Solving The Equation [(8×7)-16]÷8]+[{(4×3)-4}×5]-27 A Step-by-Step Guide

Hey guys! Today, we're diving deep into a fascinating mathematical expression: [(8×7)-16]÷8]+[{(4×3)-4}×5]-27. This might look intimidating at first glance, but don't worry, we'll break it down step by step and solve it together. Think of it as a puzzle – each operation is a piece, and we're going to fit them all together to reveal the final answer. So, grab your thinking caps, and let's embark on this mathematical adventure!

Decoding the Order of Operations: PEMDAS/BODMAS

Before we even begin crunching numbers, it's crucial that we understand the order of operations. This is the golden rule of mathematics that tells us which operations to perform first. You might have heard of the acronyms PEMDAS or BODMAS, which stand for:

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

Think of it like a traffic light for math – it guides us on the correct path. Ignoring this order can lead to some seriously wrong answers, and we definitely don't want that! So, with PEMDAS/BODMAS as our trusty guide, let's tackle the expression at hand. Our main keyword here is order of operations, and it's the backbone of solving any mathematical problem correctly. Without understanding this fundamental principle, we'd be wandering in a maze of numbers without a map. Remember, parentheses (or brackets) are our first priority. They're like little VIP sections in the expression, telling us, "Hey, solve me first!" Then come exponents, which are basically shorthand for repeated multiplication. After that, multiplication and division share the same level of importance, so we work our way from left to right. The same goes for addition and subtraction – left to right is the way to go. By adhering to this order, we ensure that we're unraveling the expression in a logical and consistent manner, paving the way for an accurate solution. It's like following a recipe – skip a step, and the final dish might not turn out as expected! So, let's keep PEMDAS/BODMAS firmly in mind as we move forward, and watch how it simplifies even the most complex-looking equations.

Unpacking the First Set of Brackets: (8×7)-16

Okay, let's zoom in on the first set of brackets: (8×7)-16. According to PEMDAS/BODMAS, we need to deal with what's inside the parentheses first. Inside, we have multiplication and subtraction. Multiplication takes precedence, so we start by multiplying 8 and 7. 8 multiplied by 7 equals 56. Now we have 56 - 16. This is a straightforward subtraction. 56 minus 16 equals 40. So, the first part simplifies to 40. See? Not so scary when we break it down! This initial step highlights the power of prioritizing operations. By focusing on the multiplication within the parentheses, we've effectively reduced the complexity of the expression. It's like decluttering a room – once you tackle the biggest pile of mess, everything else seems more manageable. The result, 40, becomes a crucial stepping stone in our journey towards the final answer. It's a testament to the importance of methodical problem-solving, where each step builds upon the previous one. We've successfully navigated the first hurdle, and with the same approach, we'll conquer the rest of the expression. Think of it as a mathematical relay race – we've completed the first leg, and now we're ready to pass the baton to the next stage. The clarity and precision we've employed in this initial calculation will serve as a foundation for the subsequent steps, ensuring that we maintain accuracy throughout the process. So, let's carry this momentum forward and continue our mathematical exploration with confidence!

Division Time: 40 ÷ 8

Now that we've simplified the first set of brackets to 40, we can move on to the next operation: dividing this result by 8. So, we have 40 ÷ 8. This is a basic division problem. How many times does 8 go into 40? The answer is 5. Simple as that! We've successfully tackled the division part of the expression. This step demonstrates how each individual operation contributes to the overall solution. The division is like a bridge, connecting the result from the first set of brackets to the rest of the expression. It's a critical link in the chain, ensuring that the different parts of the equation interact correctly. The simplicity of this step might be deceptive, but it underscores the importance of mastering fundamental arithmetic operations. Division is not just about splitting numbers; it's about understanding the relationship between them. In this case, it reveals how the simplified value from the first set of brackets is proportionally related to the divisor, 8. The result, 5, is a key ingredient that will combine with other values later in the expression. It's a reminder that even the most complex problems are built upon simple foundations. So, let's appreciate the elegance of this division and move on with a clear understanding of its role in the bigger picture. We're steadily progressing towards our final destination, and each step we take reinforces our confidence in our ability to solve this mathematical puzzle.

Cracking the Second Set of Brackets: {(4×3)-4}

Alright, let's shift our focus to the second set of brackets: {(4×3)-4}. Again, we start with what's inside the brackets. We have multiplication and subtraction here. Following PEMDAS/BODMAS, we do the multiplication first. 4 multiplied by 3 is 12. So now we have 12 - 4. Subtracting 4 from 12 gives us 8. This set of brackets simplifies to 8. Excellent work, guys! This segment reinforces the pattern of breaking down complex expressions into smaller, more manageable chunks. The nested brackets might appear daunting initially, but by consistently applying the order of operations, we can systematically unravel them. The multiplication within the brackets serves as the initial catalyst, transforming the numbers into a new form. The subsequent subtraction then refines this value, leading us to the simplified result of 8. This process highlights the dynamic interplay between different mathematical operations. It's not just about performing calculations in isolation; it's about understanding how they interact and influence each other. The number 8, emerging from this set of brackets, carries the weight of these combined operations. It's a testament to the power of mathematical transformations, where initial values are reshaped and refined through a series of steps. So, let's appreciate the elegance of this process and recognize how it contributes to the overall solution. We're steadily building our mathematical narrative, and each step brings us closer to the final resolution.

Multiplication Revisited: 8 × 5

With the second set of brackets simplified to 8, we now have to multiply this result by 5. So, we have 8 × 5. This is another straightforward multiplication. 8 multiplied by 5 is 40. We're on a roll! This step demonstrates the recurring nature of multiplication in mathematical expressions. It's not just a one-time event; it often appears multiple times, linking different parts of the equation. In this case, the multiplication acts as a bridge, connecting the simplified value from the second set of brackets to the next stage of the calculation. The result, 40, is a testament to the power of multiplicative relationships. It reveals how the value 8, derived from the previous steps, is scaled up by a factor of 5. This scaling effect is a fundamental aspect of multiplication, and it plays a crucial role in many mathematical and real-world scenarios. The simplicity of this step might belie its importance, but it underscores the interconnectedness of mathematical operations. Each multiplication, each addition, each subtraction – they all contribute to the overall tapestry of the solution. So, let's appreciate the elegance of this multiplication and move on with a clear understanding of its role in the bigger picture. We're steadily building our mathematical narrative, and each step we take reinforces our confidence in our ability to solve this puzzle.

Putting it Together: 5 + 40

Now it's time to combine the results we've obtained so far. We have 5 from the first part of the expression and 40 from the second part. We need to add these together: 5 + 40. This is a simple addition problem. 5 plus 40 equals 45. We're getting closer to the finish line! This addition step serves as a crucial synthesis point in our mathematical journey. It's where the results from the different segments of the expression converge, creating a unified value. The act of addition is not just about combining numbers; it's about creating a whole from its parts. In this case, the values 5 and 40, each derived from distinct sets of operations, come together to form the sum of 45. This unified value represents the combined effect of the calculations we've performed thus far. It's a milestone in our problem-solving process, indicating that we're well on our way to the final answer. The simplicity of this addition might be deceptive, but it underscores the importance of synthesis in mathematics. It's about bringing together disparate elements and forging them into a cohesive whole. So, let's appreciate the significance of this addition and move on with a clear understanding of its role in the overall solution. We're steadily progressing towards our final destination, and each step we take reinforces our confidence in our ability to solve this mathematical puzzle.

The Final Subtraction: 45 - 27

We're almost there! The last step is to subtract 27 from our current result, 45. So we have 45 - 27. This is our final subtraction. 45 minus 27 equals 18. And there we have it! The answer to the expression [(8×7)-16]÷8]+[{(4×3)-4}×5]-27 is 18. Congratulations, guys, we did it! This final subtraction marks the culmination of our mathematical journey. It's the last piece of the puzzle, completing the transformation from the initial complex expression to a single, concise answer. The act of subtraction is not just about taking away; it's about determining the difference between two values. In this case, it reveals the net result of all the preceding operations, taking into account both additions and subtractions. The final answer, 18, is a testament to the power of methodical problem-solving. It represents the culmination of a series of steps, each carefully executed according to the order of operations. This journey underscores the importance of precision and attention to detail in mathematics. A single error along the way could have led to a different result. But by adhering to the principles of PEMDAS/BODMAS and by carefully performing each operation, we've arrived at the correct solution. So, let's celebrate this achievement and recognize the value of perseverance and logical thinking. We've not only solved a mathematical problem; we've also honed our problem-solving skills, which will serve us well in many other areas of life.

Conclusion: The Sweet Taste of Mathematical Victory

Wow, what a ride! We've successfully navigated the complex expression [(8×7)-16]÷8]+[{(4×3)-4}×5]-27 and arrived at the answer: 18. Remember, the key is to break down complex problems into smaller, more manageable steps and to follow the order of operations (PEMDAS/BODMAS). With a little practice, you can conquer any mathematical challenge! So, keep those brains buzzing, guys, and happy calculating! This mathematical journey has been a testament to the power of structured problem-solving. By systematically applying the order of operations, we've transformed a seemingly complex expression into a clear and concise solution. The journey itself is as important as the destination. Each step we've taken has reinforced our understanding of mathematical principles and honed our problem-solving skills. We've learned to appreciate the elegance of mathematical transformations, where numbers and operations interact to reveal hidden relationships. The final answer, 18, is not just a number; it's a symbol of our accomplishment. It represents the culmination of our efforts, the reward for our perseverance, and the validation of our logical thinking. So, let's carry this sense of achievement with us as we face new challenges. Let's remember that even the most daunting problems can be solved if we break them down into smaller steps and approach them with a clear and methodical mindset. And most importantly, let's continue to explore the fascinating world of mathematics with curiosity and enthusiasm, for there's always something new to discover and learn.