Using The Order Of Operations, What Is The Last Calculation That Should Be Done To Evaluate $4(8-6) \times 5^2 - 6 \div (-3$\]?$\[ \begin{align*} 1. & \quad 4(8-6) \times 5^2 - 6 \div (-3) \\ 2. & \quad 4(2) \times 5^2 - 6 \div (-3) \\ 3. &

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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.

Evaluating the Given Expression

Let's apply the order of operations to evaluate the given expression:

$4(8-6) \times 5^2 - 6 \div (-3)$

Step 1: Evaluate Expressions Inside Parentheses

First, we need to evaluate the expression inside the parentheses:

$8-6 = 2$

So, the expression becomes:

$4(2) \times 5^2 - 6 \div (-3)$

Step 2: Evaluate Exponential Expressions

Next, we need to evaluate the exponential expression:

$5^2 = 25$

So, the expression becomes:

$4(2) \times 25 - 6 \div (-3)$

Step 3: Evaluate Multiplication and Division Operations

Now, we need to evaluate the multiplication and division operations from left to right:

$4(2) = 8$

So, the expression becomes:

$8 \times 25 - 6 \div (-3)$

$8 \times 25 = 200$

So, the expression becomes:

$200 - 6 \div (-3)$

Step 4: Evaluate Division Operation

Next, we need to evaluate the division operation:

$6 \div (-3) = -2$

So, the expression becomes:

$200 - (-2)$

Step 5: Evaluate Addition and Subtraction Operations

Finally, we need to evaluate the addition and subtraction operations from left to right:

$200 - (-2) = 200 + 2 = 202$

Therefore, the final answer is:

202

Conclusion

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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 us evaluate complex expressions and solve problems accurately. Without the order of operations, we might perform operations in the wrong order and arrive at an incorrect answer.

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

A: If you forget to follow the order of operations, you might perform operations in the wrong order and arrive at an incorrect answer. For example, if you have the expression 3 + 4 × 5, you might forget to follow the order of operations and add 3 and 4 first, resulting in 7 × 5 = 35. However, the correct answer is 3 + 4 × 5 = 3 + 20 = 23.

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: How do I apply the order of operations to evaluate expressions with multiple operations?

A: To apply the order of operations to evaluate expressions with multiple operations, follow these steps:

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

Q: What are some common mistakes to avoid when applying the order of operations?

A: Some common mistakes to avoid when applying the order of operations include:

• Forgetting to evaluate expressions inside parentheses first.
• Evaluating exponential expressions before multiplication and division operations.
• Evaluating multiplication and division operations from right to left instead of left to right.
• Forgetting to evaluate addition and subtraction operations from left to right.

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

A: Yes, you can use the order of operations to evaluate expressions with negative numbers. When evaluating expressions with negative numbers, remember to follow the order of operations and evaluate the expression step by step.

Q: How do I apply the order of operations to evaluate expressions with fractions?

A: To apply the order of operations to evaluate expressions with fractions, follow these steps:

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

Conclusion

In this article, we answered some frequently asked questions about the order of operations. We discussed the importance of the order of operations, common mistakes to avoid, and how to apply the order of operations to evaluate expressions with multiple operations, negative numbers, and fractions. By following the order of operations, you can ensure that you evaluate complex expressions accurately and arrive at the correct answer.