Applying the Order of Operations to the Given Expression

Oct 13, 2025 by magicalceylontours.com 118 views

When it comes to solving mathematical expressions, it's essential to follow a specific order of operations to ensure accuracy and avoid confusion. The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. In this article, we'll explore the correct order of operations and apply it to a given expression to determine the correct answer.

What is the Order of Operations?

The order of operations is a mnemonic device that helps individuals remember the correct sequence of operations to perform when solving mathematical expressions. The acronym PEMDAS is commonly used to represent the order of operations:

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.

Applying the Order of Operations to the Given Expression

Let's apply the order of operations to the given expression: ${ $12^2+10 \times 2-(9+6) \div 5\$}$ .

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the parentheses is ${ $9+6\$}$ . We need to evaluate this expression first.

${ $9+6 = 15\$}$

So, the expression becomes: ${ $12^2+10 \times 2-15 \div 5\$}$ .

Step 2: Evaluate Exponential Expressions

The expression ${ $12^2\$}$ is an exponential expression. We need to evaluate this expression next.

${ $12^2 = 144\$}$

So, the expression becomes: ${ $144+10 \times 2-15 \div 5\$}$ .

Step 3: Evaluate Multiplication and Division Operations

The expression ${ $10 \times 2\$}$ is a multiplication operation. We need to evaluate this expression next.

${ $10 \times 2 = 20\$}$

The expression ${ $15 \div 5\$}$ is a division operation. We need to evaluate this expression next.

${ $15 \div 5 = 3\$}$

So, the expression becomes: ${ $144+20-3\$}$ .

Step 4: Evaluate Addition and Subtraction Operations

The expression ${ $144+20-3\$}$ is a combination of addition and subtraction operations. We need to evaluate these operations from left to right.

${ $144+20 = 164\$}$

${ $164-3 = 161\$}$

Therefore, the final answer is: ${ $161\$}$ .

Conclusion

In conclusion, the correct order of operations is essential when solving mathematical expressions. By following the PEMDAS acronym, we can ensure accuracy and avoid confusion. In this article, we applied the order of operations to a given expression and determined the correct answer. Remember, when in doubt, always follow the order of operations to ensure the correct solution.

Discussion Questions

What is the order of operations in mathematics?
How does the order of operations help individuals solve mathematical expressions?
What is the correct sequence of operations to perform when solving mathematical expressions?
How does the order of operations apply to the given expression ${ $12^2+10 \times 2-(9+6) \div 5\$}$ ?
What is the final answer to the given expression?

Additional Resources

For more information on the order of operations, check out the following resources:

Khan Academy: Order of Operations
Mathway: Order of Operations
Wolfram MathWorld: Order of Operations

Final Answer

In our previous article, we explored the order of operations in mathematics and applied it to a given expression. However, we know that there are many more questions and scenarios that can arise when dealing with mathematical expressions. In this article, we'll address some of the most 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 sequence in which mathematical operations should be performed. The acronym PEMDAS is commonly used to represent the order of operations:

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.

Q: Why is the order of operations important?

A: The order of operations is essential when solving mathematical expressions because it helps individuals avoid confusion and ensure accuracy. Without the order of operations, mathematical expressions can be ambiguous and lead to incorrect solutions.

Q: How does the order of operations apply to expressions with multiple operations?

A: When dealing with expressions that contain multiple operations, the order of operations is applied in the following order:

Evaluate expressions inside parentheses first.
Evaluate any exponential expressions next.
Evaluate multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

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

A: If there are multiple operations with the same precedence, the order of operations is applied from left to right. For example, if an expression contains both multiplication and division operations, the operation on the left is evaluated first.

Q: Can the order of operations be changed?

A: No, the order of operations cannot be changed. The order of operations is a set of rules that must be followed when solving mathematical expressions.

Q: How does the order of operations apply to expressions with variables?

A: The order of operations applies to expressions with variables in the same way as it applies to expressions with constants. When dealing with expressions that contain variables, the order of operations is applied to the expression as a whole, rather than to individual variables.

Q: What is the difference between the order of operations and the order of precedence?

A: The order of operations and the order of precedence are related but distinct concepts. The order of operations refers to the sequence in which mathematical operations should be performed, while the order of precedence refers to the relative importance of different operations.

Q: Can the order of operations be used to solve expressions with multiple levels of parentheses?

A: Yes, the order of operations can be used to solve expressions with multiple levels of parentheses. When dealing with expressions that contain multiple levels of parentheses, the order of operations is applied in the following order:

Evaluate expressions inside the innermost parentheses first.
Evaluate expressions inside the next level of parentheses, and so on.
Finally, evaluate any remaining operations from left to right.

Q: How does the order of operations apply to expressions with fractions?

A: The order of operations applies to expressions with fractions in the same way as it applies to expressions with constants. When dealing with expressions that contain fractions, the order of operations is applied to the expression as a whole, rather than to individual fractions.

Conclusion

In conclusion, the order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. By following the PEMDAS acronym, individuals can ensure accuracy and avoid confusion when solving mathematical expressions. In this article, we addressed some of the most frequently asked questions about the order of operations and provided examples to illustrate the application of the order of operations to various types of expressions.

Additional Resources

For more information on the order of operations, check out the following resources:

Khan Academy: Order of Operations
Mathway: Order of Operations
Wolfram MathWorld: Order of Operations

Final Answer

The final answer is: There is no final answer, as this article is a Q&A guide to the order of operations.