Solving $5(15+10)+50$: A Step-by-Step Guide

Hey guys! Today, we're diving into a fun little math problem: figuring out the value of the expression $5(15+10)+50$. Don't worry, it's not as intimidating as it looks! We'll break it down step by step so you can see exactly how it's done. Let's get started!

Understanding the Order of Operations

Before we jump into the calculation, it's super important to remember the order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Basically, it tells us the sequence in which we need to perform the operations to get the correct answer. So, first, we tackle anything inside parentheses, then exponents, then multiplication and division (from left to right), and finally, addition and subtraction (also from left to right).

Understanding PEMDAS/BODMAS is crucial because it ensures we solve mathematical expressions in the correct order, leading to accurate results. Without this standardized order, the same expression could yield different answers depending on the sequence of operations performed. For instance, in our expression $5(15+10)+50$, if we were to add 50 to 5 before dealing with the parentheses, we would end up with a completely wrong answer. Therefore, following PEMDAS/BODMAS is not just a rule, but a fundamental principle in mathematics that maintains consistency and clarity in calculations. The beauty of math lies in its precision, and adhering to the order of operations is a key part of that. It's like following a recipe – you need to add the ingredients in the right order to bake a perfect cake! So, let's keep this in mind as we proceed. Remember, it might seem a bit rigid at first, but with practice, it becomes second nature. And trust me, mastering the order of operations opens doors to solving more complex and fascinating mathematical problems. So, let's embrace PEMDAS/BODMAS as our trusty guide in this mathematical journey!

Step 1: Parentheses First

Okay, let's look at our expression again: $5(15+10)+50$. According to PEMDAS/BODMAS, we need to deal with the parentheses first. Inside the parentheses, we have $15 + 10$. This is a simple addition, so let's do it: $15 + 10 = 25$. Now our expression looks like this: $5(25) + 50$.

Parentheses are like VIP sections in the world of mathematical expressions. They demand our immediate attention! Inside these brackets, the operations take precedence, meaning we must resolve them before anything else. Think of it as a mini-equation nestled within the larger expression. In our case, $15 + 10$ is the content of this VIP section. We diligently add these two numbers together, and just like that, we've simplified the expression inside the parentheses to a neat and tidy 25. This step is not just about getting rid of the parentheses; it's about simplifying the expression, making it easier to handle in the subsequent steps. It's like decluttering a room before you start decorating – it gives you a clear space to work with. By tackling the parentheses first, we've laid the foundation for the rest of the calculation. It's a crucial step that sets us on the right path to solving the entire expression. So, remember, when you see parentheses, salute them and solve what's inside first! It’s a small step, but a mighty one in the grand scheme of mathematical problem-solving.

Step 2: Multiplication

Great! We've handled the parentheses. Now our expression is $5(25) + 50$. Next up in PEMDAS/BODMAS is multiplication and division. In this case, we have multiplication: $5(25)$. Remember, when a number is right next to parentheses like this, it means we need to multiply. So, $5$ multiplied by $25$ is $125$. Now our expression looks even simpler: $125 + 50$.

Multiplication is the engine that drives our mathematical journey forward. In the expression $5(25) + 50$, the multiplication operation $5(25)$ is a crucial step that simplifies the expression and brings us closer to the final answer. When we see a number nestled right next to parentheses, it's a signal that multiplication is on the horizon. It's like a secret handshake in the language of math! So, we diligently multiply 5 by 25, and the result is a crisp and clear 125. This multiplication step is more than just a calculation; it's a transformation. We're converting the product of two numbers into a single, manageable value. It's like converting raw ingredients into a delicious dish. The expression is becoming more refined, more streamlined. We're shedding layers of complexity and getting closer to the core. So, let's embrace multiplication as a powerful tool in our mathematical toolkit. It allows us to combine quantities, scale values, and ultimately, unlock the solutions to our problems. With each multiplication, we're not just crunching numbers; we're building a bridge to understanding. It’s the bridge between the parts and the whole.

Step 3: Addition

We're almost there! We've simplified our expression to $125 + 50$. The final step, according to PEMDAS/BODMAS, is addition and subtraction. Here, we just have addition. So, we add $125$ and $50$, which gives us $175$.

Addition, the final flourish in our mathematical masterpiece, brings everything together. We've navigated through parentheses, conquered multiplication, and now we arrive at the grand finale: combining the fruits of our labor. In the expression $125 + 50$, addition is the harmonious blending of two quantities into one cohesive whole. It's like the final brushstroke on a painting, the last note in a symphony. We carefully add 125 and 50, and the result is a resounding 175. This addition step is more than just summing numbers; it's synthesizing the results of previous operations. It's the culmination of our efforts, the moment where all the pieces come together to form the answer. We've taken individual components and woven them into a unified solution. So, let's celebrate addition as the grand unifier in the world of mathematics. It allows us to combine values, aggregate results, and ultimately, arrive at the final destination. With each addition, we're not just crunching numbers; we're creating a tapestry of understanding. It’s the tapestry that reveals the complete picture.

The Final Answer

And that's it! The value of the expression $5(15+10)+50$ is $175$. So, the correct answer is D. 175.

The final answer, 175, is the triumphant culmination of our mathematical journey. We've traversed through the expression $5(15+10)+50$, navigating the order of operations with precision and care. We've conquered parentheses, mastered multiplication, and harmonized addition, all to arrive at this singular value. It's like reaching the summit of a mountain after a challenging climb. The final answer is more than just a number; it's a testament to our problem-solving skills, our understanding of mathematical principles, and our perseverance in the face of complexity. It's the reward for our diligent efforts, the sweet taste of success. We've transformed a complex expression into a concise and meaningful result. So, let's embrace the final answer as the embodiment of our mathematical prowess. It represents clarity, accuracy, and the power of logical reasoning. With each final answer, we're not just solving a problem; we're expanding our understanding of the world around us. It’s a testament to the power of numbers to unlock understanding.

Practice Makes Perfect

Remember, the key to mastering these types of problems is practice! The more you work through them, the more comfortable you'll become with the order of operations and the different steps involved. So, keep practicing, and you'll be a math whiz in no time!

Practice, the secret ingredient to mathematical mastery, is the compass that guides us on our journey to understanding. Just like any skill, mathematics flourishes with consistent effort and dedication. The more we engage with mathematical problems, the more we hone our problem-solving abilities and deepen our comprehension of fundamental concepts. It's like learning a new language – the more we practice speaking, reading, and writing, the more fluent we become. Practice allows us to internalize the rules and principles, transforming them from abstract concepts into intuitive tools. It's the forge where we shape our mathematical minds, strengthening our logical reasoning and analytical thinking. With each problem we tackle, we're not just finding an answer; we're building confidence, resilience, and a growth mindset. So, let's embrace practice as the cornerstone of our mathematical education. It's the key that unlocks the doors to deeper understanding, greater proficiency, and a lifelong love of learning. It’s the compass that guides us to mathematical fluency.