Solving (4x7 + 12) Divided By (3x5 + 5) A Step-by-Step Guide

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Hey guys! Math can sometimes look like a beast, but don't worry! We're going to break down this expression (4x7 + 12) : (3x5 + 5) step-by-step, making it super easy to understand. So grab your pencils, and let's dive in!

Understanding the Order of Operations

Before we jump into the calculation, it’s super crucial to understand the order of operations. Think of it as the golden rule of math! We follow a specific order to ensure we get the right answer. Remember PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This order helps us tackle complex expressions smoothly.

So, in our expression, we'll first deal with anything inside parentheses. Then, we'll handle multiplication, followed by addition. Finally, we'll tackle the division. This systematic approach is key to avoiding confusion and arriving at the correct solution. Remember, math is like building a house – you need a solid foundation (the order of operations) before you can put up the walls (the calculations).

Understanding the order of operations isn't just about following a rule; it's about understanding the logic behind it. When you grasp why we perform certain operations before others, math becomes less of a chore and more of an engaging puzzle. Think of it this way: multiplication and division are stronger operations than addition and subtraction, so they need to be handled first. It's like prioritizing the main tasks before the supporting ones. This understanding will not only help you solve this particular expression but will also be invaluable in tackling more complex mathematical problems in the future. Keep practicing, and you'll become a math whiz in no time!

Step 1: Solving the First Parenthesis (4x7 + 12)

Okay, let's tackle the first set of parentheses: (4 x 7 + 12). Remember PEMDAS? Multiplication comes before addition. So, first, we multiply 4 by 7. 4 multiplied by 7 equals 28. Easy peasy, right? Now we have 28 + 12. Next up, we add 28 and 12. 28 plus 12 equals 40. So, the value inside the first parenthesis is 40. We’ve conquered the first hurdle!

Breaking down the steps like this makes the whole process less intimidating. It’s like chopping a big problem into smaller, manageable pieces. By focusing on one operation at a time, you minimize the chances of making mistakes. And hey, it's totally okay to double-check your calculations! Math is all about accuracy, so a little extra caution never hurts. Keep in mind that mastering these basic operations is essential for tackling more advanced math concepts. The more comfortable you are with multiplication and addition, the smoother your mathematical journey will be.

Pro Tip: If you're ever feeling unsure, try using real-world examples to visualize the problem. For instance, think of 4 x 7 as having 4 groups of 7 objects each. This can make the concept more concrete and easier to grasp. The key is to find strategies that work for you and make math more accessible. Practice makes perfect, so keep at it!

Step 2: Solving the Second Parenthesis (3x5 + 5)

Now, let's move on to the second set of parentheses: (3 x 5 + 5). Just like before, we need to follow the order of operations. Multiplication first! 3 multiplied by 5 equals 15. Great! So now our expression inside the parenthesis looks like this: 15 + 5. The final step is to add 15 and 5. 15 plus 5 equals 20. We've successfully solved the second parenthesis, and the answer is 20. You're doing awesome!

Notice how we're applying the same principles we learned earlier? This consistency is what makes math so cool! Once you understand the rules, you can apply them to a wide range of problems. It’s like having a superpower! And remember, every problem you solve builds your confidence and strengthens your mathematical skills. Don't be afraid to take on challenges – they're opportunities to grow and learn.

Keep in mind that attention to detail is super important in math. A small mistake in one step can throw off the entire calculation. So, take your time, double-check your work, and don't rush the process. And hey, if you do make a mistake, that's totally okay! It's a chance to learn and improve. The important thing is to understand where you went wrong and how to avoid making the same mistake in the future. Keep up the fantastic work!

Step 3: Performing the Division (40 : 20)

Alright, we've conquered the parentheses! Now we're left with the final operation: 40 : 20. This symbol (:) means division, so we need to divide 40 by 20. Think of it as splitting 40 into groups of 20. How many groups do we get? 40 divided by 20 equals 2. That's it! We've solved the expression. The answer is 2. High five!

See how all the steps we took earlier led us to this final answer? It's like a journey – each step builds upon the previous one. And that's the beauty of math! It's a logical and structured process that leads to a clear solution. This final division step is crucial because it brings together the results we obtained from the parentheses. It’s the grand finale of our mathematical performance!

Remember: Division is the inverse operation of multiplication. So, if 40 divided by 20 equals 2, that means 20 multiplied by 2 equals 40. Understanding this relationship can help you check your answers and ensure accuracy. Plus, knowing the relationship between different operations can give you a deeper understanding of math as a whole. You’re becoming a true math master!

Final Answer and Recap

So, to recap, we started with the expression (4x7 + 12) : (3x5 + 5). We followed the order of operations (PEMDAS/BODMAS) and broke the problem down into smaller, manageable steps. First, we solved the parentheses: (4 x 7 + 12) equals 40, and (3 x 5 + 5) equals 20. Then, we performed the division: 40 divided by 20 equals 2. Therefore, the final answer is 2.

You did it! You successfully solved the expression step-by-step. Isn't it satisfying to see how all the pieces come together? Math can be challenging, but with a systematic approach and a little bit of practice, you can conquer any problem. Remember to always follow the order of operations, break down complex problems into smaller steps, and double-check your work. And most importantly, don't be afraid to ask for help if you need it!

Key Takeaways:

  • Always follow the order of operations (PEMDAS/BODMAS).
  • Break down complex problems into smaller, manageable steps.
  • Double-check your work to ensure accuracy.
  • Practice makes perfect! The more you practice, the more confident you'll become.

Keep Practicing!

Now that you've mastered this expression, why not try some more? The more you practice, the better you'll become at solving mathematical problems. You can find tons of practice problems online or in textbooks. And don't be afraid to create your own problems to challenge yourself! Math is like a muscle – the more you use it, the stronger it gets. So keep flexing those mathematical muscles!

Remember, every mathematician started somewhere. No one is born knowing how to solve complex equations. It takes time, effort, and perseverance. But with the right attitude and a willingness to learn, you can achieve anything you set your mind to. So keep exploring the world of math, keep asking questions, and keep having fun! You've got this!

And hey, if you ever get stuck, don't hesitate to reach out to a teacher, a tutor, or a friend. There are tons of resources available to help you succeed in math. The key is to be proactive and seek out the support you need. And remember, learning is a journey, not a destination. So enjoy the process, celebrate your successes, and don't get discouraged by setbacks. You're doing great!

We hope this step-by-step guide was helpful! Keep up the awesome work, and happy calculating!