Solving 12 + (50 ÷ 2 + 5 × 6 + 3 - 16) + 7 + 5: A Math Problem

Hey guys! Let's dive into a fun math problem today. We're going to break down and solve the expression: 12 + (50 ÷ 2 + 5 × 6 + 3 - 16) + 7 + 5. This looks like a mouthful, but don't worry, we'll take it step by step. Math might seem intimidating at first, but when we approach it methodically, it becomes a fascinating puzzle to solve. Think of it as a journey where each step brings us closer to the final answer. We'll be using the order of operations, also known as PEMDAS or BODMAS, to ensure we get the correct result. This means we'll handle parentheses first, then exponents (which we don't have here), followed by multiplication and division (from left to right), and finally, addition and subtraction (also from left to right). So, buckle up, grab your calculators (or not, if you're feeling brave!), and let's get started!

Our journey begins with understanding why such expressions matter. In the real world, complex calculations are everywhere, from budgeting your finances to engineering structures. Mastering the order of operations is not just about getting the right answer on a test; it's about building a foundational skill that applies to many aspects of life. When you can break down a complex problem into smaller, manageable parts, you develop critical thinking skills that are invaluable in any field. And let's be honest, there's a certain satisfaction that comes from conquering a challenging math problem. It's like climbing a mountain and reaching the summit – you feel a sense of accomplishment and pride. So, let's climb this mathematical mountain together and see what awaits us at the top!

Step 1: Tackling the Parentheses

The heart of our problem lies within the parentheses: (50 ÷ 2 + 5 × 6 + 3 - 16). Remember PEMDAS/BODMAS? We've got to tackle the operations inside in the correct order. This means we first look for any parentheses, which we've already identified. Inside the parentheses, we need to prioritize multiplication and division before we do addition and subtraction. It’s like a mathematical hierarchy, where certain operations take precedence over others. If we were to ignore this order, we would end up with the wrong answer, kind of like building a house without a solid foundation – it might look good at first, but it won't stand the test of time. So, let's make sure our mathematical house is built on a strong foundation by following the correct order of operations.

First, we spot the division: 50 ÷ 2. This is pretty straightforward, guys. 50 divided by 2 equals 25. So, we can replace 50 ÷ 2 with 25 in our expression within the parentheses. This simplifies things a bit, and we're making progress already! Next up, we've got a multiplication operation. Identifying these individual operations and performing them one by one helps to prevent errors and keeps the process manageable. It's like breaking a large task into smaller, more achievable goals – it makes the overall task seem less daunting and more approachable. So, let's keep breaking down this problem and conquer it one operation at a time.

Step 2: Multiplication Magic

Now, let's handle the multiplication: 5 × 6. This is another easy one, right? 5 multiplied by 6 gives us 30. So, we can replace 5 × 6 with 30 in our expression. See how we're slowly chipping away at the problem? Each step brings us closer to the solution, and by focusing on one operation at a time, we avoid getting overwhelmed by the complexity of the expression. Think of it like painting a picture – you don't try to paint the whole thing at once; you work on different sections, adding details and colors until the entire masterpiece comes to life. In the same way, we're adding and subtracting values in our expression until we reveal the final answer.

Our expression inside the parentheses now looks like this: (25 + 30 + 3 - 16). We've successfully taken care of the division and multiplication, and we're left with only addition and subtraction. This makes things much simpler, and we're in the home stretch for solving the parentheses! Remember, it's important to take your time and double-check your work along the way. Even a small mistake can throw off the entire calculation, so it's better to be meticulous and ensure accuracy. Now, let's move on to the next step and tackle the addition and subtraction operations.

Step 3: Addition and Subtraction Tango

With only addition and subtraction left inside the parentheses, we work from left to right. This is a crucial rule to remember, guys! It might seem arbitrary, but the order in which we perform these operations can affect the outcome. It's like reading a sentence – we read from left to right to understand the meaning, and in math, we follow a similar convention to ensure consistency and accuracy. So, let's stick to the rule and perform the operations in the correct order.

First up, we have 25 + 30, which equals 55. Now our expression looks like this: (55 + 3 - 16). We've combined the first two numbers, and we're making good progress. Next, we add 3 to 55, giving us 58. The expression is now (58 - 16). We're almost there! Finally, we subtract 16 from 58, which leaves us with 42. So, the value inside the parentheses is 42. We've conquered the parentheses! This was the most challenging part of the problem, and we did it by breaking it down into smaller steps and following the order of operations. Now, we can substitute 42 back into the original expression and simplify it further.

Step 4: The Grand Finale

Now that we've solved the parentheses, our original expression 12 + (50 ÷ 2 + 5 × 6 + 3 - 16) + 7 + 5 simplifies to 12 + 42 + 7 + 5. See how much simpler it looks now? We've eliminated the parentheses and all the complex operations within them, and we're left with a straightforward addition problem. This is a testament to the power of breaking down complex problems into smaller, more manageable parts. It's like decluttering a room – you don't try to do everything at once; you focus on one area at a time, and before you know it, the entire room is sparkling clean. In the same way, we've decluttered our mathematical expression and made it much easier to solve.

Now, we just need to add these numbers together. Let's do it from left to right: 12 + 42 = 54. Then, 54 + 7 = 61. And finally, 61 + 5 = 66. So, the final answer is 66! We did it, guys! We successfully solved the complex mathematical expression by following the order of operations and breaking the problem down into smaller, more manageable steps. Give yourselves a pat on the back – you've earned it!

Conclusion: Math Mastery Achieved!

So, there you have it! The solution to 12 + (50 ÷ 2 + 5 × 6 + 3 - 16) + 7 + 5 is 66. This exercise wasn't just about finding the right answer; it was about understanding the process, the order of operations, and how to approach complex problems. Remember, math is like a language, and the more you practice, the more fluent you become. By breaking down complex expressions into smaller, manageable steps, anyone can conquer even the most daunting mathematical challenges. It's all about building confidence and developing a systematic approach.

Whether you're tackling algebraic equations, geometric proofs, or everyday calculations, the principles we've discussed today will serve you well. So, keep practicing, keep exploring, and never be afraid to ask questions. Math is a journey, not a destination, and the more you embrace the challenge, the more rewarding it becomes. And who knows, maybe you'll even start to enjoy it! So, until next time, keep those numbers crunching and those brains buzzing!