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.
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