Evaluate $6 - (8 \div 2)$.
Introduction
In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In this article, we will evaluate the expression $6 - (8 \div 2)$ using the order of operations.
Understanding the Order of Operations
The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is as follows:
- Parentheses: Evaluate any expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any 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
To evaluate the expression $6 - (8 \div 2)$, we need to follow the order of operations.
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is $8 \div 2$. To evaluate this expression, we need to divide 8 by 2.
So, the expression inside the parentheses is equal to 4.
Step 2: Rewrite the Expression
Now that we have evaluated the expression inside the parentheses, we can rewrite the original expression as follows:
Step 3: Evaluate the Expression
Now that we have rewritten the expression, we can evaluate it by subtracting 4 from 6.
Conclusion
In this article, we evaluated the expression $6 - (8 \div 2)$ using the order of operations. We followed the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. We evaluated the expression inside the parentheses first, then rewrote the expression, and finally evaluated the expression by subtracting 4 from 6. The final answer is 2.
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 when there are multiple operations in an expression.
- How do I evaluate an expression using the order of operations? To evaluate an expression using the order of operations, follow the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
- What is the final answer to the expression $6 - (8 \div 2)$? The final answer to the expression $6 - (8 \div 2)$ is 2.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Final Answer
The final answer to the expression $6 - (8 \div 2)$ is 2.
Introduction
Evaluating mathematical expressions can be a challenging task, especially when there are multiple operations involved. In this article, we will provide a Q&A guide to help you evaluate mathematical expressions using the order of operations.
Q&A Guide
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I evaluate an expression using the order of operations?
A: To evaluate an expression using the order of operations, follow the order of operations, which is:
- Parentheses: Evaluate any expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate 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, which means that the order of the numbers does not change the result. Division, on the other hand, is a non-commutative operation, which means that the order of the numbers does change the result.
Q: How do I evaluate an expression with multiple operations?
A: To evaluate an expression with multiple operations, follow the order of operations. For example, if you have the expression $3 + 4 \times 2$, you would first multiply 4 and 2, then add 3.
Q: What is the final answer to the expression $6 - (8 \div 2)$?
A: The final answer to the expression $6 - (8 \div 2)$ is 2.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, evaluate the expression inside the parentheses first. For example, if you have the expression $2 + (3 \times 4)$, you would first multiply 3 and 4, then add 2.
Q: What is the final answer to the expression $10 - 3 + 2$?
A: The final answer to the expression $10 - 3 + 2$ is 9.
Q: How do I evaluate an expression with exponents?
A: To evaluate an expression with exponents, evaluate the exponential expression first. For example, if you have the expression $2^3 + 4$, you would first evaluate the exponential expression, then add 4.
Q: What is the final answer to the expression $2^3 + 4$?
A: The final answer to the expression $2^3 + 4$ is 12.
Conclusion
Evaluating mathematical expressions can be a challenging task, but by following the order of operations, you can simplify the process. Remember to evaluate expressions inside parentheses first, then exponents, multiplication and division, and finally addition and subtraction. With practice, you will become more confident in evaluating mathematical expressions.
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 when there are multiple operations in an expression.
- How do I evaluate an expression using the order of operations? To evaluate an expression using the order of operations, follow the order of operations, which is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
- What is the final answer to the expression $6 - (8 \div 2)$? The final answer to the expression $6 - (8 \div 2)$ is 2.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Final Answer
The final answer to the expression $6 - (8 \div 2)$ is 2.