Evaluate the multiplication

Oct 13, 2025 by miodeya.com 81 views

Understanding the Order of Operations

When simplifying mathematical expressions, it's essential to follow the order of operations, which is a set of rules that dictate the order in which operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

In the given expression, $$4 + (-3) - 2 \times (-6)$$, we need to follow the order of operations to simplify it. The expression involves addition, subtraction, and multiplication, so we need to perform the operations in the correct order.

Following the Order of Operations

To simplify the expression, we need to follow the order of operations:

Evaluate the multiplication: The expression contains a multiplication operation, which is $$2 \times (-6)$$. We need to evaluate this operation first.
Evaluate the addition and subtraction: After evaluating the multiplication, we need to perform the addition and subtraction operations from left to right.

Evaluating the Multiplication

The multiplication operation is $$2 \times (-6)$$. To evaluate this operation, we need to multiply 2 by -6.

2 \times (-6) = -12

Evaluating the Addition and Subtraction

Now that we have evaluated the multiplication, we can perform the addition and subtraction operations from left to right.

4 + (-3) - 12

Simplifying the Expression

To simplify the expression, we need to perform the addition and subtraction operations from left to right.

4 + (-3) = 1

1 - 12 = -11

Conclusion

Therefore, the simplified expression is $$-11$$.

The final answer is: D. -11

Understanding the Importance of Order of Operations

The order of operations is a crucial concept in mathematics that helps us simplify complex expressions. By following the order of operations, we can ensure that mathematical expressions are evaluated correctly and consistently.

In the given expression, $$4 + (-3) - 2 \times (-6)$$, we followed the order of operations to simplify it. We evaluated the multiplication operation first, and then performed the addition and subtraction operations from left to right.

Real-World Applications of Order of Operations

The order of operations has numerous real-world applications in mathematics, science, and engineering. For example, in physics, the order of operations is used to calculate the trajectory of objects under the influence of gravity. In engineering, the order of operations is used to design and optimize complex systems.

Common Mistakes in Order of Operations

One common mistake in order of operations is to perform operations in the wrong order. For example, in the expression $$4 + (-3) - 2 \times (-6)$$, some people might perform the addition and subtraction operations first, and then evaluate the multiplication operation. However, this is incorrect, and the correct order of operations is to evaluate the multiplication operation first, and then perform the addition and subtraction operations from left to right.

Tips for Mastering Order of Operations

To master the order of operations, it's essential to practice simplifying complex expressions. Here are some tips to help you master the order of operations:

Practice, practice, practice: The more you practice simplifying complex expressions, the more comfortable you'll become with the order of operations.
Use real-world examples: Use real-world examples to illustrate the importance of the order of operations.
Focus on the multiplication and division operations: The multiplication and division operations are often the most challenging operations to evaluate. Focus on mastering these operations first.
Use visual aids: Use visual aids such as diagrams and flowcharts to help you understand the order of operations.

Conclusion

In conclusion, the order of operations is a crucial concept in mathematics that helps us simplify complex expressions. By following the order of operations, we can ensure that mathematical expressions are evaluated correctly and consistently. With practice and patience, you can master the order of operations and become proficient in simplifying complex expressions.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: Why is it essential to follow the order of operations?

A: Following the order of operations is essential to ensure that mathematical expressions are evaluated correctly and consistently. If the order of operations is not followed, it can lead to incorrect results and confusion.

Q: What is the correct order of operations for the expression $$4 + (-3) - 2 \times (-6)$$?

A: The correct order of operations for the expression $$4 + (-3) - 2 \times (-6)$$ is to evaluate the multiplication operation first, and then perform the addition and subtraction operations from left to right.

Q: How do I evaluate the multiplication operation in the expression $$4 + (-3) - 2 \times (-6)$$?

A: To evaluate the multiplication operation in the expression $$4 + (-3) - 2 \times (-6)$$, you need to multiply 2 by -6.

2 \times (-6) = -12

Q: How do I perform the addition and subtraction operations in the expression $$4 + (-3) - 2 \times (-6)$$?

A: To perform the addition and subtraction operations in the expression $$4 + (-3) - 2 \times (-6)$$, you need to follow the order of operations:

Evaluate the multiplication operation: $$2 \times (-6) = -12$$
Perform the addition and subtraction operations from left to right: $$4 + (-3) = 1$$, $$1 - 12 = -11$$

Q: What is the final answer to the expression $$4 + (-3) - 2 \times (-6)$$?

A: The final answer to the expression $$4 + (-3) - 2 \times (-6)$$ is $$-11$$.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

Performing operations in the wrong order
Failing to evaluate parentheses and exponents correctly
Ignoring the order of operations

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by:

Using online resources and practice problems
Working with a tutor or teacher
Creating your own practice problems

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

A: Some real-world applications of the order of operations include:

Calculating the trajectory of objects under the influence of gravity
Designing and optimizing complex systems
Solving problems in physics, engineering, and mathematics

Q: How can I master the order of operations?

A: To master the order of operations, you can:

Practice simplifying complex expressions
Use real-world examples to illustrate the importance of the order of operations
Focus on mastering the multiplication and division operations
Use visual aids such as diagrams and flowcharts to help you understand the order of operations