Solving 28 ÷ 7 + 2 × 3 Equation A Step-by-Step Guide

Sam Evans · · 10 min read

Table Of Content

  1. Understanding the Order of Operations: PEMDAS/BODMAS
  2. Step-by-Step Solution: 28 ÷ 7 + 2 × 3
  3. Identifying the Correct Answer
  4. Common Mistakes to Avoid
  5. Practice Problems: Sharpen Your Skills
  6. Conclusion

Hey guys! Today, we're diving into a super common type of math problem that you'll see everywhere from your homework to standardized tests: solving equations with multiple operations. Let's break down this particular equation: 28 ÷ 7 + 2 × 3 = ? We'll walk through each step, making sure you understand the order of operations (PEMDAS/BODMAS) and how to apply it. By the end of this article, you’ll not only be able to solve this specific problem but also tackle similar equations with confidence. So, grab your pencils and let's get started!

Understanding the Order of Operations: PEMDAS/BODMAS

Before we jump into solving our equation, it's crucial to understand the order of operations. This is the golden rule that dictates the sequence in which we perform different mathematical operations. You might have heard of it as PEMDAS or BODMAS, both of which are handy acronyms to help you remember the correct order. So, what do they stand for?

  • PEMDAS:
    • Parentheses
    • Exponents
    • Multiplication and Division (from left to right)
    • Addition and Subtraction (from left to right)
  • BODMAS:
    • Brackets
    • Orders
    • Division and Multiplication (from left to right)
    • Addition and Subtraction (from left to right)

As you can see, they're essentially the same thing, just using slightly different words. The key takeaway here is that parentheses (or brackets) and exponents (or orders) come first, followed by multiplication and division (performed from left to right), and finally, addition and subtraction (also from left to right). Remember this order, and you'll be well on your way to solving any equation like a pro! For this particular problem, we don't have parentheses or exponents, but we definitely have division, multiplication, and addition to contend with. Ignoring this order and just solving left to right would give us a completely wrong answer, so paying attention to PEMDAS/BODMAS is super important. In complex mathematical expressions, understanding and applying this order of operations is not just a matter of procedure; it's the very foundation upon which correct solutions are built. It ensures consistency and accuracy in mathematical calculations, regardless of who is solving the problem or where it is being solved. Mastery of PEMDAS/BODMAS is therefore essential for anyone engaging with mathematics beyond the basics, enabling them to navigate more complex problems with confidence and precision. It also prevents common errors that arise from performing operations in the incorrect sequence, which can lead to significant discrepancies in results, particularly in fields like engineering, finance, and computer science, where accuracy is paramount. So, while it might seem like a simple rule, the order of operations is a powerful tool for mathematical success.

Step-by-Step Solution: 28 ÷ 7 + 2 × 3

Okay, let's apply the order of operations to our equation: 28 ÷ 7 + 2 × 3. Remember, we need to tackle multiplication and division before we even think about addition. So, the first things we're going to address are the division and the multiplication. Let's start with the division.

  1. Division: 28 ÷ 7 = 4. So, we've taken care of the first operation. Now our equation looks like this: 4 + 2 × 3. See how we're simplifying it step by step? This is key to avoiding confusion. Now, let's focus on the multiplication part.
  2. Multiplication: 2 × 3 = 6. Great! We've knocked out the multiplication. Our equation is now super simple: 4 + 6. We're almost there!
  3. Addition: 4 + 6 = 10. And there you have it! We've solved the equation. The answer is 10. Wasn't that satisfying? Breaking down the problem into smaller steps using the order of operations made it totally manageable. The beauty of following this methodical approach is that it minimizes the chances of making mistakes and ensures that we arrive at the correct answer. Each step builds upon the previous one, leading us logically and clearly to the final solution. Moreover, this step-by-step approach not only helps in solving the immediate problem but also reinforces our understanding of mathematical principles, making us better problem-solvers in the long run. So, remember to take your time, follow the order of operations, and break the problem down into manageable chunks – it's the recipe for success in mathematics. And it's not just about getting the right answer; it's about understanding why that answer is correct, which builds confidence and fosters a deeper appreciation for the elegance of mathematics.

Identifying the Correct Answer

Now that we've worked through the equation step-by-step and arrived at the solution, 10, let's look at the options provided to make sure we select the correct one. We had the following choices:

  • A) 10
  • B) 18
  • C) 12
  • D) 24

It's clear that option A) 10 is the correct answer. We solved the equation 28 ÷ 7 + 2 × 3 by first performing the division and multiplication, and then the addition, following the order of operations. This methodical approach not only led us to the right answer but also demonstrated the importance of adhering to mathematical principles. It's tempting sometimes to rush through problems or skip steps, but taking the time to solve equations carefully and systematically is crucial for accuracy and understanding. The other options listed – 18, 12, and 24 – are incorrect because they would result from performing the operations in the wrong order or making calculation errors. For instance, if we were to simply add 7 and 2 before multiplying and dividing, we would end up with a completely different result. This highlights why PEMDAS/BODMAS is so essential; it provides a consistent framework for solving mathematical problems, ensuring that everyone arrives at the same correct answer. So, always double-check your work, follow the order of operations, and you'll be on the path to mathematical mastery!

Common Mistakes to Avoid

When tackling equations like this, there are a few common pitfalls that students often stumble into. Knowing these mistakes can help you avoid them and boost your accuracy. Let's highlight some of these so you can be a math whiz!

  1. Ignoring the Order of Operations: This is the biggest one! As we've emphasized, solving the equation out of order will lead to a wrong answer. For example, some might be tempted to add 7 and 2 first, which is a big no-no. Remember PEMDAS/BODMAS!
  2. Forgetting to Perform Multiplication and Division (or Addition and Subtraction) from Left to Right: When you have multiple operations of the same level (like multiplication and division), you need to perform them from left to right. The same goes for addition and subtraction. It's like reading a sentence – you go from left to right.
  3. Simple Calculation Errors: Sometimes, it's not the concept that trips us up, but just a plain old calculation mistake. Maybe you accidentally say 7 times 4 is 21 instead of 28. Always double-check your arithmetic!
  4. Skipping Steps: It might seem faster to skip steps, but it actually increases your chances of making a mistake. Breaking the problem down step-by-step helps keep your work organized and makes it easier to spot any errors.
  5. Not Double-Checking Your Work: Once you have an answer, take a moment to review your steps. Did you follow the order of operations correctly? Did you make any calculation errors? A quick review can catch mistakes that you might have missed otherwise.

By being aware of these common pitfalls, you'll be much better equipped to solve equations accurately and efficiently. Remember, practice makes perfect, so keep working on these types of problems, and you'll become a pro in no time!

Practice Problems: Sharpen Your Skills

Alright, guys, now that we've conquered the equation 28 ÷ 7 + 2 × 3, let's put your newfound skills to the test with some practice problems. Practice is absolutely key to solidifying your understanding and building confidence. So, grab a piece of paper and a pencil, and let's dive in!

Here are a few equations for you to solve, keeping in mind the all-important order of operations (PEMDAS/BODMAS):

  1. 16 ÷ 4 + 3 × 2 = ?
  2. 10 – 2 × 3 + 5 = ?
  3. 36 ÷ 6 – 1 × 4 = ?
  4. 8 + 12 ÷ 2 – 3 = ?
  5. 5 × 4 – 15 ÷ 3 = ?

Take your time, work through each problem step-by-step, and remember to double-check your answers. Don't just focus on getting the right result; make sure you understand why your answer is correct. This deeper understanding will help you tackle more complex problems in the future. Once you've solved these, try creating your own equations to challenge yourself further. Mix up the operations, add some parentheses, and see what you can come up with. The more you practice, the more comfortable and confident you'll become with solving equations. And that's the goal, right? To not only get the right answers but to truly understand the math behind them. So, happy solving, and remember, every problem you solve is a step closer to mathematical mastery!

Conclusion

So, we've successfully navigated the equation 28 ÷ 7 + 2 × 3 and found the answer to be 10. But more importantly, we've reinforced the crucial concept of the order of operations (PEMDAS/BODMAS) and how it guides us to solve complex equations step-by-step. Remember, the key is to break down the problem, tackle multiplication and division before addition and subtraction, and always double-check your work. By avoiding common mistakes and practicing regularly, you'll become a confident and capable problem-solver. Math isn't just about memorizing formulas; it's about understanding the underlying principles and applying them logically. And with each problem you solve, you're not just getting the right answer; you're building a stronger foundation for future mathematical challenges. So, keep practicing, stay curious, and never stop exploring the fascinating world of math! You've got this!

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