Solving: 89307-(2074*5+296800/80)*3+4228/7

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Solving the Complex Equation: 89307-(2074*5+296800/80)*3+4228/7

Hey guys! Today, we're diving into a fun mathematical problem. It looks a bit intimidating at first glance, but don't worry! We’ll break it down step by step to make it super easy to understand. Our mission is to solve the equation: 89307-(2074*5+296800/80)*3+4228/7. Grab your calculators (or your brains!), and let's get started!

Understanding the Order of Operations

Before we jump in, remember PEMDAS/BODMAS, which is our golden rule:

  • Parentheses / Brackets
  • Exponents / Orders
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

This tells us the order in which we need to perform the operations to get the correct answer. Trust me; it's crucial! It's like having a secret recipe; you need to follow the steps in order.

Step 1: Solving Inside the Parentheses

First, let's tackle what's inside the parentheses: (2074*5 + 296800/80). According to PEMDAS, we need to handle the multiplication and division first. So, let’s break it down even further.

Multiplication

Let's multiply 2074 by 5. You can punch this into your calculator or do it manually. Either way, 2074 * 5 equals 10370. Okay, we've cleared our first mini-hurdle!

Division

Next up, we divide 296800 by 80. When you perform this division, you get 3710. Fantastic! We're making great progress. Division can sometimes be a pain, but with calculators, it’s a breeze, right?

Addition inside Parentheses

Now that we've handled the multiplication and division inside the parentheses, we can add the results together. We add 10370 and 3710, which gives us 14080. That means (2074*5 + 296800/80) simplifies to 14080. See? Piece of cake!

Step 2: Multiplication Outside the Parentheses

Now that we've simplified the parentheses, our equation looks like this: 89307 - (14080) * 3 + 4228 / 7. Next in line according to PEMDAS is multiplication. We need to multiply 14080 by 3. When you do the math, 14080 * 3 equals 42240. Almost there, guys!

Step 3: Division at the End

We're almost home! Our equation now looks like this: 89307 - 42240 + 4228 / 7. According to our beloved PEMDAS, we need to perform the division before we even think about subtraction or addition. So, let’s divide 4228 by 7. This gives us 604. Now our equation is taking its final form: 89307 - 42240 + 604.

Step 4: Subtraction and Addition

Alright, folks, it's time for the final stretch! We have subtraction and addition left. Remember, we perform these operations from left to right. So, first, we subtract 42240 from 89307. This gives us 47067. Now our equation looks super simple: 47067 + 604.

Final Addition

Last but not least, we add 604 to 47067. When we add these together, we get 47671. And that, my friends, is our final answer!

The Final Answer

So, 89307-(2074*5+296800/80)*3+4228/7 equals 47671. Wasn't that fun? (Okay, maybe not fun for everyone, but definitely satisfying when you get the right answer!) Remember, the key is to take it one step at a time and follow the order of operations. You got this!

Breaking Down the Steps for Clarity

Let's recap the entire process in a more structured way, just to make sure we're all on the same page. Understanding each step clearly can help in tackling similar problems in the future.

Detailed Breakdown

  1. Solve Inside Parentheses: (2074 * 5 + 296800 / 80)
    • 2074 * 5 = 10370
    • 296800 / 80 = 3710
    • 10370 + 3710 = 14080
  2. Multiplication: 14080 * 3 = 42240
  3. Division: 4228 / 7 = 604
  4. Subtraction: 89307 - 42240 = 47067
  5. Addition: 47067 + 604 = 47671

So, the final, verified answer is 47671. High five!

Why Order of Operations Matters

You might be wondering, why all this fuss about PEMDAS? Well, imagine if we didn't follow a standard order. We could end up with completely different answers, which would be chaos in mathematics! Seriously, it would be like trying to build a house without a blueprint. PEMDAS ensures everyone gets to the same correct answer, making it a universal language for math.

Real-World Applications

And it’s not just for textbooks; order of operations pops up everywhere. Think about coding, for instance. When you write code, the computer follows a strict order of operations to execute your commands. If you mess up the order, your program won’t work correctly. Even in everyday calculations, like figuring out discounts at a store or calculating your expenses, PEMDAS is secretly working behind the scenes to make sure you get the right numbers.

Tips for Tackling Similar Problems

  • Write it Down: Don't try to do everything in your head. Writing each step down helps you keep track and reduces errors.
  • Double-Check: Always double-check your calculations. It's easy to make a small mistake, and catching it early can save you a lot of headaches.
  • Use a Calculator: Don't be afraid to use a calculator, especially for complex calculations. It's a tool, not a crutch.
  • Practice: The more you practice, the better you'll become at recognizing and applying the order of operations.
  • Stay Calm: Don't get overwhelmed. Break the problem down into smaller, manageable steps. Take a deep breath and tackle it one step at a time.

Conclusion

So, there you have it! Solving the equation 89307-(2074*5+296800/80)*3+4228/7 might have seemed daunting at first, but by breaking it down step by step and following the order of operations, we arrived at the answer: 47671. Remember to always follow PEMDAS/BODMAS, double-check your work, and don't be afraid to use tools like calculators. Keep practicing, and you'll become a math whiz in no time! You've totally got this, guys! Keep rocking those equations!