Math Problem: Solving 100 + 36 ÷ 9 × 4 - 108

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Hey math enthusiasts! Let's dive into a classic arithmetic problem: 100 + 36 ÷ 9 × 4 - 108. This might seem simple at first glance, but it's a great opportunity to refresh our understanding of the order of operations, often remembered by the acronym PEMDAS or BODMAS. So, buckle up, grab your calculators (or your brains!), and let's break this down step-by-step. We'll explore each part of the equation, ensuring we apply the correct mathematical rules to arrive at the solution. The goal here isn't just to find the answer; it's to reinforce the importance of following a logical process in mathematics. This ensures accuracy and builds a solid foundation for more complex calculations you'll encounter down the line. We will begin with the basics, starting with the order of operations, and then we'll carefully solve the problem, highlighting each step to ensure clarity. By the end, you should feel confident in your ability to tackle similar problems. Ready? Let's go!

Understanding the Order of Operations: PEMDAS/BODMAS

Before we jump into the numbers, it’s crucial to understand the order of operations. This is the set of rules that dictates the sequence in which we solve a mathematical expression. Without these rules, we'd get a whole bunch of different answers, and math would be a chaotic mess! The most common acronyms used to remember the order are PEMDAS and BODMAS. PEMDAS stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Alternatively, BODMAS is:

  • Brackets
  • Orders (or Of)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)

Essentially, both acronyms are the same thing, just expressed with different words. They both tell us that we must deal with parentheses or brackets first, then exponents or orders (like powers and square roots), followed by multiplication and division (working from left to right), and finally, addition and subtraction (also working from left to right). Remembering this order is vital to getting the correct answer. The use of parentheses and brackets indicates the operation to be performed first. So, if your expression has those, deal with them before anything else. Then exponents, and so on. Following PEMDAS or BODMAS ensures that we solve the equation in a consistent manner, allowing everyone to arrive at the same accurate answer. Failure to follow this order can lead to incorrect results, making your calculations useless and potentially affecting real-world applications where precision is crucial. So, always keep PEMDAS or BODMAS in mind!

Step-by-Step Solution of 100 + 36 ÷ 9 × 4 - 108

Alright, let’s get down to business and solve our equation: 100 + 36 ÷ 9 × 4 - 108. We will follow the order of operations, step by step, to get the correct answer. Remember PEMDAS/BODMAS? We'll apply it here. Here’s how we break it down:

  1. Identify the operations: In this equation, we have addition, division, multiplication, and subtraction. No parentheses or exponents, so we move on!
  2. Division and Multiplication (from left to right): The first operation we encounter is division (36 ÷ 9).
    • 36 ÷ 9 = 4
    • Now, we move on to multiplication: 4 × 4 = 16
    • Rewrite the equation with these results: 100 + 16 - 108
  3. Addition and Subtraction (from left to right): Now we move on to addition and subtraction.
    • First, the addition: 100 + 16 = 116
    • Then, subtraction: 116 - 108 = 8

So, following the correct order of operations, the answer to the equation 100 + 36 ÷ 9 × 4 - 108 is 8.

Common Mistakes to Avoid

Math, like any skill, has its traps. When dealing with equations like the one we've just solved, certain mistakes are more common than others. Avoiding these pitfalls can significantly improve your accuracy and confidence. One of the most frequent errors is ignoring the order of operations. Many people will simply work from left to right, without giving any heed to PEMDAS/BODMAS. For example, some might start with 100 + 36, then divide the result, and so on. This will give you a completely incorrect answer. Remember to always prioritize operations in the correct order: parentheses/brackets, exponents/orders, then multiplication and division (from left to right), and finally, addition and subtraction (also from left to right). Another common mistake is to make errors in the individual calculations. This can be caused by simple calculation errors such as mistyping numbers on a calculator or misremembering multiplication tables. Therefore, it's wise to double-check your arithmetic. If possible, do it twice. You can do this either by repeating the calculation or by using a calculator to check your work.

Another mistake that people make is not paying attention to negative signs. The signs of numbers matter. Therefore, always carefully check the signs of each number to ensure you are adding and subtracting correctly. Finally, don't be afraid to break down the problem. Writing out each step, like we did earlier, is one of the best ways to ensure you get the right answer and minimize mistakes. It also helps in identifying where you might be going wrong. Taking your time, following the correct order of operations, and carefully checking each step are the keys to avoiding these common errors and succeeding in solving math problems.

Practice Problems and Further Exploration

Now that we've walked through the problem and learned about common mistakes, it's time to solidify your understanding. Practicing is one of the best ways to master a new skill, and math is no exception. Here are some practice problems for you to try. These are similar to the example, but with varying levels of complexity to test your skills:

  1. Problem 1: 50 + 20 ÷ 5 × 3 - 10
  2. Problem 2: 25 × 2 + (15 - 5) ÷ 2
  3. Problem 3: 100 - 8 × 6 + 48 ÷ 6

Solutions:

  1. 62
  2. 55
  3. 64

Remember to apply PEMDAS/BODMAS as you solve them. Break down each step and double-check your work. These additional problems will help you sharpen your skills and build confidence in your ability to solve equations. After solving these, you can also explore some advanced concepts related to the order of operations such as parentheses within parentheses or working with fractions and decimals. Mastering the fundamentals allows you to take on more complex mathematical challenges. There are many online resources and math workbooks available, so feel free to explore and learn. Good luck, and keep practicing!

Conclusion: Mastering the Math Problem

Well, that was fun, wasn't it? We've successfully navigated the math problem: 100 + 36 ÷ 9 × 4 - 108. We did this by understanding and carefully applying the order of operations, PEMDAS/BODMAS. The key takeaways from this exercise are simple but crucial. First, the importance of adhering to the order of operations, and second, the practice of breaking down complex problems into manageable, easy-to-solve steps. Remember that mastering math is not about memorizing a bunch of formulas, but rather about developing a methodical approach to problem-solving. This skill extends beyond just math and can be applied in countless real-life scenarios. Every time you solve a problem, you are building your problem-solving muscle. So, keep practicing, keep challenging yourself, and remember that even the most complex problems become easier when you break them down step-by-step. Keep up the great work, and don't hesitate to take on even more challenging problems! Math is a journey, not a destination, so enjoy the process and the satisfaction of solving a problem correctly!