Solve The Equation 26 X 20 X 5.4 X 3 + 5 - 6 X 0. Which Option Is Correct: A) 100, B) 93, C) 0, D) 65?

Decoding the Equation: 26 x 20 x 5.4 x 3 + 5 - 6 x 0

At first glance, the equation 26 x 20 x 5.4 x 3 + 5 - 6 x 0 might seem daunting, but with a systematic approach and a clear understanding of the order of operations, it can be easily solved. This mathematical expression combines multiplication, addition, and subtraction, requiring us to adhere to the fundamental rules of arithmetic. The key to solving this puzzle lies in the PEMDAS/BODMAS rule, which dictates the sequence in which operations must be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Neglecting this order can lead to incorrect results, highlighting the importance of following the established conventions of mathematical calculations. Understanding and applying PEMDAS/BODMAS ensures accuracy and consistency in solving mathematical expressions, making it a crucial concept for anyone dealing with arithmetic problems. In the subsequent sections, we will meticulously break down the equation, applying the order of operations to arrive at the correct solution. By carefully addressing each operation in the proper sequence, we will demystify the complexity and showcase the straightforward nature of mathematical problem-solving. Through this process, we not only find the answer but also reinforce the importance of methodical thinking in mathematics, emphasizing the value of precision and clarity in calculations. By following this systematic approach, we can tackle even the most seemingly complex equations with confidence and accuracy, solidifying our understanding of mathematical principles and enhancing our problem-solving skills.

Step-by-Step Solution: PEMDAS/BODMAS in Action

To effectively solve the equation 26 x 20 x 5.4 x 3 + 5 - 6 x 0, we must meticulously follow the order of operations dictated by the PEMDAS/BODMAS rule. This rule serves as our roadmap, ensuring we tackle the equation in the correct sequence to arrive at the accurate answer. Let's break down each step in detail:

1. Multiplication (Left to Right):

   We begin by addressing the multiplication operations, working from left to right. This is a crucial step, as multiplication takes precedence over addition and subtraction in the order of operations.

   • First, we multiply 26 x 20, which equals 520. This result sets the stage for the next multiplication in the sequence.

   • Next, we multiply 520 x 5.4, yielding 2808. This step demonstrates the importance of accuracy in each calculation, as errors at this stage can propagate through the rest of the solution.

   • Then, we multiply 2808 x 3, which results in 8424. This series of multiplications progressively simplifies the equation, bringing us closer to the final solution.

   • Finally, we address the multiplication at the end of the equation: 6 x 0, which equals 0. This step is particularly important because any number multiplied by zero results in zero, a fundamental concept in arithmetic.

2. Rewriting the Equation:

   After completing the multiplication operations, we rewrite the equation with the results obtained. This step helps to clarify the remaining operations and simplifies the equation for the next phase. The equation now looks like this: 8424 + 5 - 0. This simplified form makes it easier to visualize and execute the remaining addition and subtraction operations.

3. Addition and Subtraction (Left to Right):

   Now, we proceed with the addition and subtraction operations, working from left to right. According to the PEMDAS/BODMAS rule, addition and subtraction have equal priority, so we perform them in the order they appear in the equation.

   • First, we add 8424 + 5, which equals 8429. This addition combines the largest number with the constant, further simplifying the equation.

   • Finally, we subtract 0 from 8429. Since subtracting zero from any number does not change the number, the result remains 8429. This step underscores the identity property of subtraction, where zero has no effect on the value.

The Final Answer: Unveiling the Solution

After meticulously following the PEMDAS/BODMAS rule and performing each operation in the correct order, we arrive at the final answer. By breaking down the equation 26 x 20 x 5.4 x 3 + 5 - 6 x 0 step-by-step, we have navigated through the complexities of multiplication, addition, and subtraction. The step-by-step process not only ensures accuracy but also provides a clear understanding of the mathematical principles at play. We began by addressing the multiplication operations, progressing from left to right and carefully calculating each product. This phase was crucial in simplifying the equation and setting the stage for the subsequent operations. Once the multiplications were completed, we rewrote the equation to reflect the results, making it easier to visualize the remaining operations. Next, we tackled the addition and subtraction, again moving from left to right. This methodical approach allowed us to combine and reduce the numbers systematically, leading us closer to the final solution. The final step, subtracting zero, highlighted the identity property of subtraction, reinforcing a fundamental mathematical concept. Therefore, the solution to the equation 26 x 20 x 5.4 x 3 + 5 - 6 x 0 is 8429. This result underscores the importance of adhering to the order of operations and the power of systematic problem-solving in mathematics. By understanding and applying these principles, we can confidently tackle even the most intricate equations, reinforcing our mathematical skills and enhancing our ability to approach complex problems with clarity and precision.

Why the Order of Operations Matters

The order of operations, often remembered by the acronyms PEMDAS or BODMAS, is not just a mathematical convention; it is a fundamental principle that ensures consistency and accuracy in calculations. Without a standardized order, the same equation could yield different results depending on the sequence in which the operations are performed. This section delves into the critical importance of following the order of operations and the potential pitfalls of neglecting this rule. Imagine, for instance, the chaos that would ensue if every calculator and every mathematician followed a different set of rules for evaluating expressions. Mathematical communication would become impossible, and the very foundation of quantitative reasoning would crumble. The order of operations provides a universal language for mathematics, allowing individuals across the globe to interpret and solve equations in the same way. This consistency is paramount in fields ranging from engineering and physics to economics and computer science, where precise calculations are essential for accurate results and informed decision-making. The PEMDAS/BODMAS rule establishes a hierarchy of operations, prioritizing parentheses/brackets and exponents/orders before multiplication and division, and finally, addition and subtraction. This hierarchy is not arbitrary; it reflects the underlying structure of mathematical expressions and ensures that calculations are performed in a logical and meaningful sequence. For example, multiplication and division represent repeated addition and subtraction, respectively, and thus should be performed before these operations. Similarly, exponents represent repeated multiplication, justifying their precedence over multiplication and division. Ignoring the order of operations can lead to significant errors and misinterpretations. Consider a simple example: 2 + 3 x 4. If we perform the addition first, we get 5 x 4 = 20. However, if we follow the order of operations and perform the multiplication first, we get 2 + 12 = 14, which is the correct answer. This seemingly small discrepancy can have significant consequences in more complex calculations and real-world applications. Inaccurate calculations can lead to flawed designs, incorrect predictions, and costly mistakes. Therefore, understanding and adhering to the order of operations is not merely a matter of mathematical correctness; it is a critical skill for problem-solving and decision-making in various domains. By mastering this principle, we equip ourselves with a powerful tool for navigating the complexities of quantitative reasoning and ensuring the accuracy and reliability of our calculations. The order of operations is the backbone of mathematical consistency, and its importance cannot be overstated.

Common Mistakes to Avoid

When tackling mathematical equations, it's easy to fall into common traps that can lead to incorrect answers. Understanding these pitfalls and how to avoid them is crucial for ensuring accuracy and building confidence in your mathematical abilities. One of the most frequent mistakes is neglecting the order of operations, the very principle we've emphasized throughout this discussion. As we've seen, deviating from the PEMDAS/BODMAS rule can lead to drastically different results. Forgetting to prioritize multiplication and division over addition and subtraction, or failing to address parentheses or exponents first, are common errors that can easily be avoided with careful attention and practice. Another common mistake is overlooking negative signs or misapplying the rules of signed numbers. For instance, subtracting a negative number is equivalent to adding its positive counterpart, and multiplying or dividing two negative numbers results in a positive number. These rules can be tricky to remember and apply, but they are essential for accurate calculations. Taking the time to double-check your work and ensure that you've correctly handled negative signs can save you from costly errors. Careless arithmetic errors, such as simple addition or multiplication mistakes, are also a frequent source of errors. Even the most experienced mathematicians are not immune to these slips, especially when dealing with complex equations or under time pressure. To minimize these errors, it's helpful to write out each step of your calculations clearly and methodically, double-checking your work as you go. Using a calculator can also help reduce the risk of arithmetic mistakes, but it's important to remember that calculators are tools, not replacements for understanding the underlying mathematical principles. Additionally, misinterpreting the problem or failing to read the instructions carefully can lead to errors, even if your calculations are correct. Before you start solving an equation, take a moment to fully understand what is being asked and ensure that you have all the necessary information. Pay attention to any specific instructions or constraints that may apply, and make sure you're answering the question that was actually asked. By being mindful of these common mistakes and actively working to avoid them, you can significantly improve your accuracy and problem-solving skills in mathematics. Remember, practice and attention to detail are key to mastering mathematical concepts and avoiding errors.

Practice Problems: Sharpen Your Skills

To solidify your understanding of the order of operations and enhance your problem-solving abilities, it's essential to engage in practice. Working through various problems allows you to apply the PEMDAS/BODMAS rule in different contexts and identify areas where you may need further clarification. This section provides a series of practice problems designed to challenge your skills and reinforce your grasp of mathematical concepts. Each problem offers a unique opportunity to apply the principles we've discussed, encouraging you to think critically and methodically. As you work through these problems, remember to write out each step of your calculations clearly and double-check your work to minimize errors. This practice not only improves your accuracy but also helps you develop a systematic approach to problem-solving, a valuable skill in mathematics and beyond. Furthermore, practice helps you build confidence in your abilities, making you more comfortable tackling complex equations and real-world applications. The more you practice, the more natural the order of operations will become, and the easier it will be to identify and avoid common mistakes. The key to mastering mathematics is consistent effort and a willingness to learn from your mistakes. Don't be discouraged if you encounter challenges along the way; view them as opportunities for growth and improvement. Each problem you solve successfully brings you one step closer to mastering mathematical concepts and achieving your goals. So, dive into these practice problems, embrace the challenge, and watch your skills soar. Remember, practice is not just about finding the right answers; it's about developing a deeper understanding of the underlying principles and building a solid foundation for future learning. Make the most of these opportunities to sharpen your skills and become a confident and capable problem-solver. This dedication to practice will serve you well in all your mathematical endeavors and beyond, empowering you to tackle challenges with clarity and precision.