Solving The Complex Math Expression: A Step-by-Step Guide

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Decoding the Math Puzzle: A Step-by-Step Solution to 48 + 2 * {1740 - 8 * [30 + 3 * (250 - 10918 : 53)]}

Hey there, math enthusiasts! Ever stumbled upon a math problem that looks like it belongs in a complex puzzle? Well, today we're diving headfirst into one such expression: 48 + 2 * 1740 - 8 * [30 + 3 * (250 - 10918 53)]. Don't worry, it might seem daunting at first, but we're going to break it down step-by-step, so you'll be a pro at solving these in no time. This isn't just about getting the right answer; it's about understanding the order of operations and how to tackle even the most intimidating equations. So, grab your calculators (or your mental math muscles) and let's get started!

Understanding the Order of Operations (PEMDAS/BODMAS)

Before we even think about plugging in numbers, let's quickly revisit the golden rule of math: the order of operations. You might know it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Essentially, it's the roadmap that tells us which operations to perform first. Think of it as a set of traffic rules for numbers, ensuring we all arrive at the same destination (the correct answer!).

  • Parentheses/Brackets First: Anything inside these gets top priority. It's like the VIP section of the math world.
  • Exponents/Orders: Next up are those little powers that tell us to multiply a number by itself.
  • Multiplication and Division: These guys are on equal footing, so we work from left to right.
  • Addition and Subtraction: Just like multiplication and division, we tackle these from left to right.

Knowing this order is crucial for solving our complex expression. Mess it up, and you'll end up in a mathematical maze. So, let's keep PEMDAS/BODMAS in the back of our minds as we move forward.

Cracking the Code: Step-by-Step Solution

Now that we've got the rules down, let's break down our expression 48 + 2 * 1740 - 8 * [30 + 3 * (250 - 10918 53)] piece by piece. Remember, we're going inside-out, starting with the innermost parentheses and working our way outwards. It's like peeling an onion, but instead of tears, we'll get a satisfying solution!

1. Innermost Parentheses: 10918 : 53

The very core of our problem lies within the division inside the innermost parentheses. Let's tackle 10918 : 53 first. When you perform this division, you'll find that 10918 divided by 53 equals 206. This is a crucial first step, as it simplifies the most nested part of our expression. Getting this right sets the stage for the rest of the calculation, so double-check your work!

2. Continuing Inside: (250 - 206)

Now that we've solved the division, we can complete the operation within the innermost parentheses: (250 - 206). This subtraction is straightforward, and 250 minus 206 gives us 44. See how we're slowly chipping away at the complexity? It's like a mathematical excavation, revealing the answer bit by bit. This step is all about careful calculation and paying attention to detail.

3. Moving Outwards: 3 * 44

Next, we move to the multiplication within the square brackets: 3 * 44. Multiplying 3 by 44 results in 132. It's important to follow the order of operations diligently here; otherwise, you might end up with a completely different result. Each step we take brings us closer to the final solution, and this multiplication is a key piece of the puzzle.

4. Brackets Continue: 30 + 132

We're still working within the square brackets, so let's add 30 + 132. This addition gives us 162. Notice how we're simplifying the expression step-by-step, making it more manageable. This part of the calculation reinforces the importance of PEMDAS/BODMAS, as we're now resolving the addition within the brackets.

5. Curly Braces: 8 * 162

Now we move to the curly braces and perform the multiplication: 8 * 162. This calculation yields 1296. It's essential to keep track of where you are in the expression and which operations you've already completed. This multiplication is a significant step, as it further reduces the complexity of the overall problem.

6. More Curly Braces: 1740 - 1296

Still within the curly braces, we subtract 1296 from 1740. This subtraction results in 444. We're getting closer to the outer layers of the expression, and with each step, the problem becomes clearer. This subtraction is another critical step in isolating the final calculation.

7. Multiplication Time: 2 * 444

Now we perform the multiplication outside the curly braces: 2 * 444. Multiplying 2 by 444 gives us 888. It's crucial to accurately perform each multiplication, as errors here can cascade through the rest of the calculation. This multiplication is one of the final steps in our journey to the solution.

8. The Grand Finale: 48 + 888

Finally, we arrive at the last operation: 48 + 888. Adding these two numbers together gives us the grand total of 936. Congratulations, we've cracked the code! It might have seemed like a long journey, but by following the order of operations and breaking the problem down, we arrived at the solution with confidence.

The Final Answer and Key Takeaways

So, after all that mathematical maneuvering, the answer to the expression 48 + 2 * 1740 - 8 * [30 + 3 * (250 - 10918 53)] is 936. Give yourself a pat on the back for making it through! This wasn't just about finding a number; it was about understanding how to approach complex problems and the importance of following the rules.

Key Takeaways from Our Math Adventure:

  • PEMDAS/BODMAS is Your Best Friend: Never underestimate the power of the order of operations. It's the foundation for solving any mathematical expression.
  • Break It Down: Complex problems become much easier when you tackle them step-by-step. Divide and conquer, my friends!
  • Double-Check Your Work: A small error early on can throw off the entire calculation. Accuracy is key.
  • Practice Makes Perfect: The more you solve these kinds of problems, the more comfortable you'll become. Keep challenging yourself!

Practice Problems to Sharpen Your Skills

Now that you've conquered this expression, why stop there? Here are a few more problems to test your newfound skills. Remember, the key is to break them down, follow the order of operations, and take your time. Happy calculating!

  1. 100 - 2 * (35 + 15 ÷ 3)
  2. 5 * [24 - 3 * (18 - 12)] + 10
  3. 72 ÷ (8 + 4) * 3 - 1

Solving these types of complex mathematical expressions isn't just an academic exercise; it's a fantastic way to sharpen your mind and improve your problem-solving skills. Whether you're a student tackling homework or just a curious mind seeking a challenge, mastering the order of operations and learning to break down problems into manageable steps is a valuable skill. So, keep practicing, keep exploring, and most importantly, keep enjoying the world of mathematics! You've got this, guys!