and Division from left to right.
First, we encounter multiplication \(4 \times 35\):
\(4 \times 35 = 140\)
The expression becomes: \(15 + 140 \div 70 - 16\)
Next, we encounter division \(140 \div 70\):
\(140 \div 70 = 2\)
The expression becomes: \(15 + 2 - 16\)
Step 2: Perform Addition and Subtraction from left to right.
First, we encounter addition \(15 + 2\):
\(15 + 2 = 17\)
The expression becomes: \(17 - 16\)
Finally, we perform subtraction \(17 - 16\):
\(17 - 16 = 1\)
The final value of the expression is 1.
Summary of Steps
| Original Expression | \(15 \times 4 \div 35 - 70 + 16\) |
|---|---|
| Coded Expression | \(15 + 4 \times 35 \div 70 - 16\) |
| After \(4 \times 35\) | \(15 + 140 \div 70 - 16\) |
| After \(140 \div 70\) | \(15 + 2 - 16\) |
| After \(15 + 2\) | \(17 - 16\) |
| Final Result | \(1\) |
The calculated answer is 1.
Revision Table: Coded Mathematical Operations
| Original Operator | Coded Meaning |
|---|---|
| × | + |
| ÷ | × |
| - | ÷ |
| + | - |
Additional Information: BODMAS/PEMDAS Rule
The BODMAS (or PEMDAS) rule is a mnemonic used to remember the correct order of operations in mathematical expressions. Following this order ensures a unique and correct result for any given expression.
- B/P: Brackets / Parentheses - Operations inside brackets are performed first.
- O/E: Orders / Exponents - Powers, roots, etc., are evaluated next.
- DM: Division and Multiplication - These are performed from left to right as they appear in the expression.
- AS: Addition and Subtraction - These are performed from left to right as they appear in the expression, after division and multiplication.
Understanding and applying this rule is crucial for solving mathematical expressions correctly, especially in problems involving multiple operations like the coded language problem we just solved.
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 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
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?
34 A 15 B 3 C 11 B 2 A (51 D 17) = ?
