Solving The Math Puzzle 278-(34+12)-(12+15-9)-153-12 A Step-by-Step Guide
Delving into the realm of mathematics, we encounter a seemingly complex expression: 278-(34+12)-(12+15-9)-153-12. This expression, a blend of addition, subtraction, and parentheses, presents a captivating challenge that demands a systematic approach to unravel. In this comprehensive exploration, we embark on a journey to dissect this mathematical puzzle, meticulously applying the order of operations to arrive at the ultimate solution. Our journey will not only provide the answer but also illuminate the fundamental principles that govern mathematical calculations.
Embracing the Order of Operations: A Guiding Light
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), serves as our guiding light in this mathematical endeavor. This set of rules dictates the sequence in which mathematical operations must be performed, ensuring consistency and accuracy in our calculations. By adhering to PEMDAS, we transform a seemingly intricate expression into a series of manageable steps.
Our initial focus lies on the parentheses, the innermost sanctums of mathematical expressions. Within these enclosures, we encounter expressions that demand our immediate attention. By resolving these parenthetical expressions first, we pave the way for a streamlined and accurate calculation process.
Taming the Parentheses: A Step-by-Step Subquest
Within our expression, we encounter two sets of parentheses: (34+12) and (12+15-9). These parenthetical expressions beckon us to embark on a subquest, a focused exploration within the confines of the parentheses. Let us begin with the first set, (34+12). This simple addition problem yields the result 46. With the first set of parentheses conquered, we turn our attention to the second set, (12+15-9). Here, we encounter both addition and subtraction. Adhering to the order of operations, we perform addition before subtraction. 12+15 equals 27, and subtracting 9 from 27 gives us 18. With both sets of parentheses tamed, we have successfully navigated the first hurdle in our mathematical journey.
Rewriting the Expression: A Clearer Path
Having conquered the parentheses, we can now rewrite the expression, replacing the parenthetical expressions with their calculated values. Our expression now transforms into 278-46-18-153-12. This revised expression, devoid of parentheses, presents a clearer path forward, allowing us to focus on the remaining operations: subtraction. With the parentheses out of the way, we can proceed with the subtraction operations, moving from left to right.
Subtraction's Reign: Unveiling the Numerical Truth
With our revised expression in hand, we embark on the reign of subtraction, meticulously subtracting each number from the previous result. Starting from the left, we subtract 46 from 278, which gives us 232. Next, we subtract 18 from 232, resulting in 214. Continuing our subtraction spree, we subtract 153 from 214, leaving us with 61. Finally, we subtract 12 from 61, culminating in the ultimate solution: 49. The numerical truth, hidden within the intricate expression, is now unveiled.
The Grand Finale: 49, the Ultimate Solution
After a meticulous journey through the realms of addition, subtraction, and the order of operations, we arrive at the grand finale: 49. This number, the culmination of our efforts, represents the solution to the mathematical puzzle 278-(34+12)-(12+15-9)-153-12. Our systematic approach, guided by the principles of PEMDAS, has transformed a seemingly complex expression into a clear and concise solution.
Summary of Steps:
-
Solve Parentheses:
- (34 + 12) = 46
- (12 + 15 - 9) = 18
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Rewrite Expression:
- 278 - 46 - 18 - 153 - 12
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Perform Subtraction from Left to Right:
- 278 - 46 = 232
- 232 - 18 = 214
- 214 - 153 = 61
- 61 - 12 = 49
Final Answer: 49
Key Concepts Revisited
- Order of Operations (PEMDAS): This principle ensures calculations are performed in the correct sequence: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
- Simplifying Expressions: Breaking down complex expressions into smaller, manageable steps.
- Left-to-Right Rule: Performing operations of the same precedence (like subtraction) from left to right.
Practice Problems for Skill Reinforcement
To solidify your understanding of order of operations and simplifying mathematical expressions, consider tackling these practice problems:
- 300 - (25 + 15) - (10 + 5 - 2) - 100 - 20
- 150 + (40 - 10) - (20 + 8) + 35 - 12
- 200 - (12 x 2) + (36 ÷ 6) - 10
Working through these problems will not only sharpen your skills but also deepen your appreciation for the elegance and precision of mathematics.
Conclusion: A Mathematical Victory
In conclusion, our journey through the expression 278-(34+12)-(12+15-9)-153-12 has been a testament to the power of systematic problem-solving and the importance of adhering to the order of operations. By meticulously dissecting the expression, we have not only arrived at the solution of 49 but also gained a deeper understanding of the fundamental principles that govern mathematical calculations. As we continue our mathematical explorations, let us carry with us the lessons learned from this journey, embracing the challenges and celebrating the victories that lie ahead.