Step-by-Step Solution 23 + 67 - 88 ÷ 34 × 40 =

by Scholario Team 47 views

Let's embark on a mathematical journey to solve the intriguing expression: 23 + 67 - 88 ÷ 34 × 40 = ? This seemingly complex equation can be easily conquered by understanding and applying the fundamental order of operations, often remembered by the acronym PEMDAS/BODMAS. This guide will meticulously break down each step, ensuring a clear and comprehensive understanding of the solution.

Understanding the Order of Operations: PEMDAS/BODMAS

Before we dive into the calculation, it's crucial to grasp the concept of the order of operations. This mathematical principle dictates the sequence in which operations must be performed to arrive at the correct answer. The acronyms PEMDAS and BODMAS serve as handy mnemonics to remember this order:

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

Both acronyms essentially convey the same order, with Parentheses and Brackets representing the same concept, and Orders encompassing exponents and roots. The key takeaway is that multiplication and division hold equal priority and are performed from left to right, as do addition and subtraction.

Step 1: Division

Following the order of operations, we first encounter division in our expression: 88 ÷ 34. Performing this division yields an approximate result:

88 ÷ 34 ≈ 2.588

For the sake of precision, we'll carry this result to several decimal places throughout our calculation. Understanding the importance of accurate division is crucial in obtaining a reliable final answer. Properly executing this step sets the foundation for the subsequent operations, ensuring the integrity of our mathematical journey. The quotient we've obtained will now be used in the next step, where it will be multiplied, further unraveling the mystery of the equation.

Step 2: Multiplication

With the division completed, we proceed to the multiplication operation: 2.588 × 40. Multiplying these values gives us:

2.  588 × 40 ≈ 103.52

The product we've calculated now represents a significant component of our original expression. Multiplication, in this context, serves to amplify the result of the division, bringing us closer to the final solution. It's essential to ensure precision in this step as any error here can cascade through the remaining calculations, potentially leading to an incorrect answer. This product will be a crucial element in the next phase, where we will integrate it with the addition and subtraction operations to reveal the ultimate result of the equation.

Step 3: Addition

Now that we've handled the division and multiplication, we move on to addition. Our expression now looks like this: 23 + 67 - 103.52. Performing the addition: 23 + 67 yields:

23 + 67 = 90

The sum we've obtained is a significant milestone in our journey towards solving the equation. Addition here serves as a crucial step in combining the initial values, setting the stage for the final subtraction. The accuracy of this step is paramount as it directly influences the outcome of the subsequent operation. By meticulously adding the numbers, we're ensuring the integrity of our calculation, paving the way for a precise final answer. This sum will now be used in the concluding step, where we will subtract the product we previously calculated, unveiling the ultimate solution to the expression.

Step 4: Subtraction

Finally, we arrive at the subtraction step. Our expression is now simplified to: 90 - 103.52. Subtracting these values gives us:

90 - 103.52 = -13.52

The difference we've calculated represents the ultimate solution to our original expression. Subtraction, in this final step, serves to reconcile the accumulated values, revealing the definitive answer. The precision maintained throughout the preceding steps culminates here, ensuring the accuracy of our result. This final value, a negative number, signifies the culmination of our mathematical journey, answering the initial question posed by the equation. The process of subtraction brings closure to our calculation, providing us with a clear and concise resolution.

The Final Answer

Therefore, the solution to the expression 23 + 67 - 88 ÷ 34 × 40 is approximately -13.52. This result is obtained by meticulously following the order of operations and performing each step with precision. Understanding and applying PEMDAS/BODMAS is paramount in solving mathematical expressions accurately.

By meticulously dissecting the equation and adhering to the order of operations, we've successfully navigated the complexities of the expression, arriving at a definitive solution. This journey through mathematical operations underscores the importance of precision and adherence to fundamental principles. The negative result we've obtained adds an intriguing layer to the solution, showcasing the versatility of mathematical outcomes. Through each step, from division to subtraction, we've unraveled the layers of the equation, revealing the ultimate answer that lies at the heart of the expression. This process not only solves the specific problem but also reinforces the broader understanding of mathematical principles and their application in unraveling numerical mysteries.

Key Takeaways

  • The order of operations (PEMDAS/BODMAS) is crucial for solving mathematical expressions correctly.
  • Division and multiplication are performed from left to right.
  • Addition and subtraction are performed from left to right.
  • Precision in each step is essential for obtaining an accurate final answer.

Practice Makes Perfect

To solidify your understanding, try solving similar expressions using the same step-by-step approach. The more you practice, the more confident you'll become in tackling complex mathematical problems. Remember, mathematics is a journey of exploration and discovery, and each equation solved is a step forward in your understanding of the world around us.

By practicing diverse mathematical problems, we hone our skills and deepen our comprehension of mathematical principles. Each equation we conquer adds to our arsenal of problem-solving techniques, empowering us to tackle more complex challenges with confidence. The journey of mathematical exploration is a continuous one, filled with opportunities to learn, grow, and expand our understanding of the intricate relationships between numbers and operations. As we delve deeper into the world of mathematics, we not only enhance our analytical abilities but also cultivate a mindset of logical reasoning and critical thinking, skills that are invaluable in various aspects of life.

Conclusion

Solving mathematical expressions can be an engaging and rewarding experience. By understanding the order of operations and practicing regularly, you can confidently conquer any equation that comes your way. Remember to break down complex problems into smaller, manageable steps, and always double-check your work to ensure accuracy. With dedication and perseverance, you can unlock the beauty and power of mathematics.

The world of mathematics is a vast and fascinating realm, offering endless opportunities for exploration and discovery. Each equation we solve, each concept we grasp, adds to our understanding of the underlying principles that govern the universe. The journey through mathematics is not just about finding answers; it's about developing a mindset of logical reasoning, critical thinking, and problem-solving. These skills are not only valuable in academic pursuits but also in navigating the complexities of everyday life. By embracing the challenges and rewards of mathematics, we empower ourselves to become more analytical, resourceful, and confident individuals. The beauty of mathematics lies not just in its precision but also in its ability to unlock the mysteries of the world around us, providing us with a powerful tool for understanding and shaping our reality.