Evaluate The Following Numerical Expression:${ 6 + 3 \cdot 4 = }$ {\square\}
Introduction
In mathematics, numerical expressions are used to represent a value or a quantity. These expressions can be simple or complex, involving various mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the numerical expression: 6 + 3 * 4. We will follow the order of operations (PEMDAS) to simplify the expression and find the final result.
Understanding the Order of Operations
The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS is a popular acronym that stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., 2^3).
- 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 Numerical Expression
Now that we understand the order of operations, let's apply it to the given expression: 6 + 3 * 4.
Step 1: Multiply 3 and 4
According to the order of operations, we need to perform the multiplication operation first. So, we multiply 3 and 4:
3 * 4 = 12
Step 2: Add 6 and 12
Now that we have the result of the multiplication operation, we can add 6 and 12:
6 + 12 = 18
Conclusion
In this article, we evaluated the numerical expression: 6 + 3 * 4. We followed the order of operations (PEMDAS) to simplify the expression and find the final result. By multiplying 3 and 4 first, and then adding 6 and 12, we arrived at the final answer: 18.
Frequently Asked Questions
- What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
- How do I evaluate a numerical expression? To evaluate a numerical expression, 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 answer to the expression 6 + 3 * 4? The final answer to the expression 6 + 3 * 4 is 18.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Final Thoughts
Evaluating numerical expressions is an essential skill in mathematics. By following the order of operations (PEMDAS), we can simplify complex expressions and find the final result. In this article, we evaluated the numerical expression: 6 + 3 * 4, and arrived at the final answer: 18. We hope this article has provided you with a better understanding of the order of operations and how to evaluate numerical expressions.
Introduction
In our previous article, we evaluated the numerical expression: 6 + 3 * 4. We followed the order of operations (PEMDAS) to simplify the expression and find the final result. In this article, we will answer some frequently asked questions related to numerical expression evaluation.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS is a popular acronym that stands for: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate a numerical expression?
A: To evaluate a numerical expression, 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.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication is a commutative operation, meaning that the order of the numbers does not change the result (e.g., 2 * 3 = 3 * 2). Division, on the other hand, is a non-commutative operation, meaning that the order of the numbers does change the result (e.g., 6 / 3 ≠3 / 6).
Q: How do I handle parentheses in a numerical expression?
A: When you have parentheses in a numerical expression, you need to evaluate the expression inside the parentheses first. This means that you need to follow the order of operations (PEMDAS) within the parentheses before moving on to the rest of the expression.
Q: What is the final answer to the expression 2 + 5 * 3?
A: To evaluate the expression 2 + 5 * 3, we need to follow the order of operations (PEMDAS). First, we multiply 5 and 3:
5 * 3 = 15
Then, we add 2 and 15:
2 + 15 = 17
So, the final answer to the expression 2 + 5 * 3 is 17.
Q: How do I handle exponents in a numerical expression?
A: When you have exponents in a numerical expression, you need to evaluate the exponent first. This means that you need to raise the base number to the power of the exponent before moving on to the rest of the expression.
Q: What is the final answer to the expression 2^3 + 5?
A: To evaluate the expression 2^3 + 5, we need to follow the order of operations (PEMDAS). First, we evaluate the exponent:
2^3 = 8
Then, we add 5:
8 + 5 = 13
So, the final answer to the expression 2^3 + 5 is 13.
Conclusion
In this article, we answered some frequently asked questions related to numerical expression evaluation. We covered topics such as the order of operations, handling parentheses and exponents, and evaluating expressions with multiple operations. We hope this article has provided you with a better understanding of numerical expression evaluation and how to apply the order of operations to simplify complex expressions.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Final Thoughts
Numerical expression evaluation is an essential skill in mathematics. By following the order of operations (PEMDAS), we can simplify complex expressions and find the final result. We hope this article has provided you with a better understanding of numerical expression evaluation and how to apply the order of operations to simplify complex expressions.