Solve It! Math Problem: $8 + 9 imes 3$

Hey math whizzes! Let's dive into a classic math problem that tests your understanding of the order of operations. We're talking about the expression: $8 + 9 \cdot 3$. The goal? To find the correct answer from the multiple-choice options. This isn't just about getting the right number; it's about showcasing that you understand the fundamental rules of arithmetic. So, are you ready to flex your mental muscles? Let's get started!

Understanding the Order of Operations: The Key to Unlocking the Answer

First things first, guys, let's talk about the order of operations. You might have heard of the acronym PEMDAS or BODMAS. These are handy memory aids to help you remember the sequence in which you should solve a math problem. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS is the same but uses Brackets instead of Parentheses, and Order instead of Exponents. In our case, the expression is $8 + 9 \cdot 3$. We don't have any parentheses or exponents, so we skip to the next step. Following PEMDAS/BODMAS, multiplication comes before addition. Therefore, we must perform the multiplication of $9 \cdot 3$ first. This gives us 27. Now, our expression becomes $8 + 27$. Finally, we add 8 and 27, which gives us 35. So, the correct answer is 35. Now that we've walked through the correct steps, let's look at why getting the order wrong can lead to some tricky wrong answers. It's a common mistake, but if you remember the rules, you're golden!

Let's break it down further. Why is it so crucial to follow PEMDAS/BODMAS? Imagine, if we didn't, and we simply went from left to right, we'd add 8 and 9 first. That would give us 17. Then, we'd multiply 17 by 3, which equals 51. But that is incorrect. It's an example of how a simple oversight in the order of operations can lead to a completely wrong result. That's why understanding and using the order of operations is super important. It ensures everyone arrives at the same answer, regardless of who is solving the problem or how they are doing it. It's the universal language of math, ensuring consistency and accuracy.

The Importance of PEMDAS/BODMAS

• Consistency: Ensures everyone solves the problem in the same way, leading to a single correct answer.
• Accuracy: Prevents errors that can arise from solving operations in the wrong order.
• Foundation for More Complex Math: Understanding the order of operations is essential for more advanced math concepts.

Solving the Problem Step-by-Step

Alright, let's get down to the actual solution. We've got our expression: $8 + 9 \cdot 3$. Using PEMDAS/BODMAS, we know that multiplication comes first. So, we'll start with $9 \cdot 3$. What do we get? Yup, 27! Now, we substitute this back into our original expression, which changes to $8 + 27$. Next, we add 8 to 27, and what do we get? Bingo! 35. That's our final answer. See, not so hard, right? The key is to break down the problem step-by-step and follow the rules.

Now, let's go back and discuss why the other options were wrong and why our answer, 35, is the correct one. The process that we followed, of solving multiplication before addition, is the crucial step. We have to follow this to guarantee we are correct. This understanding of the order of operations is essential. Without this, it's very easy to get confused. We have to remember that to arrive at a correct answer, it's not enough to simply use the correct numbers; we have to follow the steps in the correct order.

Step-by-Step Breakdown

1. Multiplication: $9 \cdot 3 = 27$
2. Addition: $8 + 27 = 35$

Analyzing the Answer Choices: Why is 35 the Right Choice?

Okay, let's take a look at the answer choices. We already know the correct answer is 35, but let's see why the others aren't. Our options were A. 35, B. 51, C. 14, and D. 11. We've confirmed that 35 is the correct answer, based on the order of operations. Option B, 51, is the result you'd get if you added 8 and 9 first (which is wrong), and then multiplied that sum by 3. See how the order makes a massive difference? Option C, 14, is just completely wrong. Option D, 11, is also incorrect. The only way to achieve the correct answer is to perform multiplication before any addition is performed.

Now, let's look at it another way. Consider how easy it is to make a mistake when you are working through a problem like this. That's why being very careful is important. If you just went from left to right, you'd get the wrong answer. Understanding the underlying rules makes it much easier to avoid mistakes. The best part is once you master these, the concept gets easier. So, next time you are faced with a similar problem, you will be prepared and confident.

Detailed Analysis of Answer Choices

• A. 35: Correct answer. This is what we obtained following PEMDAS/BODMAS rules.
• B. 51: This is what you would get if you added 8 and 9 first and then multiplied by 3. It's a clear example of the wrong order.
• C. 14: Incorrect. This does not follow the rules.
• D. 11: Incorrect. This does not follow the rules.

Conclusion: Mastering the Order of Operations

There you have it, guys! We've tackled the problem $8 + 9 \cdot 3$, and found the correct answer is 35. We've emphasized the importance of the order of operations and PEMDAS/BODMAS. Remember, math isn't about memorization; it's about understanding. When you understand the basic principles, you can solve all kinds of problems. Keep practicing and keep up the great work! This particular problem is very common on tests and quizzes, so knowing how to solve it will certainly help you in the future. Now go forth and conquer those math problems with confidence!

So next time you come across a similar problem, you'll be able to solve it with ease. The order of operations is one of the most important concepts you'll learn in math. Keep practicing, and you'll be a math whiz in no time!