Evaluate The Expression:${ 2(-3) - (5) - 4 \left( \frac{6}{-3} \right) }$Choose The Correct Answer:A. 5-6 B. 22 C. 9 D. 3

Mar 13, 2025 by ADMIN 126 views

Evaluate the Expression: 2(-3) - (5) - 4(6/-3)

Understanding the Expression

The given expression is a mathematical equation that involves various operations such as multiplication, division, and subtraction. To evaluate this expression, we need to follow the order of operations (PEMDAS) and perform the calculations step by step.

Breaking Down the Expression

Let's break down the expression into smaller parts and evaluate each part separately.

Part 1: 2(-3)

The first part of the expression is 2(-3). To evaluate this, we need to multiply 2 by -3.

2(-3) = -6

Part 2: -(5)

The second part of the expression is -(5). The negative sign outside the parentheses indicates that we need to change the sign of the number inside the parentheses.

-(5) = -5

Part 3: 4(6/-3)

The third part of the expression is 4(6/-3). To evaluate this, we need to follow the order of operations and perform the division inside the parentheses first.

6/-3 = -2

Now, we can multiply 4 by -2.

4(-2) = -8

Combining the Parts

Now that we have evaluated each part of the expression, we can combine them to get the final result.

2(-3) - (5) - 4(6/-3) = -6 - 5 - (-8)

To evaluate this expression, we need to follow the order of operations and perform the subtractions from left to right.

-6 - 5 = -11
-11 - (-8) = -11 + 8 = -3

Conclusion

The final result of the expression 2(-3) - (5) - 4(6/-3) is -3.

Comparison with Answer Choices

Let's compare our result with the answer choices provided.

A. 5-6: This is not equal to our result.
B. 22: This is not equal to our result.
C. 9: This is not equal to our result.
D. 3: This is not equal to our result.

However, if we re-evaluate the expression, we can see that the correct answer is actually not among the options provided. The correct answer is indeed -3, but it is not listed among the options.

Final Answer

The final answer is not among the options provided. The correct answer is -3.

Importance of Following the Order of Operations

The order of operations (PEMDAS) is a fundamental concept in mathematics that helps us evaluate expressions correctly. By following the order of operations, we can avoid errors and ensure that our calculations are accurate.

Real-World Applications

The concept of following the order of operations is not limited to mathematical expressions. It is also applicable in real-world scenarios where we need to perform multiple tasks in a specific order.

Conclusion

In conclusion, evaluating the expression 2(-3) - (5) - 4(6/-3) requires us to follow the order of operations and perform the calculations step by step. By doing so, we can arrive at the correct answer, which is -3. The importance of following the order of operations cannot be overstated, as it helps us avoid errors and ensure that our calculations are accurate.

Understanding the Expression

Q&A Session

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions correctly. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. We need to follow this order to ensure that our calculations are accurate.

Q: How do we evaluate expressions with parentheses?

A: When we encounter an expression with parentheses, we need to evaluate the expression inside the parentheses first. This means that we need to perform any calculations inside the parentheses before moving on to the next step.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do we evaluate expressions with negative numbers?

A: When we encounter an expression with negative numbers, we need to remember that a negative number is the opposite of a positive number. For example, -3 is the opposite of 3.

Q: What is the final answer to the expression 2(-3) - (5) - 4(6/-3)?

A: The final answer to the expression 2(-3) - (5) - 4(6/-3) is -3.

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

A: Following the order of operations is crucial in mathematics because it helps us avoid errors and ensure that our calculations are accurate. By following the order of operations, we can evaluate expressions correctly and arrive at the correct answer.

Q: Can you provide an example of a real-world application of the order of operations?

A: Yes, the order of operations is not limited to mathematical expressions. It is also applicable in real-world scenarios where we need to perform multiple tasks in a specific order. For example, when cooking a recipe, we need to follow the order of operations to ensure that the dish is prepared correctly.

Q: What are some common mistakes that people make when evaluating expressions?

A: Some common mistakes that people make when evaluating expressions include:

Not following the order of operations
Not evaluating expressions inside parentheses first
Not remembering that a negative number is the opposite of a positive number
Not performing calculations correctly

Q: How can we avoid making mistakes when evaluating expressions?

A: To avoid making mistakes when evaluating expressions, we need to:

Follow the order of operations
Evaluate expressions inside parentheses first
Remember that a negative number is the opposite of a positive number
Perform calculations correctly

Conclusion

Final Answer

The final answer to the expression 2(-3) - (5) - 4(6/-3) is -3.

Importance of Following the Order of Operations

Real-World Applications

The concept of following the order of operations is not limited to mathematical expressions. It is also applicable in real-world scenarios where we need to perform multiple tasks in a specific order.