Step-by-Step Guide To Solving 350 ÷ (46 + 24) × 12

Jul 28, 2025 by ADMIN 51 views

Solving 350 ÷ (46 + 24) × 12: A Step-by-Step Mathematical Guide

Hey guys! Let's break down this math problem together: 350 ÷ (46 + 24) × 12. Math can seem daunting, but when we take it one step at a time, it becomes super manageable. This guide will walk you through each part of the equation, ensuring you understand exactly how we arrive at the solution. So, grab your calculators (or your brainpower!) and let's dive in!

Understanding the Order of Operations

Before we jump into solving, it's crucial to understand the order of operations. Think of it as the golden rule of mathematics. It's often remembered by the acronym PEMDAS, which stands for:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

This order tells us exactly what to tackle first. In our equation, we have parentheses, division, multiplication, and addition. Following PEMDAS, we'll deal with the parentheses first, then division and multiplication (in the order they appear), and finally, we don’t have addition or subtraction in this problem, so we can skip that step. Ignoring this order can lead to a totally wrong answer, so always keep PEMDAS in mind!

In the context of our specific problem, the order of operations dictates that we first resolve the operation within the parentheses, which is (46 + 24). Once we've simplified the parentheses, we proceed with division and multiplication. It's important to note that multiplication and division are performed from left to right, meaning we'll tackle the division (350 ÷ result of parentheses) before moving on to the multiplication (result of division × 12). This methodical approach ensures that we maintain mathematical accuracy and arrive at the correct solution. Remember, PEMDAS isn't just a set of letters; it's the roadmap to solving mathematical expressions correctly and efficiently.

Step 1: Solve the Parentheses (46 + 24)

The first thing we need to do, according to PEMDAS, is to tackle what's inside the parentheses. We have 46 + 24. This is a straightforward addition problem. Adding these two numbers together is pretty simple:

46 + 24 = 70

So, we've simplified the expression inside the parentheses to 70. Now, our equation looks like this:

350 ÷ 70 × 12

See? We're already making progress! Breaking it down like this makes the whole thing feel less intimidating.

The importance of correctly solving the parentheses cannot be overstated. It sets the foundation for the rest of the calculation. A mistake here will ripple through the entire problem, leading to an incorrect final answer. So, always double-check your work when dealing with parentheses. In our case, 46 plus 24 undeniably equals 70. This clear and correct intermediate result allows us to confidently move forward. We've successfully reduced the complexity of the original expression by resolving the parentheses, making the subsequent steps more manageable. This highlights why understanding and applying PEMDAS is crucial for accurate mathematical problem-solving.

Step 2: Perform the Division (350 ÷ 70)

Now that we've handled the parentheses, we move on to the next operation in our equation: division. We need to divide 350 by 70. Think of it as splitting 350 into 70 equal groups. How big would each group be?

350 ÷ 70 = 5

So, 350 divided by 70 equals 5. Our equation now looks even simpler:

5 × 12

We're getting closer to the final answer, guys! Keep up the great work!

The division operation serves as a critical reduction step in our problem. It transforms the larger number, 350, into a significantly smaller one, 5, by distributing it evenly across 70 units. This not only simplifies the equation but also brings us closer to a manageable multiplication. Accurate execution of this division is paramount, as it directly impacts the final result. For instance, an error in this step would propagate through the remainder of the calculation, leading to a flawed solution. So, ensuring the correctness of 350 ÷ 70 = 5 is essential. With this simplified value, we're now poised to perform the final multiplication and arrive at the conclusive answer. The division has effectively narrowed the scope of the problem, making the ultimate calculation more straightforward.

Step 3: Perform the Multiplication (5 × 12)

We've arrived at the final step! All that's left is to multiply 5 by 12. This is a classic multiplication problem. If you know your times tables, this should be a breeze. If not, don't worry, we can figure it out together.

5 × 12 = 60

So, 5 multiplied by 12 equals 60. And that's it! We've solved the equation.

The multiplication step is the culmination of all our previous efforts. It synthesizes the simplified values derived from the parentheses and division operations into a single, conclusive answer. Multiplying 5 by 12 efficiently combines these quantities, revealing the overall result of the expression. The accuracy of this step is, of course, vital, as it represents the final mathematical act. Any error here would nullify the correctness of the preceding steps. However, with our meticulous approach and careful calculations, we've confidently arrived at the product of 60. This final multiplication not only provides the solution but also underscores the sequential nature of mathematical problem-solving, where each operation builds upon the last to unveil the ultimate answer.

Final Answer: 60

Therefore, 350 ÷ (46 + 24) × 12 = 60. We did it! By following the order of operations and breaking the problem down into smaller, more manageable steps, we were able to solve it successfully. Remember, math isn't about being a genius; it's about understanding the rules and taking your time. You've got this!

Our journey through this mathematical problem demonstrates the power of a systematic approach. By adhering to the order of operations (PEMDAS) and methodically working through each step, we transformed a seemingly complex expression into a straightforward calculation. The final answer, 60, represents not just a numerical solution, but also the reward for careful attention to detail and a commitment to accurate computation. This exercise reinforces the idea that even intricate mathematical problems can be conquered by breaking them down into smaller, more manageable components. The success we achieved here underscores the importance of building a solid foundation in mathematical principles, as well as the confidence to tackle challenges with a step-by-step strategy.

Practice Makes Perfect

The best way to get better at math is to practice! Try solving similar problems on your own. You can even change the numbers in this equation and see if you can still solve it correctly. The more you practice, the more comfortable you'll become with the order of operations and different mathematical concepts. Don't be afraid to make mistakes; they're a part of the learning process. Keep challenging yourself, and you'll be a math whiz in no time!

Consistent practice is the cornerstone of mathematical proficiency. By engaging with similar problems and manipulating numerical values, you reinforce your understanding of core concepts and refine your problem-solving skills. This iterative process not only solidifies your grasp of PEMDAS and other mathematical principles but also fosters adaptability in the face of varying challenges. Remember, mistakes are invaluable learning opportunities. They highlight areas for improvement and encourage a deeper engagement with the material. Embrace the challenge of practice, and you'll witness a marked improvement in your mathematical abilities. The journey from mathematical novice to expert is paved with consistent effort and a willingness to learn from every attempt.

So there you have it, guys! We've successfully solved the equation 350 ÷ (46 + 24) × 12. I hope this step-by-step guide has been helpful. Keep practicing, keep learning, and keep crushing those math problems!