67 > 27 $ 9 < 4If < means -, > means +, = means ×, and $ means ÷, then the value of:
66
Understanding Symbol Replacement in Math Problems
This problem asks us to evaluate a mathematical expression where standard operators are replaced by symbols. We need to first understand what each symbol represents and then substitute the correct operators into the expression before calculating its value.
Decoding the Symbols
The problem provides the following symbol-to-operator mapping:
| Symbol | Represents | Mathematical Operator |
|---|---|---|
| < | - | Subtraction |
| > | + | Addition |
| = | × | Multiplication |
| $ | ÷ | Division |
Rewriting the Expression
The given expression is 67 > 27 $ 9 < 4.
Using the mapping above, we replace each symbol with its corresponding mathematical operator:
- > becomes +
- $ becomes ÷
- < becomes -
So, the expression becomes: 67 + 27 ÷ 9 - 4.
Evaluating the Expression Using Order of Operations
To find the value of the expression 67 + 27 ÷ 9 - 4, we must follow the standard order of operations, often remembered by acronyms like BODMAS or PEMDAS.
- Brackets / Parentheses
- Orders / Exponents
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate the expression step-by-step:
- First, perform the Division: \(27 \div 9\). $$67 + \frac{27}{9} - 4$$ $$67 + 3 - 4$$
- Next, perform the Addition and Subtraction from left to right. First, the Addition: \(67 + 3\). $$70 - 4$$
- Finally, perform the Subtraction: \(70 - 4\). $$66$$
Final Result
The value of the expression 67 > 27 $ 9 < 4, after replacing symbols and following the order of operations, is 66.
Revision Table: Key Concepts Reviewed
| Concept | Description | Importance in this Problem |
|---|---|---|
| Symbol Mapping | Assigning specific meanings (operators) to symbols. | Crucial first step to translate the expression. |
| Expression Translation | Rewriting the symbolic expression with standard operators. | Necessary to apply mathematical rules. |
| Order of Operations (BODMAS/PEMDAS) | Rules for the sequence of performing calculations in an expression. | Ensures the calculation is performed correctly to get the unique right answer. |
| Arithmetic Operations | Performing basic math (addition, subtraction, division). | The final steps in evaluating the translated expression. |
Additional Information: Mathematical Operators and Order of Operations
Mathematical operators are symbols that tell us to perform a specific mathematical action. Common operators include:
- + (Addition)
- - (Subtraction)
- × (Multiplication)
- ÷ (Division)
When an expression contains more than one operation, the order in which they are performed matters. This is where the Order of Operations comes in. BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) are mnemonics to help remember this order.
Division and Multiplication have the same priority and should be performed from left to right as they appear in the expression. Similarly, Addition and Subtraction have the same priority and are performed from left to right after Division and Multiplication.
Understanding and applying the correct order of operations is fundamental to solving mathematical expressions accurately. In this problem, failing to perform division before addition and subtraction would lead to an incorrect result.
Important Questions from Quant Based Puzzle
Three years ago, the difference between the age of Ravish and the age of Kailash was 18 years. Three years from today, Ravish will be three times as old as Kailash. What is the present age of Ravish (in years)?
Seven years from now, Anamika will be as old as Malini was 4 years ago. Srinidhi was born 2 years ago. The average age of Anamika, Malini and Srinidhi 10 years from now will be 33 years. What is the present age of Anamika?
An amount of ₹1,003 is to be distributed among A, B and C in the ratio of 11 : 23 : 25. How many rupees would B get more than A?
In an exam of 80 questions, a correct answer gives 1 marks but a wrong answer deducts 1 marks, and if a question in not attempted there is no deduction in marks. If a student attempted only 80% of the question and got 32 marks, then how many questions did he answer correctly?
The ratio of the present ages of Asha and Lata is 5 : 6. If the difference between their ages is 6 years, then what will be Lata’s age after 5 years?
