Evaluate The Following Expression:${ 40 \div [2 + 3 \times (16 - 14)] }$
Introduction
In this article, we will evaluate the given mathematical expression: 40 ÷ [2 + 3 × (16 - 14)]. This expression involves various mathematical operations such as division, addition, multiplication, and subtraction. We will follow the order of operations (PEMDAS) to simplify the expression and find the final result.
Understanding the Order of Operations
Before we start evaluating the expression, it's essential to understand the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Evaluating the Expression
Now that we understand the order of operations, let's evaluate the given expression:
40 ÷ [2 + 3 × (16 - 14)]
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is (16 - 14). We will evaluate this expression first.
16 - 14 = 2
So, the expression becomes:
40 ÷ [2 + 3 × 2]
Step 2: Evaluate the Multiplication Operation
Next, we will evaluate the multiplication operation: 3 × 2.
3 × 2 = 6
Now, the expression becomes:
40 ÷ [2 + 6]
Step 3: Evaluate the Addition Operation
Next, we will evaluate the addition operation: 2 + 6.
2 + 6 = 8
Now, the expression becomes:
40 ÷ 8
Step 4: Evaluate the Division Operation
Finally, we will evaluate the division operation: 40 ÷ 8.
40 ÷ 8 = 5
Conclusion
In this article, we evaluated the given mathematical expression: 40 ÷ [2 + 3 × (16 - 14)]. We followed the order of operations (PEMDAS) to simplify the expression and find the final result. The final result is 5.
Frequently Asked Questions
- What is the order of operations? The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
- How do I evaluate an expression with multiple operations? To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.
- What is the final result of the expression 40 ÷ [2 + 3 × (16 - 14)]? The final result of the expression 40 ÷ [2 + 3 × (16 - 14)] is 5.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
References
- "Order of Operations" by Khan Academy
- "Order of Operations" by Mathway
- "Order of Operations" by Wolfram Alpha
Introduction
Evaluating mathematical expressions can be a challenging task, especially when dealing with complex expressions that involve multiple operations. In this article, we will answer some of the most frequently asked questions related to evaluating mathematical expressions.
Q&A
Q1: What is the order of operations?
A1: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q2: How do I evaluate an expression with multiple operations?
A2: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.
Q3: What is the difference between multiplication and division?
A3: Multiplication and division are both binary operations that involve two numbers. The main difference between the two is that multiplication involves repeated addition, while division involves repeated subtraction.
Q4: How do I evaluate an expression with fractions?
A4: To evaluate an expression with fractions, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with fractions, remember to simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
Q5: What is the final result of the expression 40 ÷ [2 + 3 × (16 - 14)]?
A5: The final result of the expression 40 ÷ [2 + 3 × (16 - 14)] is 5.
Q6: How do I evaluate an expression with exponents?
A6: To evaluate an expression with exponents, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with exponents, remember to evaluate the exponentiation operation before any other operations.
Q7: What is the difference between a variable and a constant?
A7: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.
Q8: How do I evaluate an expression with variables?
A8: To evaluate an expression with variables, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with variables, remember to substitute the value of the variable into the expression.
Q9: What is the final result of the expression 2x + 5?
A9: The final result of the expression 2x + 5 depends on the value of x. If x is a specific value, then the expression can be evaluated to a specific value. However, if x is a variable, then the expression cannot be evaluated to a specific value.
Q10: How do I evaluate an expression with multiple variables?
A10: To evaluate an expression with multiple variables, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then any exponential expressions, followed by multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with multiple variables, remember to substitute the values of the variables into the expression.
Conclusion
Evaluating mathematical expressions can be a challenging task, especially when dealing with complex expressions that involve multiple operations. By following the order of operations (PEMDAS) and understanding the rules of arithmetic, you can evaluate even the most complex expressions with ease.
Frequently Asked Questions
- What is the order of operations?
- How do I evaluate an expression with multiple operations?
- What is the difference between multiplication and division?
- How do I evaluate an expression with fractions?
- What is the final result of the expression 40 ÷ [2 + 3 × (16 - 14)]?
- How do I evaluate an expression with exponents?
- What is the difference between a variable and a constant?
- How do I evaluate an expression with variables?
- What is the final result of the expression 2x + 5?
- How do I evaluate an expression with multiple variables?
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
References
- "Order of Operations" by Khan Academy
- "Order of Operations" by Mathway
- "Order of Operations" by Wolfram Alpha