Calculating Absolute Value Of 9-{(240+220) .(19-19)} A Step-by-Step Guide

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Hey guys! Let's break down this math problem together. We're going to dive into calculating the absolute value of a slightly complex expression. Don't worry, it's not as scary as it looks! We'll take it step by step, making sure everyone understands the process. Our main goal here is to solve the expression 9-{(240+220) .(19-19)} and then find the absolute value of the result. So, grab your thinking caps, and let's get started!

Understanding the Problem

Before we jump into calculations, let's make sure we understand what the problem is asking. We have the expression 9-{(240+220) .(19-19)}, and we need to find its absolute value. But what does that even mean?

The absolute value of a number is its distance from zero on the number line. It's always a non-negative value, meaning it's either positive or zero. Think of it as stripping away the negative sign, if there is one. For example, the absolute value of 5 (written as |5|) is 5, and the absolute value of -5 (written as |-5|) is also 5.

Now, let's look at the expression itself. It involves several operations: addition, subtraction, and multiplication, all nestled within parentheses and brackets. To solve it correctly, we need to follow the order of operations, which you might remember as PEMDAS or BODMAS. This tells us the order in which to perform the operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

So, in our expression, we'll first tackle the operations inside the parentheses, then the brackets, and finally the subtraction outside. Understanding this order is crucial for getting the right answer. We need to be methodical, ensuring each step is correctly executed before moving on to the next. This approach not only helps us solve the problem accurately but also builds a solid foundation for tackling more complex mathematical challenges in the future. Remember, math is like building blocks – each concept builds upon the previous one, so a clear understanding of the basics is key.

Step-by-Step Solution

Okay, let's get our hands dirty and solve this problem step by step. Remember, we're following the order of operations (PEMDAS/BODMAS) to make sure we do everything in the right sequence. This will ensure we arrive at the correct answer without any confusion. Let's break it down!

Step 1: Parentheses

First, we need to deal with the operations inside the parentheses. We have two sets of parentheses in our expression: (240+220) and (19-19).

  • Let's tackle (240+220) first. This is a simple addition: 240 + 220 = 460. So, we've simplified the first set of parentheses to 460.
  • Next up is (19-19). This is a straightforward subtraction: 19 - 19 = 0. The second set of parentheses simplifies to 0.

Now our expression looks like this: 9- {460 . 0}. We've successfully taken care of the parentheses, and we're one step closer to the final solution. The key here is to be meticulous and double-check each calculation to avoid any errors. Small mistakes in the early stages can snowball and lead to an incorrect final answer. So, always take a moment to verify your work before moving on.

Step 2: Brackets

Now that we've simplified the parentheses, we move on to the brackets. Inside the brackets, we have the expression 460 . 0, which means 460 multiplied by 0.

  • Any number multiplied by 0 is 0. So, 460 . 0 = 0. This means the entire expression within the brackets simplifies to 0.

Our expression now looks much simpler: 9 - 0. We're making great progress! You can see how breaking down the problem into smaller steps makes it much more manageable. Instead of being overwhelmed by the original expression, we've systematically reduced it to a simple subtraction. This is a powerful technique in mathematics – complex problems often become much easier when approached in a step-by-step manner. Always look for ways to simplify and break down problems into smaller, more digestible parts.

Step 3: Subtraction

We're almost there! Our expression has been simplified to 9 - 0. This is a very basic subtraction.

  • 9 - 0 = 9. So, the result of the expression 9-{(240+220) .(19-19)} is 9.

We've successfully navigated through all the operations, following the correct order, and arrived at the value 9. Now, remember, the final step is to find the absolute value of this result. This is where the concept of absolute value comes into play. We're not just looking for the answer to the expression; we're looking for its distance from zero on the number line. So, let's take that final step and find the absolute value.

Step 4: Absolute Value

We've calculated that the expression 9-{(240+220) .(19-19)} equals 9. Now, the final step is to find the absolute value of 9.

  • The absolute value of a number is its distance from zero. Since 9 is 9 units away from zero, its absolute value is simply 9.

So, |9| = 9. That's it! We've successfully solved the problem and found the absolute value. It's important to remember that the absolute value is always non-negative. It essentially tells us the magnitude of a number without considering its sign. This concept is useful in many areas of mathematics and real-world applications, such as calculating distances or measuring errors, where we're only interested in the size of the difference, not its direction.

Final Answer

Alright, guys, we've reached the end! After carefully working through each step, we've found the absolute value of the expression 9-{(240+220) .(19-19)}.

The final answer is |9| = 9.

We started with a seemingly complex expression, but by breaking it down into smaller, manageable steps and following the order of operations, we were able to solve it without any hassle. Remember, the key to success in math is often about being organized, patient, and meticulous in your approach. Double-check your calculations, understand the underlying concepts, and don't be afraid to break down problems into smaller parts. With practice and a clear understanding of the fundamentals, you can tackle even the most challenging math problems with confidence. So, keep practicing, keep learning, and most importantly, keep enjoying the process of problem-solving!

Conclusion

So, there you have it! We've successfully navigated the absolute value calculation of 9-{(240+220) .(19-19)}. We've walked through each step, from understanding the order of operations to applying the concept of absolute value. Hopefully, this detailed explanation has made the process clear and understandable for everyone.

The most important takeaway here is that complex problems can be solved by breaking them down into smaller, more manageable steps. This approach not only makes the problem less intimidating but also reduces the chances of making errors. Remember to always follow the order of operations (PEMDAS/BODMAS) and double-check your calculations along the way.

Understanding the fundamental concepts, like absolute value, is also crucial. The absolute value represents the distance from zero, which is always a non-negative value. This concept has many applications in various fields, from mathematics and physics to everyday life situations.

Math can sometimes feel challenging, but with practice and a clear understanding of the basics, you can overcome any hurdle. Keep practicing, keep exploring, and never stop learning. And remember, if you ever get stuck, don't hesitate to ask for help or seek out resources that can guide you. Math is a journey, and every step you take brings you closer to mastering it. So, keep up the great work, and I'm confident you'll continue to excel in your mathematical endeavors!