Apply The Order Of Operations To Determine Whether The Following Statement Is True Or False:$\[ -9-[1-(4 \cdot(-1)-11)] \neq 8 \\]

The order of operations is a set of rules that helps us evaluate mathematical expressions in the correct order. It is essential to follow these rules to avoid confusion and ensure that mathematical expressions are evaluated consistently. In this article, we will apply the order of operations to determine whether the given statement is true or false.

What is 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 any 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

The given expression is:

$$-9-[1-(4 \cdot(-1)-11)] \neq 8$$

To evaluate this expression, we need to follow the order of operations.

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the innermost parentheses is:

$$4 \cdot(-1)-11$$

Using the order of operations, we first evaluate the multiplication:

$$4 \cdot(-1) = -4$$

Then, we subtract 11:

$$-4 - 11 = -15$$

So, the expression inside the innermost parentheses is:

$$-15$$

Step 2: Evaluate the Expression Inside the Outermost Parentheses

Now, we evaluate the expression inside the outermost parentheses:

$$1 - (-15)$$

Using the order of operations, we first evaluate the subtraction:

$$1 - (-15) = 1 + 15 = 16$$

So, the expression inside the outermost parentheses is:

$$16$$

Step 3: Evaluate the Final Expression

Now, we can evaluate the final expression:

$$-9 - 16$$

Using the order of operations, we first subtract 16:

$$-9 - 16 = -25$$

So, the final expression is:

$$-25$$

Step 4: Compare the Final Expression with 8

The given statement is:

$$-9-[1-(4 \cdot(-1)-11)] \neq 8$$

We have evaluated the expression and found that it is equal to -25. Therefore, we can compare -25 with 8:

$$-25 \neq 8$$

This statement is TRUE.

Conclusion

In this article, we applied the order of operations to evaluate a given mathematical expression. We followed the rules of PEMDAS to ensure that the expression was evaluated consistently. By evaluating the expression step by step, we found that the statement is true. This demonstrates the importance of following the order of operations in mathematics.

Common Mistakes to Avoid

When evaluating mathematical expressions, it is essential to follow the order of operations. Some common mistakes to avoid include:

• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

By following the order of operations and avoiding these common mistakes, we can ensure that mathematical expressions are evaluated consistently and accurately.

Real-World Applications

The order of operations has many real-world applications. For example:

• In computer programming, the order of operations is used to evaluate mathematical expressions in code.
• In science and engineering, the order of operations is used to evaluate complex mathematical expressions that describe physical phenomena.
• In finance, the order of operations is used to evaluate mathematical expressions that describe financial transactions.

By understanding the order of operations and applying it consistently, we can solve mathematical problems accurately and efficiently.

Final Thoughts

In conclusion, the order of operations is a set of rules that helps us evaluate mathematical expressions in the correct order. By following the rules of PEMDAS, we can ensure that mathematical expressions are evaluated consistently and accurately. In this article, we applied the order of operations to evaluate a given mathematical expression and found that the statement is true. This demonstrates the importance of following the order of operations in mathematics.