Calculating The Value Of The Expression: Step-by-Step Guide

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Hey guys! Let's break down how to calculate the value of the expression (8 - √100 - |-16|) / ((-10) ÷ (-5) * (-3)). This might look intimidating at first, but we'll take it one step at a time, making it super easy to understand. We'll focus on each part of the expression, simplify it, and then put it all together to get our final answer. So, grab your calculators (or not, if you're feeling like a math whiz!), and let's dive in!

Understanding the Expression

Before we jump into solving, it’s crucial to understand the expression we’re dealing with: (8 - √100 - |-16|) / ((-10) ÷ (-5) * (-3)). This expression involves several mathematical operations, including square roots, absolute values, division, and multiplication. To solve this correctly, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This ensures we tackle each operation in the correct sequence, leading us to the right answer. Understanding the order of operations is key to simplifying any complex mathematical expression, so let's keep PEMDAS in mind as we move forward.

The expression consists of a numerator and a denominator. The numerator is (8 - √100 - |-16|), and the denominator is ((-10) ÷ (-5) * (-3)). We'll simplify each part separately and then divide the numerator by the denominator. This approach breaks down the problem into manageable chunks, making it less overwhelming. Remember, guys, math is all about taking things one step at a time. Breaking down complex expressions into smaller, more digestible parts is a fantastic strategy for success. So, let's get started with the numerator!

Simplifying the Numerator: 8 - √100 - |-16|

Okay, let's tackle the numerator: 8 - √100 - |-16|. Remember, PEMDAS tells us to deal with exponents and roots first, followed by absolute values, and then addition and subtraction. So, let's start with the square root of 100. The square root of 100 is 10 because 10 multiplied by itself equals 100. So, we can replace √100 with 10, and our expression now looks like this: 8 - 10 - |-16|. Calculating the square root is a fundamental step, and knowing common square roots like this can save you time. Next, we need to deal with the absolute value.

The absolute value of a number is its distance from zero, which is always a positive value. The absolute value of -16, written as |-16|, is 16. So, we replace |-16| with 16, and our expression becomes 8 - 10 - 16. Now, we just have subtraction left. Understanding absolute values is crucial, as it ensures we're working with positive magnitudes. Let's continue with the subtraction. We subtract 10 from 8, which gives us -2. So, our expression is now -2 - 16. Finally, we subtract 16 from -2, which gives us -18. Therefore, the simplified numerator is -18. Performing subtraction operations carefully is essential to avoid errors. Now that we've simplified the numerator, let's move on to the denominator.

Simplifying the Denominator: (-10) ÷ (-5) * (-3)

Now, let's dive into simplifying the denominator: (-10) ÷ (-5) * (-3). Again, we'll follow the order of operations (PEMDAS). In this case, we have division and multiplication. Since these operations have the same priority, we perform them from left to right. First, we divide -10 by -5. Remember, guys, a negative number divided by a negative number results in a positive number. So, -10 ÷ -5 equals 2. Our expression now looks like this: 2 * (-3). Mastering division with negative numbers is key to getting the right result.

Next, we multiply 2 by -3. A positive number multiplied by a negative number results in a negative number. So, 2 * (-3) equals -6. Therefore, the simplified denominator is -6. Understanding the rules of multiplication with positive and negative numbers is crucial for accurate calculations. Now that we've simplified both the numerator and the denominator, we're ready to put them together and find the final value of the expression. Let's move on to the final calculation.

Final Calculation: Numerator / Denominator

Alright, we've simplified the numerator to -18 and the denominator to -6. Now, it's time for the final calculation: -18 / -6. We're dividing a negative number by a negative number, which, as we know, will result in a positive number. So, -18 divided by -6 equals 3. Therefore, the value of the expression (8 - √100 - |-16|) / ((-10) ÷ (-5) * (-3)) is 3. Performing the final division is the last step in solving the expression, and it's great to see how all the previous steps come together. We made it, guys!

Conclusion

So, there you have it! We've successfully calculated the value of the expression (8 - √100 - |-16|) / ((-10) ÷ (-5) * (-3)), and the answer is 3. We walked through each step, from simplifying the numerator and denominator to the final division, making sure to follow the order of operations (PEMDAS). Understanding and applying PEMDAS is crucial for solving complex mathematical expressions accurately. We also highlighted the importance of working with square roots, absolute values, and positive and negative numbers.

Remember, guys, the key to tackling complex problems is to break them down into smaller, manageable steps. Breaking down problems into smaller steps makes them less intimidating and easier to solve. Math can be fun when you approach it methodically and understand the underlying concepts. Keep practicing, and you'll become a math whiz in no time! We hope this step-by-step guide was helpful and made the process clear and easy to follow. If you have any more questions or expressions you'd like us to break down, just let us know. Keep up the great work, and happy calculating!