Which Of These Is Equal To The Value Of $9 - (-5$\]?A. $-9 - 5$ B. $9 - 5$ C. $-9 + 5$ D. $9 + 5$

When dealing with mathematical expressions, it's essential to follow the correct order of operations to ensure accurate results. 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. In this article, we will explore the concept of the order of operations and how it applies to the given expression $9 - (-5)$.

The Order of Operations

The order of operations is a set of rules that helps to avoid confusion when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Understanding Negative Numbers

Before we dive into the order of operations, it's essential to understand how negative numbers work. A negative number is a number that is less than zero. When we subtract a negative number, we are essentially adding a positive number. For example, $-5$ is equivalent to $-5 + 0$, where $0$ is the additive identity.

Evaluating the Expression $9 - (-5)$

Now that we have a basic understanding of the order of operations and negative numbers, let's evaluate the expression $9 - (-5)$. According to the order of operations, we should first evaluate the expression inside the parentheses, which is $-5$. Since $-5$ is a negative number, we can rewrite it as $-5 + 0$.

Now, we can rewrite the original expression as $9 - ( -5 + 0 )$. According to the order of operations, we should evaluate the expression inside the parentheses first. So, we have $9 - ( -5 + 0 ) = 9 - (-5)$.

Next, we can apply the rule for subtracting a negative number, which states that subtracting a negative number is equivalent to adding a positive number. So, $9 - (-5)$ is equivalent to $9 + 5$.

Comparing the Options

Now that we have evaluated the expression $9 - (-5)$, let's compare it to the given options:

A. $-9 - 5$ B. $9 - 5$ C. $-9 + 5$ D. $9 + 5$

We can see that option D, $9 + 5$, is equivalent to the evaluated expression $9 - (-5)$.

Conclusion

In conclusion, when dealing with mathematical expressions, it's essential to follow the correct order of operations to ensure accurate results. 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. By understanding the order of operations and how negative numbers work, we can evaluate expressions like $9 - (-5)$ and compare them to the given options.

Final Answer

In the previous article, we explored the concept of the order of operations and how it applies to the given expression $9 - (-5)$. In this article, we will answer some frequently asked questions (FAQs) about the order of operations.

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 acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is the order of operations important?

A: The order of operations is important because it helps to avoid confusion when there are multiple operations in an expression. Without the order of operations, mathematical expressions could be evaluated in different ways, leading to incorrect results.

Q: What happens when there are multiple operations with the same precedence?

A: When there are multiple operations with the same precedence, we need to evaluate them from left to right. For example, in the expression $3 + 4 \times 2$, we need to evaluate the multiplication operation first, and then the addition operation.

Q: How do I remember the order of operations?

A: There are several ways to remember the order of operations. One way is to use the acronym PEMDAS, which stands for:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

You can also use a mnemonic device, such as "Please Excuse My Dear Aunt Sally," to help you remember the order of operations.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both inverse operations, meaning that they "undo" each other. For example, $3 + 4 = 7$ and $7 - 4 = 3$. However, when we have multiple operations in an expression, we need to evaluate them in the correct order, using the order of operations.

Q: Can I use the order of operations to simplify complex expressions?

A: Yes, the order of operations can be used to simplify complex expressions. By following the order of operations, we can evaluate expressions step by step, simplifying them as we go.

Q: What are some common mistakes to avoid when using the order of operations?

A: Some common mistakes to avoid when using the order of operations include:

• Not following the order of operations correctly
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

By avoiding these common mistakes, you can ensure that you are using the order of operations correctly and getting accurate results.

Conclusion

In conclusion, 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. By understanding the order of operations and how to apply it, you can simplify complex expressions and get accurate results. Remember to use the acronym PEMDAS to help you remember the order of operations, and avoid common mistakes by following the order of operations correctly.