Solving The Arithmetic Expression $3-(-3)+7-4=$ A Step-by-Step Guide
In the captivating world of mathematics, arithmetic expressions stand as the bedrock of numerical computations. These expressions, woven together by a tapestry of numbers and operations, hold the key to unlocking a myriad of mathematical problems. Among these expressions, the seemingly simple yet subtly intricate form of beckons us to embark on a journey of arithmetical exploration.
Deciphering the Expression: A Step-by-Step Approach
To conquer this numerical puzzle, we must arm ourselves with the fundamental principles of arithmetic operations and the revered order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let us embark on this step-by-step solution, shedding light on each stage of the calculation:
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Tackling the Negatives: Our expedition begins with the intriguing encounter of subtracting a negative number. The expression -(-3) presents itself as a captivating challenge. Recall that subtracting a negative number is akin to adding its positive counterpart. Thus, -(-3) metamorphoses into +3, and our expression gracefully transforms into 3 + 3 + 7 - 4.
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The Dance of Addition and Subtraction: With the negative hurdle cleared, we now encounter a harmonious blend of addition and subtraction. Following the sacred order of operations, we traverse from left to right, performing these operations with meticulous precision. The initial pair, 3 + 3, intertwines to yield the sum of 6. Our expression now serenely evolves into 6 + 7 - 4.
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Continuing the Summation: The addition melody continues as we encounter 6 + 7. These two numerical notes resonate to produce the sum of 13, transforming our expression into 13 - 4.
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The Subtraction Finale: The grand finale arrives as we perform the final subtraction: 13 - 4. This subtraction act culminates in the result of 9. Thus, we have reached the summit of our calculation, unveiling the answer to our numerical quest.
Unveiling the Correct Answer: Option C
Our meticulous journey through the arithmetic landscape has led us to the definitive answer of 9. This revelation illuminates Option C as the true solution to the expression .
The order of operations, enshrined in the acronym PEMDAS, serves as the guiding compass in the realm of arithmetic expressions. It dictates the precise sequence in which operations must be performed, ensuring the attainment of a unique and accurate solution. Let us delve deeper into the importance of this mathematical protocol:
Maintaining Harmony and Consistency
The order of operations acts as the conductor of an orchestra, harmonizing the various mathematical instruments into a cohesive and melodious whole. Without this order, mathematical expressions would descend into chaos, yielding a cacophony of conflicting interpretations. PEMDAS ensures that every calculation follows the same rhythmic pattern, leading to a consistent and reliable outcome.
Resolving Ambiguity and Ensuring Clarity
Consider the expression 2 + 3 x 4. Without the order of operations, ambiguity would reign supreme. Should we perform addition first, arriving at 5 x 4 = 20? Or should we prioritize multiplication, yielding 2 + 12 = 14? The order of operations decisively resolves this conundrum, mandating that multiplication precedes addition. Thus, the correct interpretation is 2 + (3 x 4) = 14.
Empowering Complex Calculations
The order of operations proves its mettle in the face of complex mathematical expressions, those intricate webs of numbers and operations. Imagine an expression adorned with parentheses, exponents, and a medley of arithmetic operations. Without PEMDAS, navigating this labyrinth would be a daunting task. The order of operations acts as our guiding thread, leading us step by step through the intricate calculations, ensuring that we arrive at the correct solution with unwavering confidence.
Proficiency in arithmetic expressions is not an innate gift; it is a skill cultivated through diligent practice and unwavering dedication. Like a virtuoso honing their craft, we must immerse ourselves in the world of numerical calculations, tackling expressions of varying complexity.
Unleashing the Power of Practice Problems
Practice problems serve as the training ground for our mathematical prowess. They present us with diverse scenarios, challenging our understanding of arithmetic operations and the order of operations. By diligently solving these problems, we fortify our mathematical foundation, sharpening our skills and building confidence.
Seeking Guidance from Worked Examples
Worked examples, those meticulously crafted solutions, serve as our guiding lights in the realm of arithmetic expressions. They illuminate the path to problem-solving, revealing the step-by-step process and rationale behind each calculation. By studying worked examples, we gain valuable insights, expanding our problem-solving toolkit.
Embracing the Challenge of Word Problems
Word problems, those narratives woven around mathematical concepts, present a unique challenge. They demand that we translate real-world scenarios into mathematical expressions, bridging the gap between theory and application. By conquering word problems, we hone our analytical skills, learning to extract the essence of a problem and formulate the appropriate solution strategy.
Our expedition through the arithmetic landscape, centered around the expression , has culminated in the triumphant unveiling of the solution: 9. We have navigated the intricacies of negative numbers, embraced the order of operations, and emerged with a deeper appreciation for the power of arithmetic expressions.
As we conclude this mathematical journey, let us carry forward the lessons learned, applying them to the myriad numerical challenges that lie ahead. With unwavering dedication and persistent practice, we shall continue to unravel the mysteries of mathematics, transforming into confident and proficient problem-solvers.
