Solve (25+15)×2÷10: Step-by-Step Guide & Explanation

by Omar Yusuf 53 views

Hey guys! Ever stumbled upon a math problem that looks like a jumbled mess of numbers and operations? You're not alone! Combined operations can seem daunting at first, but once you break them down, they're actually quite straightforward. Today, we're going to tackle the problem (25+15)×2÷10 together, step by step. We will clarify the process and also provide actionable advice, for example, using PEMDAS/BODMAS for simplifying the process, so you can conquer any similar equation that comes your way! It's like unlocking a secret code to the world of math!

Understanding the Order of Operations: PEMDAS/BODMAS

Before we dive into the specifics of our problem, let's talk about the golden rule of combined operations: the order of operations. This is a set of rules that tells us which operations to perform first, second, and so on. Think of it as the GPS for your math journey – it ensures you reach the correct destination. The most common mnemonic devices for remembering the order of operations are PEMDAS and BODMAS. Let's break them down:

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

Notice that both acronyms essentially convey the same order. The key takeaway is that we always deal with parentheses (or brackets) first, then exponents (or orders), followed by multiplication and division (performed from left to right), and finally addition and subtraction (also performed from left to right). This order is crucial because changing it can lead to vastly different results. Imagine trying to build a house by putting the roof on before the walls – it just wouldn't work! The same principle applies to math; we need to follow the correct order to get the right answer.

Mastering PEMDAS/BODMAS is like learning the rules of a game. Once you know them, you can play with confidence and precision. Think of each operation as a player on a team, each with its own role and importance. Understanding the order in which they play ensures a winning strategy. For example, if you have a problem with both multiplication and addition, you wouldn't add first – that's like passing the ball to the wrong player at a critical moment. Instead, you'd multiply first, setting up the perfect play for the addition that follows. This strategic approach not only helps you solve problems accurately but also enhances your overall mathematical intuition. It's about understanding the underlying structure of the equation and knowing how each component interacts with the others. So, embrace PEMDAS/BODMAS as your guiding principle, and watch how your math skills transform from tentative steps to confident strides.

Solving (25+15)×2÷10: A Step-by-Step Walkthrough

Now that we've got our PEMDAS/BODMAS compass, let's navigate our way through the problem (25+15)×2÷10. Remember, the first thing we tackle are the parentheses (or brackets). This is like clearing the first hurdle in a race – it sets the pace for the rest of the solution. So, let's start there:

  1. Parentheses: Inside the parentheses, we have 25 + 15. Adding these numbers together is straightforward: 25 + 15 = 40. So, we've simplified our expression to 40×2÷10. This step is crucial because it condenses the initial complexity into a more manageable form. It's like taking a cluttered room and organizing it into neat sections, making it easier to navigate. By addressing the parentheses first, we isolate a key part of the problem and resolve it before moving on, ensuring that we're building on a solid foundation.
  2. Multiplication and Division: Next up, we have multiplication and division. Remember, PEMDAS/BODMAS tells us to perform these operations from left to right. It's like reading a sentence; we move sequentially, addressing each part in the order it appears. So, we first encounter 40 × 2. Multiplying these gives us 80. Our expression now looks like 80÷10. This sequential approach is vital because it maintains the logical flow of the equation. Imagine if you were baking a cake and decided to skip a step – the result might not be what you expected. Similarly, in math, performing operations out of order can lead to incorrect answers. By consistently moving from left to right, we ensure that each operation is performed in its proper context, leading to a correct and coherent solution.
  3. Final Division: Finally, we have 80 ÷ 10. This is the last step in our journey, the final piece of the puzzle. Dividing 80 by 10 gives us 8. And there you have it! The solution to (25+15)×2÷10 is 8. This final division is like the finishing touch on a masterpiece, bringing all the previous steps together into a single, elegant result. It demonstrates the power of methodical problem-solving, where each step builds upon the last, leading to a clear and concise answer. By following the order of operations and breaking down the problem into manageable chunks, we've successfully navigated a combined operation and arrived at our destination with confidence.

Common Mistakes and How to Avoid Them

Even with PEMDAS/BODMAS as our guide, it's easy to stumble if we're not careful. Math, like any skill, requires attention to detail and a mindful approach. Let's look at some common pitfalls and how to sidestep them. These common mistakes are like potholes on the road to mathematical mastery – they can trip you up if you're not aware of them. But with a bit of knowledge and practice, you can learn to navigate around them with ease.

One of the most frequent errors is ignoring the order of operations. This often happens when we rush through a problem or try to take shortcuts. For example, someone might mistakenly add 15 × 2 before addressing the parentheses, leading to a completely different outcome. It's like trying to assemble a piece of furniture without reading the instructions – you might end up with a wobbly, unstable structure. To avoid this, always double-check your steps and ensure you're adhering to PEMDAS/BODMAS. It's not about speed; it's about accuracy. Slow down, take a deep breath, and approach the problem with a clear, methodical mindset. Think of each operation as a step in a dance – you need to get the sequence right to create a harmonious performance. By consistently applying the order of operations, you'll build a solid foundation for more complex mathematical concepts and avoid unnecessary errors.

Another common mistake is misinterpreting the left-to-right rule for multiplication and division (or addition and subtraction). Remember, these operations have equal priority, so we perform them in the order they appear from left to right. Failing to do this can lead to errors. Imagine you're reading a map and you skip a turn – you might end up in the wrong place. Similarly, in math, if you divide before you multiply when the division comes first, you'll likely get the wrong answer. A helpful way to avoid this is to rewrite the expression step by step, clearly showing each operation you're performing. This not only helps you keep track of your progress but also makes it easier to spot any mistakes. It's like creating a visual roadmap of your solution, ensuring you stay on the right path. Furthermore, practice is key. The more you work through problems involving combined operations, the more intuitive the order of operations will become. It's like learning to ride a bike – at first, it feels awkward and challenging, but with practice, it becomes second nature.

Finally, careless arithmetic errors can derail even the most well-intentioned solutions. Simple mistakes like adding incorrectly or miscalculating a multiplication can throw off the entire answer. This is like having a perfectly crafted argument undermined by a single factual error – it weakens the overall impact. To minimize these errors, take your time and double-check your calculations. If you're working on a complex problem, consider using a calculator to verify your arithmetic. It's not about being incapable of doing the math in your head; it's about ensuring accuracy and minimizing the risk of silly mistakes. Think of it as proofreading a document before you submit it – you're catching those little errors that could have a big impact. Additionally, break down the problem into smaller, more manageable steps. This not only makes the problem less overwhelming but also reduces the chances of making a mistake along the way. By focusing on each step individually and verifying your calculations, you'll build a habit of accuracy and precision that will serve you well in all areas of math.

Practice Makes Perfect: More Examples to Try

Alright, guys, now that we've dissected the problem (25+15)×2÷10 and explored common pitfalls, it's time to put our knowledge into action! Math isn't a spectator sport; it's something you learn by doing. The more you practice, the more comfortable and confident you'll become. Think of it like learning to play a musical instrument – you wouldn't expect to become a virtuoso overnight. It takes dedication, repetition, and a willingness to experiment. Similarly, in math, consistent practice is the key to mastery. It's about building muscle memory for your brain, so that the steps and processes become automatic.

Here are a few more examples for you to try. Treat them like mini-challenges, each one designed to test and strengthen your understanding of combined operations and PEMDAS/BODMAS. Grab a pen and paper, clear your mind, and dive in! Don't be afraid to make mistakes – they're a natural part of the learning process. Each error is an opportunity to identify a misunderstanding, refine your approach, and emerge stronger. It's like a video game – you might not beat the boss on your first try, but with each attempt, you learn more about its weaknesses and develop new strategies.

  • Example 1: (10 + 5) × 3 – 12 ÷ 2
  • Example 2: 18 ÷ (6 – 3) + 4 × 2
  • Example 3: 7 × (4 + 1) ÷ 5 – 3

Remember to follow the order of operations diligently. Start with the parentheses, then tackle exponents (if any), followed by multiplication and division (from left to right), and finally addition and subtraction (also from left to right). It's like following a recipe – each step has its place and purpose, and skipping or reordering them can lead to a less-than-desirable result. As you work through these examples, pay attention to the process, not just the answer. Break down each problem into smaller, more manageable steps. This not only makes the problem less intimidating but also allows you to track your progress and identify any areas where you might be struggling. It's like learning a new dance routine – you wouldn't try to master the whole sequence at once. Instead, you'd focus on one step at a time, gradually building up to the full performance.

After you've worked through the problems, take the time to check your answers. This is a crucial step in the learning process, as it allows you to identify any mistakes and reinforce your understanding. If you get an answer wrong, don't get discouraged! Instead, try to figure out where you went wrong. Did you misapply the order of operations? Did you make a simple arithmetic error? Understanding your mistakes is the key to preventing them in the future. It's like analyzing a game you lost – you wouldn't just shrug it off and move on. Instead, you'd review your moves, identify your weaknesses, and develop a plan to improve your strategy. So, embrace the challenge, embrace the practice, and watch your math skills soar!

Conclusion: Mastering Combined Operations for Math Success

So, guys, we've journeyed through the world of combined operations, conquered the problem (25+15)×2÷10, and learned how to navigate the sometimes-tricky waters of PEMDAS/BODMAS. We've explored common mistakes and armed ourselves with the knowledge to avoid them. And we've emphasized the importance of practice, practice, practice! Mastering combined operations is more than just learning a set of rules; it's about developing a logical and systematic approach to problem-solving. It's like learning to drive a car – at first, it might seem overwhelming, with so many things to pay attention to. But with practice, it becomes second nature, and you can navigate even the most complex routes with confidence.

The skills you've gained today are not just limited to the realm of math class. They're transferable skills that will serve you well in all areas of life. The ability to break down complex problems into smaller, more manageable steps is invaluable in fields ranging from science and engineering to finance and even everyday decision-making. It's about developing a problem-solving mindset, a way of approaching challenges with clarity, logic, and a systematic approach. Think of it as building a mental toolkit, filled with the tools you need to tackle any obstacle that comes your way.

Remember, math is not a mountain to be feared but a landscape to be explored. There will be peaks and valleys, challenges and triumphs. But with perseverance, a positive attitude, and a solid understanding of fundamental concepts, you can conquer any mathematical terrain. So, embrace the journey, celebrate your successes, and learn from your mistakes. The world of math is vast and fascinating, and the more you explore it, the more you'll discover its beauty and power. Keep practicing, keep learning, and keep pushing your boundaries. You've got this!