How To Solve 2 * {350 * [491 - 3 * (125 - 78)] + 350} A Step-by-Step Guide
Hey guys! Today, we're diving into a seemingly complex mathematical expression and breaking it down step-by-step so you can conquer it with confidence. We'll be tackling this beast: 2 * {350 * [491 - 3 * (125 - 78)] + 350}. Don't worry, it's not as scary as it looks! We'll use the order of operations (PEMDAS/BODMAS) to guide us. So, grab your calculators and let's get started!
Understanding the Order of Operations (PEMDAS/BODMAS)
Before we jump into the problem, let's quickly recap the order of operations. This is the golden rule that dictates the sequence in which we perform mathematical operations:
- Parentheses / Brackets
- Exponents / Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Think of it as a roadmap for solving mathematical expressions. If you follow this order, you'll arrive at the correct answer every time. Ignoring PEMDAS can lead to some seriously wonky results, so it’s super important to keep this in mind. Imagine trying to build a house without a blueprint – that’s what solving math problems without the order of operations is like! You might end up with a mathematical mess, and nobody wants that. We want clean, precise solutions, and PEMDAS is our best friend in achieving that.
This order ensures that everyone solving the same problem arrives at the same answer. It's like a universal mathematical language that helps us communicate results clearly and effectively. So, whether you're a student tackling homework or a professional working on complex calculations, remember PEMDAS/BODMAS – it's the key to mathematical success. Let’s keep this in our mental toolkit as we move forward and break down our complex expression. Now, let's get back to our main problem and see how we can apply these rules to make it much more manageable. Remember, breaking down a large problem into smaller, digestible steps is a fantastic strategy for problem-solving in general, not just in math!
Step 1: Solving the Innermost Parentheses (125 - 78)
Our first mission is to tackle the innermost parentheses: (125 - 78). This is a simple subtraction problem. So, let's do the math:
125 - 78 = 47
Great! We've simplified the expression inside the parentheses to 47. Now, let's replace the parentheses with this value in our original expression. Our expression now looks like this:
2 * {350 * [491 - 3 * 47] + 350}
See? We're already making progress. It's like peeling an onion – we're taking it one layer at a time. This is a crucial step because it helps to simplify the problem and make it less intimidating. By focusing on the smallest, most manageable part first, we can gradually work our way towards the final solution. It's all about breaking down the complexity into smaller, more digestible chunks. This approach is not only effective in mathematics but also in many other areas of life. When faced with a daunting task, remember the power of breaking it down into smaller, more manageable steps. You'll be surprised at how much you can accomplish! So, let's keep this momentum going and move on to the next set of operations in our expression.
Step 2: Multiplication within the Brackets (3 * 47)
Next up, we need to deal with the multiplication within the brackets: 3 * 47. Let's multiply these numbers:
3 * 47 = 141
Now we substitute this result back into the expression. Our expression now transforms to:
2 * {350 * [491 - 141] + 350}
We're getting closer to simplifying this whole thing! Notice how each step makes the expression a little less daunting. It’s like slowly untangling a knot – with each loop you loosen, the rest becomes easier to handle. This is a perfect illustration of how following the order of operations can make even the most complex-looking problems manageable. By focusing on one operation at a time, we avoid getting overwhelmed and ensure accuracy. This step also highlights the importance of careful calculation. A small error in multiplication here could throw off the entire result, so it’s crucial to double-check our work. Let's keep this focus as we move on to the next operation within the brackets. Remember, precision is key in mathematics, and each step we take brings us closer to the final, correct answer.
Step 3: Subtraction within the Brackets [491 - 141]
Now, we tackle the subtraction inside the brackets: [491 - 141]. Let's subtract:
491 - 141 = 350
We replace the brackets with the result:
2 * {350 * 350 + 350}
The expression is becoming much simpler, isn't it? We've successfully navigated the parentheses and brackets, and now we're left with a much cleaner expression to work with. This step really showcases the power of working from the inside out. By focusing on the innermost operations first, we gradually reduce the complexity of the problem. It’s like chiseling away at a block of stone to reveal the sculpture within. Each operation we perform brings us closer to the final form, the solution we're seeking. This is also a good point to pause and appreciate how far we've come. We started with a long, intimidating expression, and now we're down to something much more manageable. This can be a great morale booster when tackling challenging problems – recognizing your progress can keep you motivated and focused. So, let's keep that momentum going as we move on to the next set of operations!
Step 4: Multiplication within the Curly Braces {350 * 350}
Inside the curly braces, we first perform the multiplication: 350 * 350.
350 * 350 = 122,500
Substitute the result back into the expression:
2 * {122,500 + 350}
Wow, that's a big number! But don't let it intimidate you. We're still following the same rules, step by step, and that's what matters. This step is a great reminder that even in complex problems, each individual operation is usually quite straightforward. It’s the combination of operations that can make things seem daunting, but by breaking it down, we can handle it. This multiplication also highlights the importance of having a good grasp of basic arithmetic. While calculators are helpful, understanding the underlying principles of multiplication allows us to estimate and check our results, ensuring accuracy. So, let's keep this in mind as we move on to the next operation within the curly braces. We're on the home stretch now, and the final solution is within our grasp! Let’s keep going with the same methodical approach that has brought us this far.
Step 5: Addition within the Curly Braces {122,500 + 350}
Now, let's add the numbers inside the curly braces: 122,500 + 350.
122,500 + 350 = 122,850
Replace the curly braces with the sum:
2 * 122,850
We're almost there! The expression has been simplified beautifully. We've conquered the parentheses, brackets, and curly braces, and now we're left with a single multiplication. This is a testament to the power of the order of operations and the effectiveness of our step-by-step approach. This addition step, while seemingly simple, is crucial for accuracy. It's easy to make a small mistake when adding large numbers, so it's always a good idea to double-check your work. This also highlights the importance of neatness and organization in mathematical problem-solving. By keeping our calculations clear and easy to read, we reduce the chances of making errors. So, let's take a deep breath, double-check our addition, and move on to the final step. We're just one multiplication away from solving this complex expression!
Step 6: Final Multiplication 2 * 122,850
Finally, we perform the last multiplication: 2 * 122,850.
2 * 122,850 = 245,700
The Solution
Therefore, the solution to the mathematical expression 2 * {350 * [491 - 3 * (125 - 78)] + 350} is 245,700.
Congratulations! We've successfully navigated a complex mathematical expression by breaking it down into manageable steps and following the order of operations. You did it! Give yourself a pat on the back. This final multiplication brings us to the end of our journey, and it's a satisfying moment to see the solution so clearly. This step underscores the importance of precision and accuracy in the final stages of problem-solving. A small error here would negate all the hard work we've put in so far. So, it’s crucial to approach the final step with the same focus and attention to detail that we've maintained throughout the process. And there you have it – the final answer, 245,700. This is a testament to the power of systematic problem-solving and the importance of following the order of operations. We’ve taken a seemingly daunting expression and broken it down into simple, manageable steps, ultimately arriving at the correct solution. This is a valuable skill that can be applied not only in mathematics but in many other areas of life. So, the next time you encounter a complex problem, remember this step-by-step approach, and you'll be well on your way to success. Well done, everyone!
Key Takeaways
- PEMDAS/BODMAS is your friend: Always follow the order of operations. It's the golden rule for solving mathematical expressions.
- Break it down: Complex expressions become much easier when you tackle them step-by-step.
- Double-check your work: A small error can throw off the entire result. So, take the time to verify each step.
So, there you have it! We've successfully solved a complex mathematical expression. Remember these steps, and you'll be a math whiz in no time! Keep practicing, keep exploring, and most importantly, keep enjoying the world of mathematics!
