Calculate: ( − 126 ) ÷ ( − 3 ) ÷ ( − 2 ) × ( + 11 (-126) \div (-3) \div (-2) \times (+11 ( − 126 ) ÷ ( − 3 ) ÷ ( − 2 ) × ( + 11 ]A. +231 B. -231 C. +1441 D. -1331

When dealing with mathematical expressions that involve multiple operations, 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 focus on calculating the expression $(-126) \div (-3) \div (-2) \times (+11)$ and understand the correct order of operations to arrive at the correct answer.

The Order of Operations

The order of operations is often remembered using the acronym PEMDAS, which stands for:

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.

Calculating the Expression

Now that we understand the order of operations, let's focus on calculating the expression $(-126) \div (-3) \div (-2) \times (+11)$. To do this, we need to follow the order of operations and perform the calculations step by step.

Step 1: Divide $(-126)$ by $(-3)$

When dividing two negative numbers, the result is a positive number. Therefore, $(-126) \div (-3) = 42$.

Step 2: Divide the result by $(-2)$

Now that we have the result of the first division, we need to divide it by $(-2)$. Again, when dividing two negative numbers, the result is a positive number. Therefore, $42 \div (-2) = -21$.

Step 3: Multiply the result by $(+11)$

Finally, we need to multiply the result of the second division by $(+11)$. When multiplying a negative number by a positive number, the result is a negative number. Therefore, $-21 \times (+11) = -231$.

Conclusion

In conclusion, the correct answer to the expression $(-126) \div (-3) \div (-2) \times (+11)$ is $-231$. This result is obtained by following the order of operations and performing the calculations step by step.

Common Mistakes to Avoid

When dealing with mathematical expressions that involve multiple operations, it's essential to avoid common mistakes that can lead to incorrect results. Some common mistakes to avoid include:

• Not following the order of operations
• Not performing calculations step by step
• Not considering the signs of the numbers involved in the calculation

By following the order of operations and avoiding common mistakes, you can ensure accurate results and build confidence in your mathematical abilities.

Practice Problems

To reinforce your understanding of the order of operations, try solving the following practice problems:

1. Calculate the expression $(-24) \div (-4) \div (-3) \times (+8)$.
2. Calculate the expression $(-36) \div (-6) \div (-5) \times (+9)$.
3. Calculate the expression $(-48) \div (-8) \div (-6) \times (+7)$.

By practicing these problems, you can develop your skills and build confidence in your ability to calculate mathematical expressions involving multiple operations.

Conclusion

In this article, we will address some of the most frequently asked questions about the order of operations. Whether you're a student, a teacher, or simply someone who wants to improve their math skills, this article will provide you with the answers you need to understand 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 order of operations is often remembered using the acronym PEMDAS, which stands for:

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 ensure that mathematical expressions are evaluated correctly. Without the order of operations, mathematical expressions can be ambiguous and lead 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, the order of operations dictates that they should be evaluated from left to right. For example, in the expression $3 \times 2 + 4$, the multiplication operation is evaluated first, followed by the addition operation.

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, you can break down complex expressions into simpler ones and evaluate them step by step.

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
• Not performing calculations step by step
• Not considering the signs of the numbers involved in the calculation
• Not using parentheses to clarify the order of operations

Q: How can I practice using the order of operations?

A: You can practice using the order of operations by working through math problems and exercises that involve multiple operations. You can also try solving puzzles and brain teasers that require the use of the order of operations.

Q: What are some real-world applications of the order of operations?

A: The order of operations has many real-world applications, including:

• Scientific calculations: The order of operations is used in scientific calculations to ensure that mathematical expressions are evaluated correctly.
• Financial calculations: The order of operations is used in financial calculations to ensure that mathematical expressions are evaluated correctly.
• Engineering calculations: The order of operations is used in engineering calculations to ensure that mathematical expressions are evaluated correctly.

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 and avoiding common mistakes, you can ensure accurate results and build confidence in your mathematical abilities. Remember to practice using the order of operations and to apply it in real-world situations.

Additional Resources

If you're looking for additional resources to help you understand the order of operations, here are a few suggestions:

• Khan Academy: Khan Academy has a comprehensive video series on the order of operations that covers the basics and beyond.
• Mathway: Mathway is an online math problem solver that can help you practice using the order of operations.
• Wolfram Alpha: Wolfram Alpha is a powerful online calculator that can help you evaluate mathematical expressions and understand the order of operations.

By using these resources and practicing regularly, you can become proficient in using the order of operations and achieve success in math and beyond.