Solving Combined Operations 958 × 65 + 72478 A Step-by-Step Guide
Hey guys! Math can sometimes feel like navigating a maze, especially when you're dealing with combined operations. But don't worry, we're here to break down one such problem and make it super easy to understand. Today, we're tackling the operation 958 × 65 + 72478. This might look intimidating at first glance, but with the right approach, it's totally manageable. So, let's dive in and solve this together, step by step!
Understanding the Order of Operations
Before we jump into the calculation, it’s crucial to understand the order of operations. This is the golden rule in mathematics that tells us which operations to perform first. Remember the acronym PEMDAS, which stands for:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
In our case, the expression 958 × 65 + 72478 involves multiplication and addition. According to PEMDAS, we need to perform the multiplication before the addition. Ignoring this order can lead to a completely wrong answer, so it’s super important to stick to the rules. Think of PEMDAS as your roadmap to solving any mathematical expression correctly. By following this order, you ensure that you're tackling the problem in the most efficient and accurate way. This foundational understanding is key to mastering more complex mathematical problems in the future. It's like building a house – you need a strong foundation before you can add the walls and roof! So, keep PEMDAS in mind, and you'll be solving combined operations like a pro in no time!
Step 1 Multiplication: 958 × 65
The first step in solving 958 × 65 + 72478 is to tackle the multiplication: 958 × 65. Let’s break this down using the standard multiplication method. We’ll multiply 958 by each digit of 65 separately and then add the results.
First, multiply 958 by 5 (the ones digit of 65):
958
× 65
------
4790 (958 × 5)
Next, multiply 958 by 6 (the tens digit of 65). Remember to add a zero as a placeholder because we’re multiplying by a tens digit:
958
× 65
------
4790
57480 (958 × 60)
Now, add these two results together:
4790
+57480
------
62270
So, 958 × 65 = 62270. This is a crucial intermediate result. We’ve completed the multiplication part of the operation, and now we have a new, simplified expression to work with. Take a moment to double-check your work here. Accuracy in this step is vital because any error will carry through to the final answer. Think of it like a relay race – if the first runner stumbles, it affects the whole team. So, make sure you’re confident with your multiplication before moving on to the next step. This methodical approach not only ensures accuracy but also builds a solid foundation for tackling more complex calculations in the future. Remember, practice makes perfect, so the more you work through these steps, the more confident and efficient you’ll become!
Step 2 Addition: 62270 + 72478
Now that we've successfully completed the multiplication, we move on to the addition part of our problem. We have the result from the multiplication, which is 62270, and we need to add it to 72478. This step is pretty straightforward, but accuracy is still key. Let’s align the numbers properly and add them column by column, starting from the rightmost column (the ones place).
62270
+72478
------
Starting with the ones column: 0 + 8 = 8
Moving to the tens column: 7 + 7 = 14. Write down 4 and carry over 1 to the hundreds column.
In the hundreds column: 2 + 4 + 1 (carried over) = 7
In the thousands column: 2 + 2 = 4
Finally, in the ten-thousands column: 6 + 7 = 13. Write down 13.
So, the addition looks like this:
62270
+72478
------
134748
Therefore, 62270 + 72478 = 134748. We've now completed the second and final operation. This result is the culmination of our step-by-step approach, and it’s important to feel confident in the process we used to get here. Double-checking your addition is always a good idea, just to ensure there were no small errors. Think of it as proofreading your work – it's the final polish that makes sure everything is just right. With this final step completed, we’ve successfully navigated the combined operation and arrived at the solution. It’s a testament to the power of breaking down complex problems into manageable steps, and it’s a skill that will serve you well in all sorts of mathematical challenges!
Final Answer
After meticulously performing the multiplication and addition, we've arrived at the final answer. The solution to the combined operation 958 × 65 + 72478 is 134748. This wasn't just about crunching numbers; it was about understanding the order of operations and applying it systematically. We broke down a complex problem into smaller, more manageable steps, which made the whole process much less daunting.
To recap, we first tackled the multiplication 958 × 65, which gave us 62270. Then, we added this result to 72478, which led us to our final answer: 134748. Each step was crucial, and accuracy at each stage ensured the correct final result. Think of it like building a puzzle – each piece needs to be in the right place to see the complete picture. Similarly, each operation needs to be performed correctly to arrive at the right solution.
This exercise demonstrates the importance of following the order of operations (PEMDAS). By adhering to this rule, we avoided potential errors and ensured a smooth calculation process. Moreover, this approach isn't just applicable to this specific problem; it’s a universal method that can be applied to a wide range of mathematical expressions. It’s like having a reliable tool in your toolbox that you can use for various tasks. So, remember the steps we took, practice them, and you'll be well-equipped to tackle any combined operation that comes your way!
Why This Matters
Understanding and being able to solve combined operations like 958 × 65 + 72478 is super important for a bunch of reasons. First off, it's a fundamental skill in mathematics. These types of problems pop up everywhere, from basic arithmetic to more advanced algebra and calculus. Mastering them now sets you up for success in future math courses.
But it's not just about school. Combined operations are also a big part of everyday life. Think about calculating expenses, figuring out discounts while shopping, or even planning a budget. You use these skills more often than you might realize. For example, imagine you're buying several items at a store, and some have discounts. You need to multiply the original prices by the discount percentages and then add those amounts to the non-discounted items. That’s a combined operation in action!
Moreover, solving combined operations helps develop your problem-solving skills. It teaches you to break down complex problems into smaller, manageable steps, which is a valuable skill in any field. It’s like learning to strategize – you identify the different components of a problem and tackle them one at a time. This approach isn't just useful in math; it can be applied to all sorts of challenges, whether it's planning a project at work or organizing an event.
Finally, mastering combined operations boosts your logical thinking and attention to detail. You need to follow a specific order, be accurate in your calculations, and double-check your work. These are skills that are highly valued in academics, professional settings, and everyday decision-making. So, by getting comfortable with combined operations, you're not just learning math; you're honing skills that will benefit you in countless ways. Keep practicing, and you'll see how these skills become second nature!
Practice Makes Perfect
Okay, guys, we've walked through the solution to 958 × 65 + 72478 step by step. But remember, the key to truly mastering math is practice. Just like learning to ride a bike or play an instrument, you need to put in the time and effort to build your skills. So, let’s talk about how you can continue to improve your ability to solve combined operations.
First off, try tackling more problems like this one. Look for similar exercises in your math textbook or online. The more you practice, the more comfortable you'll become with the process. Start with simpler problems and gradually work your way up to more complex ones. It's like building your strength at the gym – you don’t start with the heaviest weights; you gradually increase the load as you get stronger.
Another great strategy is to break down the problems into smaller parts, just like we did in this article. Focus on one operation at a time and make sure you're confident with each step before moving on. This methodical approach helps prevent errors and builds a strong understanding of the underlying concepts. Think of it as learning to cook a complicated recipe – you follow the steps one at a time to ensure the final dish is perfect.
Don't be afraid to ask for help if you're struggling. Talk to your teacher, a tutor, or a friend who's good at math. Sometimes, a different explanation or perspective can make all the difference. It’s like having a coach who can offer guidance and support when you need it.
And most importantly, be patient with yourself. Learning math takes time and effort. You might make mistakes along the way, but that's okay! Mistakes are opportunities to learn and grow. The important thing is to keep practicing and keep pushing yourself. Remember, every expert was once a beginner. So, keep practicing, and you'll be solving combined operations like a pro in no time!