Evaluate: $6[4-9.4]$ - A Step-by-Step Solution

Hey everyone! Today, we're going to break down a math problem step-by-step. Specifically, we need to figure out the value of the expression $6[4-9.4]$. Don't worry, it's not as scary as it looks! We'll take it slow and make sure everyone understands each step. So, grab your pencils, and let's get started!

Understanding the Expression

First, let's make sure we understand what the expression $6[4-9.4]$ actually means. The square brackets [] indicate that we need to perform the operation inside them first. In this case, that means we need to subtract 9.4 from 4. Once we've done that, we'll multiply the result by 6. Remember the order of operations (often remembered by the acronym PEMDAS or BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following this order is crucial to getting the correct answer. Many common mistakes in math come from not following the correct order of operations, so always double-check that you are doing things in the right sequence. Before we jump into the calculations, let's think for a moment about what we expect the answer to be. We are subtracting a larger number (9.4) from a smaller number (4), so we know the result inside the brackets will be negative. Then, we're multiplying that negative number by 6, which will also give us a negative number. This helps us eliminate any positive answer choices right away and gives us a good sense of what our final answer should look like.

Step-by-Step Calculation

Let's begin by calculating the value inside the brackets:

$4 - 9.4 = -5.4$

Now, we substitute this value back into the original expression:

$6[-5.4] = 6 simes (-5.4)$

Next, we multiply 6 by -5.4:

$6 simes (-5.4) = -32.4$

So, the value of the expression $6[4-9.4]$ is $-32.4$.

Analyzing the Answer Choices

Now that we've calculated the value, let's look at the answer choices provided:

A. $-36$ B. $-33$ C. $-32$ D. $-30$

Our calculated value is $-32.4$. Looking at the options, we see that -32 is the closest, but it's not an exact match. This might make us pause and double-check our work, which is always a good idea! Let's go back and carefully review each step to ensure we haven't made any mistakes. It's easy to make a small arithmetic error, especially when dealing with decimals, so a thorough review is essential. In this case, we were looking to approximate the answer since -32.4 wasn't explicitly listed. However, it is important to perform accurate calculations.

Approximation vs. Exact Value

In some cases, the answer choices might be rounded or approximate values. If we had to choose the closest answer from the given options, -32 would be the most reasonable choice. However, in a precise mathematical context, it's important to recognize that -32 is not exactly equal to -32.4. Therefore, none of the provided options A, B, C, or D are perfectly correct. This is a good reminder to always be aware of whether you're looking for an exact answer or an approximation.

Common Mistakes to Avoid

• Incorrect Order of Operations: Always follow PEMDAS/BODMAS.
• Sign Errors: Pay close attention to positive and negative signs, especially when subtracting larger numbers from smaller numbers.
• Decimal Miscalculations: Double-check your decimal placement when multiplying or dividing.
• Rushing Through Steps: Take your time and write out each step clearly to minimize errors.

By being mindful of these potential pitfalls, you can increase your accuracy and confidence in solving mathematical problems.

Real-World Applications

While this specific problem might seem abstract, the skills we used to solve it are applicable in many real-world situations. For example:

• Finance: Calculating profits and losses, especially when dealing with debts and credits.
• Engineering: Determining tolerances and margins of error in measurements.
• Science: Analyzing experimental data and interpreting results.
• Everyday Life: Budgeting, shopping, and making informed decisions based on numerical information.

The ability to confidently work with numbers and algebraic expressions is a valuable asset in countless aspects of life.

Practice Problems

To further solidify your understanding, try solving these similar problems:

1. Evaluate: $5[3 - 7.2]$
2. Evaluate: $-2[8 - 12.5]$
3. Evaluate: $10[1.5 - 6]$

Work through each problem step-by-step, and be sure to double-check your answers. The more you practice, the more comfortable and proficient you'll become with these types of calculations.

Conclusion

Alright guys, we successfully evaluated the expression $6[4-9.4]$! While the exact answer (-32.4) wasn't among the provided choices, we understood the importance of accurate calculations and how to select the closest approximation when necessary. Remember to always follow the order of operations, pay attention to signs, and double-check your work. Keep practicing, and you'll become a math whiz in no time! If you have any questions or need further clarification, feel free to ask. Happy calculating!