Solving The Math Problem: 5 X (3 + 2 X 4)

Hey everyone! Today, we're diving into a cool little math problem: 5 x (3 + 2 x 4). Don't worry, it's not as scary as it looks! We'll break it down step-by-step, making sure it's super easy to follow. This problem is a classic example of how important it is to remember the order of operations, sometimes remembered by the acronym PEMDAS or BODMAS. So, grab your pencils (or your calculators, no judgment here!), and let's get started. We'll go through each part methodically, ensuring you understand not just how to solve it, but why we do it in that particular order. This will help you tackle similar problems with confidence. It is a fantastic way to sharpen your math skills. Remember, the key to solving this lies in following the correct sequence and keeping track of each operation.

First, let's talk about the order of operations. In math, there's a specific order we need to follow to make sure we get the right answer. It's like a recipe; if you mix the ingredients in the wrong order, you won't get the desired result. The standard order is often remembered using acronyms like PEMDAS or BODMAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is similar, standing for Brackets, Orders (powers/indices), Division and Multiplication, and Addition and Subtraction. Essentially, both acronyms are just handy ways to remember the order of which we should approach a math problem. The crucial thing is to stick to this order consistently.

In our problem, 5 x (3 + 2 x 4), the parentheses are our first priority. Inside the parentheses, we see two operations: addition and multiplication. According to PEMDAS/BODMAS, multiplication comes before addition. Therefore, we first calculate 2 x 4, which equals 8. Next, we replace the 2 x 4 within the parentheses with its answer, turning the equation into 5 x (3 + 8). Next, we resolve what's inside the parentheses. Now we have a simple addition problem. Finally, we perform the addition operation within the parentheses: 3 + 8 = 11. Now our equation is 5 x 11. This completes our work within the parentheses, we get 5 x 11. Next, we move onto the multiplication. Multiply 5 by 11 to solve the problem. The final step is to perform the multiplication: 5 x 11 = 55. This gives us our final answer, which is 55. See? Not too tough, right? Let's break it down in more detail in the next sections.

Decoding the Parentheses: The First Step

Alright, let's get down to the nitty-gritty and tackle the problem step-by-step. Remember, our goal is to solve 5 x (3 + 2 x 4). The first thing we need to address are the parentheses. It's like the VIP section of the equation; we need to sort things out there before we can move on. Inside the parentheses, we have (3 + 2 x 4). Within this, we see addition and multiplication. According to PEMDAS/BODMAS, we need to do the multiplication before the addition. So, we start by calculating 2 x 4, which gives us 8. You'll now replace the "2 x 4" with "8", inside the parentheses, resulting in (3 + 8). This is a much simpler problem now, isn't it? We've successfully isolated the multiplication and solved it.

Now, inside the parentheses, we are left with a simple addition problem: 3 + 8. This step highlights the importance of working from left to right when resolving operations of the same precedence, like multiplication and division, or addition and subtraction. Performing the addition, we get 11. Now, our expression inside the parentheses simplifies to 11. The parentheses essentially acted as a container to prioritize that internal operation. That leaves us with the equation 5 x 11. Remember, this is why the order of operations is crucial! Without it, you might have tried to add 5 and 3 first, and you would have ended up with a completely different (and wrong) answer.

So, to recap, the first step is always to deal with what's inside those parentheses, keeping the order of operations in mind. Always tackle the multiplication and division first, from left to right, then the addition and subtraction, from left to right. Now that we have worked out what's inside the parentheses, let's move on to the next step!

Conquering the Multiplication: The Final Stage

Now that we've expertly navigated the parentheses, we're ready for the final act: the multiplication. Remember our equation after simplifying the parentheses? It's 5 x 11. This is the last operation we need to perform to find the solution. Multiplication is a fundamental operation in math, and in this case, it's pretty straightforward. We're simply multiplying 5 by 11. This means adding 11 to itself five times (or, if you prefer, adding 5 to itself eleven times). Performing the multiplication, we have: 5 x 11 = 55. And there you have it! We've successfully solved the equation 5 x (3 + 2 x 4), and the answer is 55. This is the final answer to our initial question. It demonstrates how, by carefully following the order of operations, we can solve complex-looking problems.

Congratulations, you have now mastered a basic mathematical problem involving multiple operations. The answer, 55, is the result of applying the correct order of operations – first dealing with the parentheses by prioritizing multiplication, and then performing the final multiplication. This methodical approach ensures that we arrive at the correct answer every time. This problem highlights how a systematic approach and understanding of fundamental math concepts can help you solve problems. Keep practicing, and you'll find that these kinds of calculations become second nature! The whole process is much easier when broken down into manageable steps. Keep practicing. This is important for developing confidence in your math abilities.

Why Order of Operations Matters

Understanding the order of operations (PEMDAS/BODMAS) is crucial in mathematics. It ensures consistency and accuracy in solving mathematical expressions. Without a standardized order, the same equation could yield multiple answers, leading to confusion and incorrect results. Think of it like this: if everyone followed different rules for how to solve an equation, communication and collaboration in mathematics would be impossible. So, why is this important? Because it establishes a clear set of rules that everyone can agree on. This leads to consistency and accuracy in our calculations.

The order of operations isn't just an arbitrary set of rules; it reflects the fundamental structure of mathematical operations. For instance, multiplication and division are performed before addition and subtraction because they represent repeated addition and subtraction, respectively. Parentheses are used to group operations that need to be prioritized. They act as a way to override the standard order, telling us