Solving 15 X 4 + 5 X 10 - 38 A Step-by-Step Guide

by ADMIN 50 views

Hey guys! Today, we're going to break down a math problem that might look a little intimidating at first glance: 15 × 4 + 5 × 10 - 38. But don't worry, we'll tackle it together step by step, making sure everyone understands the process. Math can be fun, especially when you know the rules and how to apply them. So, let's jump right in and solve this equation! We’ll use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), to ensure we get the correct answer. This order is crucial for solving any mathematical expression correctly. Without it, we might end up with a completely different result, and that’s not what we want. So, keep PEMDAS in mind as we go through each step.

Understanding PEMDAS: The Key to Solving Math Problems

Before we dive into the problem, let's quickly recap PEMDAS. It stands for:

  • Parentheses: First, we solve anything inside parentheses.
  • Exponents: Next up are exponents (like squares and cubes).
  • Multiplication and Division: These are done from left to right.
  • Addition and Subtraction: Finally, these are also done from left to right.

Think of PEMDAS as your roadmap for solving math problems. It tells you the exact order in which to perform operations, ensuring you arrive at the correct solution every time. Ignoring PEMDAS can lead to errors, so it’s essential to follow it diligently. For instance, if we were to add before multiplying, we’d get a completely different answer. That’s why this order of operations is so important in mathematics. It provides a standardized way of approaching equations, making them solvable and consistent.

Step 1: Multiplication – Tackling 15 × 4 and 5 × 10

Looking at our problem, 15 × 4 + 5 × 10 - 38, we see that we have multiplication operations first. According to PEMDAS, we need to handle these before we can even think about addition or subtraction.

Let's start with 15 × 4. What's that? If you said 60, you're absolutely right! Now, let’s move on to the next multiplication: 5 × 10. This one's a bit easier, isn't it? It equals 50. So now, we've simplified our equation a little. We’ve taken care of the multiplications and are ready to move on to the next operations. This is how we break down complex problems into smaller, more manageable chunks. By focusing on one operation at a time, we avoid confusion and ensure accuracy. Multiplication is a fundamental operation, and mastering it is crucial for solving more complex mathematical problems.

Step 2: Rewriting the Equation

After performing the multiplications, our equation now looks like this: 60 + 50 - 38. See how much simpler it's becoming? We've eliminated the multiplication steps, and now we're left with just addition and subtraction. This is a great example of how following the order of operations can make a problem much less daunting. By systematically addressing each operation, we reduce the complexity and move closer to the final answer. Rewriting the equation after each step helps us keep track of our progress and avoid making mistakes. It's a visual way to see how the problem is evolving and becoming more manageable. This is a good habit to develop when solving any mathematical problem, as it promotes clarity and accuracy.

Step 3: Addition – Adding 60 and 50

Now that we have 60 + 50 - 38, we move on to addition and subtraction. Remember, PEMDAS tells us to perform these from left to right. So, let's tackle the addition first: 60 + 50. What does that give us? That's right, it's 110! We're making great progress here. We've successfully completed the addition, and now we're just one step away from the final answer. This step highlights the importance of following the left-to-right rule for addition and subtraction. If we were to subtract before adding, we would end up with the wrong result. So, sticking to the order of operations is key to accuracy. Addition is another fundamental operation, and its correct application is crucial for solving mathematical expressions.

Step 4: Subtraction – Subtracting 38 from 110

We're almost there! Our equation is now 110 - 38. The final step is to subtract 38 from 110. Can you do it? Let's break it down. 110 minus 38 equals 72. Fantastic! We've solved the problem. We've gone through each step, followed PEMDAS, and arrived at the final answer. Subtraction is the last operation we need to perform in this problem, and it brings us to the solution. This step demonstrates the importance of accuracy in each operation. A mistake in any step can lead to an incorrect final answer. Therefore, it’s crucial to double-check our work and ensure we’ve performed each operation correctly. With the subtraction complete, we can confidently say we’ve solved the equation.

The Final Answer: 72

So, the answer to 15 × 4 + 5 × 10 - 38 is 72. Great job, guys! We did it together, step by step. You've now seen how breaking down a problem using PEMDAS can make even complex equations manageable. Remember, practice makes perfect, so keep working on these types of problems, and you'll become a math whiz in no time! Understanding and applying the order of operations is a fundamental skill in mathematics. It’s not just about getting the right answer; it’s about understanding the process and building a solid foundation for more advanced mathematical concepts. So, keep practicing, and you’ll see how your confidence and skills grow over time. Remember, math is a journey, and every problem you solve is a step forward.

Tips for Mastering Order of Operations

To really nail the order of operations, here are a few extra tips:

  • Write it down: When you're first learning, it can be helpful to write out PEMDAS at the top of your paper as a reminder.
  • Show your work: Breaking down each step makes it easier to track your progress and spot any mistakes.
  • Practice regularly: The more you practice, the more natural the order of operations will become.
  • Double-check: Always double-check your work, especially when dealing with longer equations.

Mastering the order of operations is like learning a new language. It takes time and effort, but the rewards are well worth it. The ability to solve mathematical problems accurately and efficiently is a valuable skill that will benefit you in many areas of life. So, don’t be discouraged if you encounter challenges along the way. Keep practicing, stay persistent, and you’ll see your skills improve over time. Remember, every mathematician started somewhere, and with dedication and effort, you can achieve your mathematical goals.

Common Mistakes to Avoid

Even with PEMDAS in mind, it's easy to make mistakes. Here are a few common pitfalls to watch out for:

  • Forgetting the left-to-right rule: Remember, addition and subtraction, as well as multiplication and division, are performed from left to right.
  • Skipping steps: Make sure you break down the problem into manageable steps and don't try to do too much at once.
  • Misinterpreting the operations: Double-check that you're performing the correct operation at each step.
  • Rushing through the problem: Take your time and work carefully to avoid careless errors.

Avoiding these common mistakes is crucial for achieving accuracy in your calculations. It’s like proofreading a piece of writing before submitting it. Taking the time to review your work and identify potential errors can save you from making mistakes that might otherwise go unnoticed. So, cultivate the habit of checking your work and paying attention to the details. This will not only improve your accuracy but also enhance your understanding of the mathematical concepts involved. Remember, attention to detail is a hallmark of a skilled mathematician.

Practice Problems

Want to test your skills? Try solving these problems using PEMDAS:

  1. 20 + 5 × 3 - 10
  2. (12 ÷ 4) + 8 × 2
  3. 3^2 + 15 - 5 × 2

Solving practice problems is one of the best ways to reinforce your understanding of PEMDAS and improve your problem-solving skills. These exercises allow you to apply the concepts you’ve learned and identify any areas where you may need further practice. The more problems you solve, the more confident and proficient you’ll become in using the order of operations. So, don’t hesitate to challenge yourself with a variety of problems. Start with simpler ones and gradually work your way up to more complex equations. Remember, each problem you solve is a step closer to mastering the order of operations.

Conclusion

Congratulations! You've successfully solved the problem 15 × 4 + 5 × 10 - 38 and learned how to use the order of operations (PEMDAS). Keep practicing, and you'll be tackling even tougher math problems in no time. Remember, math is a skill that improves with practice, so keep at it, and you'll see yourself grow. You've got this! We've reached the end of our guide, and I hope you found it helpful and informative. Remember, the key to mastering math is consistency and a willingness to learn. So, keep practicing, stay curious, and you’ll unlock the fascinating world of mathematics.