Calculate 8 + 2 × 5 - 3 ÷ 1: Order Of Operations

by Chloe Fitzgerald 49 views

Hey everyone! Let's break down this math problem together: 8 + 2 × 5 - 3 ÷ 1. It looks a bit complex at first, but don't worry, we'll tackle it step by step using the order of operations. You might have heard of it as PEMDAS or BODMAS, but it's essentially the same thing. This order tells us which operations to perform first to get the correct answer. So, let's dive in and make sure we get this right!

Understanding the Order of Operations (PEMDAS/BODMAS)

The order of operations is super important in math because it ensures we all get the same answer when solving a problem. Imagine if we didn't have an agreed-upon order – we'd have different people getting different results, which would be a total mess! The acronyms PEMDAS and BODMAS help us remember the correct sequence. Let's break it down:

  • Parentheses / Brackets: First up, we deal with anything inside parentheses or brackets. This is where we start to simplify the expression.
  • Exponents / Orders: Next, we tackle exponents or orders (like squares and cubes). These guys tell us to multiply a number by itself a certain number of times.
  • Multiplication and Division: After that, we handle multiplication and division. It's crucial to remember that we perform these operations from left to right. Whichever one comes first as we read the expression from left to right, that's the one we do first.
  • Addition and Subtraction: Finally, we take care of addition and subtraction. Just like multiplication and division, we work from left to right. The order in which they appear matters!

So, with PEMDAS/BODMAS in mind, we know exactly where to start and how to proceed with our problem. It's like having a roadmap for math – it keeps us on the right track and ensures we reach the correct destination. Ignoring this order can lead to some seriously wrong answers, so it's a fundamental concept to grasp. Understanding this order is like having a superpower in math; it enables you to solve all sorts of complex problems with confidence and accuracy. Think of it as the golden rule of arithmetic – follow it, and you'll ace your calculations every time!

Step-by-Step Solution: 8 + 2 × 5 - 3 ÷ 1

Alright, let's apply the order of operations to our problem: 8 + 2 × 5 - 3 ÷ 1. We'll take it one step at a time to make sure we don't miss anything. Remember, PEMDAS/BODMAS is our guide here.

  1. Multiplication and Division: According to the order, we tackle multiplication and division first, working from left to right. So, let's start with the multiplication: 2 × 5 = 10. Now our expression looks like this: 8 + 10 - 3 ÷ 1.
  2. Next up, we have a division: 3 ÷ 1 = 3. This simplifies our expression further to: 8 + 10 - 3.
  3. Addition and Subtraction: Now that we've handled the multiplication and division, we move on to addition and subtraction. Again, we work from left to right. First, let's do the addition: 8 + 10 = 18. Our expression is now super simple: 18 - 3.
  4. Finally, we perform the subtraction: 18 - 3 = 15. And there we have it! The result of the sequence of operations is 15.

So, as we worked through the problem step by step, it became clear how important the order of operations is. If we had jumped straight into adding 8 and 2, or subtracting 3 from 5, we would have ended up with a totally different answer. By following PEMDAS/BODMAS, we made sure each operation was performed in the correct sequence, leading us to the accurate result. This method not only solves the problem but also gives us confidence that we've done it right. It’s like following a recipe – if you stick to the instructions, you're much more likely to bake a perfect cake!

Identifying the Correct Answer

Now that we've gone through the step-by-step solution, we've found that the correct answer to the expression 8 + 2 × 5 - 3 ÷ 1 is 15. Let's quickly recap how we got there to reinforce our understanding.

We started with the original expression and remembered the golden rule of math: PEMDAS/BODMAS. This told us to prioritize multiplication and division before we even think about addition and subtraction. So, we first tackled 2 × 5, which gave us 10. Then, we handled the division: 3 ÷ 1, which resulted in 3. Our expression was now simplified to 8 + 10 - 3.

Next up were the addition and subtraction operations. Working from left to right, we added 8 + 10, getting 18. Finally, we subtracted 3 from 18, which left us with our final answer: 15. Each step was crucial, and by following the correct order, we ensured we arrived at the right solution.

Now, let's look at the options provided in the question:

  • A) 10
  • B) 12
  • C) 14
  • D) 16

None of these options match our calculated result of 15. This is a bit of a surprise, but it gives us a chance to double-check our work. Sometimes, even with careful calculations, it's good to review our steps. However, in this case, our step-by-step breakdown confirms that 15 is indeed the correct answer. It seems there might be a discrepancy in the provided options. It’s a great reminder that sometimes the correct answer isn't listed, and it's important to trust your calculations. Math isn’t just about picking an option; it’s about understanding the process and arriving at the right conclusion, even if it means the given choices aren't correct!

Why the Order of Operations Matters

You might be wondering, why all the fuss about the order of operations? Why can't we just solve the problem from left to right? Well, let's explore why this order is so crucial and what happens if we ignore it.

The order of operations ensures consistency in mathematical calculations. Without a standardized order, different people could interpret the same expression in different ways and arrive at different answers. Imagine the chaos in fields like engineering, finance, or even cooking if mathematical expressions weren't consistent! Structures could collapse, financial transactions could go haywire, and your favorite recipe might turn into a culinary disaster. The order of operations acts like a universal language for math, ensuring everyone is on the same page.

To illustrate this, let’s consider our original problem again: 8 + 2 × 5 - 3 ÷ 1. We know the correct answer is 15, but what if we ignored PEMDAS/BODMAS and solved it from left to right?

  1. First, we'd do 8 + 2, which equals 10.
  2. Then, we'd multiply 10 × 5, giving us 50.
  3. Next, we'd subtract 50 - 3, which is 47.
  4. Finally, we'd divide 47 ÷ 1, leaving us with 47.

Wow, we ended up with 47, which is vastly different from the correct answer of 15! This stark difference highlights the importance of adhering to the order of operations. Solving from left to right completely distorts the mathematical relationships within the expression.

By following PEMDAS/BODMAS, we respect the inherent structure of mathematical expressions. Multiplication and division have a higher precedence than addition and subtraction because they represent repeated addition and subtraction, respectively. Think of multiplication as a shortcut for adding the same number multiple times, and division as a shortcut for subtracting the same number multiple times. This is why we tackle them first – they simplify the expression more efficiently.

In essence, the order of operations is not just a set of rules; it's a fundamental principle that underpins mathematical logic. It ensures accuracy, consistency, and clarity in all sorts of calculations. So, next time you're faced with a mathematical expression, remember PEMDAS/BODMAS, and you'll be well on your way to solving it correctly!

Conclusion: Mastering the Order of Operations

So, guys, we've journeyed through a math problem together, and hopefully, you've gained a solid understanding of why the order of operations is so vital. We started with the expression 8 + 2 × 5 - 3 ÷ 1, and by carefully following PEMDAS/BODMAS, we arrived at the correct answer. Remember, this order – Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction – is our roadmap for solving mathematical expressions accurately.

We broke down each step, starting with multiplication and division, moving from left to right. Then, we tackled addition and subtraction, again moving from left to right. This methodical approach not only helped us find the solution but also reinforced the logic behind the order of operations. We saw how crucial it is to prioritize multiplication and division before jumping into addition and subtraction.

In our specific problem, we found that the answer is 15. However, the options provided in the question didn't include 15, which gave us an excellent opportunity to double-check our work and trust our calculations. This is a valuable lesson in itself – math is about understanding the process and arriving at the correct conclusion, even if it means the provided choices aren't accurate.

We also explored what happens if we ignore the order of operations. By solving the problem from left to right, we ended up with a completely different answer, highlighting the importance of consistency and the inherent structure of mathematical expressions. Without a standardized order, math could become a chaotic and unreliable tool.

Mastering the order of operations is more than just memorizing PEMDAS/BODMAS; it's about understanding the underlying mathematical principles. It's about recognizing the relationships between different operations and the impact they have on the outcome. Once you grasp this concept, you'll be able to tackle a wide range of mathematical problems with confidence and precision. So keep practicing, keep applying the order of operations, and you'll become a math whiz in no time! Remember, every math problem is a puzzle waiting to be solved, and with the right tools and understanding, you can crack any code.