Solving 2 + (2 × 3) - 6 = ? Math Problem Explained

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Solving 2 + (2 × 3) - 6 = ? Math Problem Explained

Hey guys! Let's dive into this interesting math problem together: 2 + (2 × 3) - 6 = 2 × 1 = 1 - 9. We're going to break it down step by step to make sure we understand exactly how to get to the solution. We'll also look at the answer choices provided: (a) 8, (b) 12, (c), and (d) 6. So, grab your thinking caps, and let's get started!

Understanding the Order of Operations

Before we even begin to tackle this problem, it's super important to understand something called the order of operations. You might have heard of it as PEMDAS or BODMAS. This is just a fancy way of saying there's a specific order we need to follow when solving math problems with different operations. PEMDAS stands for:

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

Basically, this means we do anything inside parentheses first, then exponents, then multiplication and division, and finally, addition and subtraction. This order is crucial for getting the correct answer.

Following this order, we first deal with any expressions inside parentheses. Then, we perform multiplication and division from left to right. Finally, we handle addition and subtraction, also from left to right. This systematic approach ensures that we solve the equation accurately, avoiding common mistakes that can occur when operations are performed in the wrong sequence. Understanding and applying the order of operations is fundamental to solving mathematical problems correctly and efficiently.

Breaking Down the Problem Step-by-Step

Okay, now that we've got PEMDAS in mind, let's apply it to our problem: 2 + (2 × 3) - 6 = 2 × 1 = 1 - 9.

  1. Parentheses: We see an expression inside parentheses: (2 × 3). So, let's do that first. 2 multiplied by 3 equals 6. Now our equation looks like this: 2 + 6 - 6 = 2 × 1 = 1 - 9.
  2. Multiplication: Next up, we have some multiplication to handle. We see 2 × 1, which equals 2. Our equation now looks like this: 2 + 6 - 6 = 2 = 1 - 9.
  3. Addition and Subtraction (Left to Right): Now we just have addition and subtraction. We'll do these from left to right.
    • First, 2 + 6 = 8. So our equation is now: 8 - 6 = 2 = 1 - 9.
    • Next, 8 - 6 = 2. This gives us: 2 = 2 = 1 - 9.
  4. Final Subtraction: Lastly, we have 1 - 9, which equals -8. So, the last part of the equation is -8.

So, putting it all together, we've got: 2 + (2 × 3) - 6 = 2 and the final part 1 - 9 = -8. It seems like there's a bit of a discrepancy in how the problem is written, but let's focus on the first part first: 2 + (2 × 3) - 6 = ?

Breaking down the problem step-by-step helps to clarify the process and reduces the likelihood of making errors. By focusing on each operation individually and following the correct order, we can solve even complex equations with confidence. This methodical approach is not only useful for this specific problem but also provides a solid foundation for tackling other mathematical challenges.

Focusing on the First Part of the Equation: 2 + (2 × 3) - 6

Let's zoom in on the first part of the equation: 2 + (2 × 3) - 6. We've already done the hard work, but let's recap to make sure we're crystal clear.

  1. Parentheses: (2 × 3) = 6
  2. Equation: This leaves us with 2 + 6 - 6.
  3. Addition and Subtraction (Left to Right):
    • 2 + 6 = 8
    • 8 - 6 = 2

So, 2 + (2 × 3) - 6 = 2. Now, let's look at those answer choices again.

By concentrating on this segment, we can methodically apply the order of operations to arrive at a definitive solution. This focused approach not only aids in solving the immediate problem but also enhances our ability to handle similar mathematical expressions in the future. Ensuring accuracy in each step is crucial, and by isolating the relevant portion of the equation, we can minimize errors and achieve a reliable result.

Evaluating the Answer Choices

Okay, so we've determined that 2 + (2 × 3) - 6 = 2. Now, let's circle back to those answer choices and see if any of them match our result.

We had the following options:

  • (a) 8
  • (b) 12
  • (c) (This one seems to be missing a number)
  • (d) 6

None of these options directly match our calculated answer of 2. However, it's important to remember that the original equation had an extra bit: 2 × 1 = 1 - 9, which led to 2 = -8. This suggests there might be a mistake in the original problem statement or the answer choices provided.

When the provided answer choices don't match the calculated result, it's crucial to critically evaluate both the solution and the options. This discrepancy highlights the importance of double-checking each step of the calculation and considering whether there may be an error in the initial problem statement or the given choices. By thoroughly reviewing our work and the available information, we can ensure accuracy and identify any potential mistakes.

Addressing the Discrepancy and Possible Errors

Alright, guys, it seems like we've hit a bit of a snag. Our calculation for 2 + (2 × 3) - 6 clearly gives us 2. But none of the answer choices match that. Plus, the extra part of the equation, 2 × 1 = 1 - 9, doesn't really make sense mathematically since 2 does not equal -8. So, what's going on?

There are a couple of possibilities here:

  1. Typo in the Problem: It's possible there's a typo in the original problem. Math problems sometimes have errors, especially when they're written out quickly. Maybe a number is wrong, or an operation is missing.
  2. Typo in the Answer Choices: It's also possible there's a mistake in the answer choices. Maybe the correct answer (which is 2) was accidentally left out.

In situations like this, the best thing to do is to double-check our work (which we've done!) and then consider the most likely source of the error. If this were a test or homework problem, it would be a good idea to ask the teacher or professor about the discrepancy. They can clarify whether there's a mistake in the problem or the answer choices.

When faced with a discrepancy between the calculated answer and the provided options, it's essential to systematically analyze potential sources of error. This involves not only reevaluating our own calculations but also considering the possibility of mistakes in the original problem statement or the given answer choices. By addressing these discrepancies methodically, we can improve our problem-solving skills and ensure accuracy in our mathematical work.

Key Takeaways and Conclusion

So, let's wrap things up! We've tackled the math problem 2 + (2 × 3) - 6 = 2 × 1 = 1 - 9 and broken it down step by step. Here are the key things we learned:

  • Order of Operations (PEMDAS/BODMAS): This is super important for solving math problems correctly. We always do parentheses first, then exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
  • Step-by-Step Approach: Breaking down a problem into smaller steps makes it much easier to solve. We avoid confusion and reduce the chance of making mistakes.
  • Double-Checking: Always double-check your work! It's easy to make a small mistake, so it's good to be sure.
  • Discrepancies: If your answer doesn't match the choices given, don't panic! There might be an error in the problem itself. It's okay to question things and seek clarification.

In this case, we found that 2 + (2 × 3) - 6 = 2, but none of the provided answer choices matched. This suggests there might be an error in the original problem or the choices. But hey, we still learned a lot by working through it! Keep practicing, guys, and you'll become math whizzes in no time!

By summarizing the key points and emphasizing the importance of methodical problem-solving, we reinforce the learning experience. Encouraging continuous practice and highlighting the value of critical thinking, especially when encountering discrepancies, helps to build confidence and resilience in mathematical problem-solving. This comprehensive approach ensures that learners not only grasp the specific solution but also develop broader skills applicable to various mathematical challenges.