Solving 11-{16-[18-(60–49)]}: Step-by-Step Solution

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Solving the Mathematical Expression 11-{16-[18-(60–49)]}

Hey guys! Today, we're going to tackle the mathematical expression 11-{16-[18-(60–49)]}. Don't worry if it looks intimidating; we'll break it down step by step, making it super easy to understand. Math can be fun, especially when we approach it methodically. We'll go through each part, ensuring you grasp not just the answer but also the process. So, let's dive in and get started!

Understanding the Order of Operations

Before we jump into solving the expression, it's crucial to understand the order of operations. Remember the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This order helps us simplify expressions correctly.

  1. Parentheses: Solve operations inside parentheses first.
  2. Exponents: Calculate any exponents.
  3. Multiplication and Division: Perform these operations from left to right.
  4. Addition and Subtraction: Perform these operations from left to right.

Following PEMDAS ensures we arrive at the correct solution. For this particular expression, we'll focus mainly on parentheses and subtraction, but keeping the order in mind is always a good practice. Let's keep this in mind as we work through the problem together, making sure we don’t miss any steps. This foundational knowledge is super important for tackling more complex problems later on, so pay close attention, guys!

Step 1: Solving the Innermost Parentheses (60 – 49)

Okay, let's start with the innermost parentheses in our expression: (60 – 49). This is a straightforward subtraction problem. Think of it like having 60 apples and eating 49 of them. How many are left?

To solve this, we simply subtract 49 from 60:

60 – 49 = 11

So, the result of the innermost parentheses is 11. Now we can replace (60 – 49) with 11 in our original expression. This simplifies our problem and makes it easier to tackle the next layer. Remember, guys, breaking down complex problems into smaller, manageable steps is the key to success in math! Next, we’ll move on to the next set of brackets, and you’ll see how smoothly this process goes. Keep up the good work!

Step 2: Solving the Next Brackets [18 – 11]

Now that we've solved the innermost parentheses, let's move to the next set of brackets: [18 – 11]. We've already simplified (60 – 49) to 11, so our expression now looks like this: 11-{16-[18-11]}. Again, this is a simple subtraction problem.

To find the value of [18 – 11], we subtract 11 from 18:

18 – 11 = 7

So, [18 – 11] equals 7. We can replace [18 – 11] with 7 in our expression, which further simplifies our problem. We're making great progress, guys! By taking it one step at a time, these complex-looking expressions become much less daunting. Next, we’ll tackle the curly braces, and you’ll see how each step builds upon the last, making the final solution crystal clear. Keep going, you're doing awesome!

Step 3: Solving the Curly Braces {16 – 7}

Alright, we're moving right along! Next up are the curly braces: {16 – 7}. We've already simplified the inner parts, so we now have 11-{16-7}. This is another subtraction problem, and by now, you're probably getting the hang of it!

To solve {16 – 7}, we subtract 7 from 16:

16 – 7 = 9

So, {16 – 7} equals 9. We replace the curly braces with 9 in our expression. Our problem is getting simpler and simpler, right? We're almost at the finish line, guys! Taking each step methodically like this not only gets us the right answer but also builds our confidence in tackling more challenging math problems. Now, let’s do the final subtraction, and we’ll have our solution!

Step 4: The Final Subtraction 11 – 9

We've reached the last step! Our expression has been simplified to 11 – 9. This is the final subtraction we need to perform to solve the entire problem. You've done an amazing job getting here, guys!

To find the answer, we subtract 9 from 11:

11 – 9 = 2

So, the final answer is 2! Congratulations, you've successfully solved the mathematical expression 11-{16-[18-(60–49)]}. See? It wasn’t as scary as it looked initially. By following the order of operations and breaking it down step by step, you made it through. High five!

Conclusion: Final Answer and Key Takeaways

To recap, the solution to the mathematical expression 11-{16-[18-(60–49)]} is 2. Great job, guys, for sticking with it and working through each step!

Key Takeaways:

  • PEMDAS is Your Friend: Always remember the order of operations (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). It’s the golden rule for solving mathematical expressions correctly.
  • Break It Down: Complex problems become manageable when you break them into smaller, simpler steps. Just like we tackled this expression, one set of brackets at a time.
  • Practice Makes Perfect: The more you practice, the more comfortable you'll become with math. Keep solving problems, and you’ll see yourself improving.
  • Don't Be Afraid to Ask for Help: If you get stuck, don’t hesitate to ask for help or clarification. We’re all learning together!

I hope this step-by-step solution was helpful and made the process clear for you. Keep up the great work, and remember, math can be fun when you approach it with the right mindset and tools. Until next time, keep solving, keep learning, and keep rocking, guys!