Compute: 1 − ( − 12 1 - (-12 1 − ( − 12 ]Answer Attempt: 2 Out Of 2Submit Answer: 1 + 12 1 + 12 1 + 12

Mar 13, 2025 by ADMIN 103 views

**Understanding the Order of Operations in Mathematics**

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 a specific mathematical expression.

The Order of Operations

The order of operations is a set of rules that helps to clarify 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:

Parentheses: Evaluate 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.

Applying the Order of Operations to the Given Expression

Now that we have a basic understanding of the order of operations, let's apply it to the given expression: $1 - (-12)$ . To evaluate this expression, we need to follow the order of operations.

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the parentheses is $-12$ . Since there are no other operations inside the parentheses, we can move on to the next step.

Step 2: Evaluate Exponents

There are no exponential expressions in this problem, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division

There are no multiplication or division operations in this problem, so we can move on to the next step.

Step 4: Evaluate Addition and Subtraction

Now we are left with the expression $1 - (-12)$ . To evaluate this expression, we need to follow the order of operations. When subtracting a negative number, we can change the subtraction sign to an addition sign and change the negative sign to a positive sign. Therefore, the expression becomes $1 + 12$ .

Conclusion

In conclusion, when dealing with mathematical expressions, it's essential to follow the correct order of operations to ensure accurate results. By applying the order of operations to the given expression $1 - (-12)$ , we can evaluate the expression as $1 + 12$ . This demonstrates the importance of following the order of operations in mathematics.

Common Mistakes to Avoid

When dealing with mathematical expressions, there are several common mistakes to avoid. Some of these mistakes include:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect results.
Not changing the subtraction sign to an addition sign when subtracting a negative number: Failing to change the subtraction sign to an addition sign when subtracting a negative number can lead to incorrect results.

Real-World Applications

The order of operations has several real-world applications. Some of these applications include:

Computer programming: The order of operations is essential in computer programming, where mathematical expressions are used to perform calculations.
Science and engineering: The order of operations is essential in science and engineering, where mathematical expressions are used to model and analyze complex systems.
Finance: The order of operations is essential in finance, where mathematical expressions are used to calculate interest rates and investment returns.

Conclusion

In this article, we will answer some frequently asked questions 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:

Parentheses: Evaluate 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: Why is the order of operations important?

A: The order of operations is important because it helps to clarify the order in which mathematical operations should be performed when there are multiple operations in an expression. Without the order of operations, mathematical expressions can be ambiguous and lead to incorrect results.

Q: What happens if I forget to follow the order of operations?

A: If you forget to follow the order of operations, you may get incorrect results. For example, if you have the expression $3 + 4 \times 2$ , you may forget to follow the order of operations and get $3 + 4 = 7$ instead of $3 + 8 = 11$ .

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

A: Yes, you can use the order of operations to simplify complex expressions. By following the order of operations, you can break down complex expressions into simpler ones and evaluate them step by step.

Q: Are there any exceptions to the order of operations?

A: Yes, there are some exceptions to the order of operations. For example, when evaluating expressions with parentheses, you should evaluate the expressions inside the parentheses first, regardless of the order of operations.

Q: Can I use the order of operations to evaluate expressions with fractions?

A: Yes, you can use the order of operations to evaluate expressions with fractions. By following the order of operations, you can evaluate fractions step by step and get the correct result.

Q: Are there any online resources that can help me learn the order of operations?

A: Yes, there are many online resources that can help you learn the order of operations. Some of these resources include:

Math websites: There are many math websites that provide tutorials and examples on the order of operations.
Online calculators: Online calculators can help you practice the order of operations and get instant feedback on your answers.
Math apps: Math apps can provide interactive lessons and exercises on the order of operations.

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 following the order of operations, you can ensure accurate results and avoid common mistakes. If you have any questions or need further clarification, feel free to ask.

Common Mistakes to Avoid

When dealing with mathematical expressions, there are several common mistakes to avoid. Some of these mistakes include:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect results.
Not changing the subtraction sign to an addition sign when subtracting a negative number: Failing to change the subtraction sign to an addition sign when subtracting a negative number can lead to incorrect results.

Real-World Applications

The order of operations has several real-world applications. Some of these applications include:

Computer programming: The order of operations is essential in computer programming, where mathematical expressions are used to perform calculations.
Science and engineering: The order of operations is essential in science and engineering, where mathematical expressions are used to model and analyze complex systems.
Finance: The order of operations is essential in finance, where mathematical expressions are used to calculate interest rates and investment returns.