Solving 3 - (-3) + 7 - 4 A Step-by-Step Arithmetic Guide

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Arithmetic forms the bedrock of mathematics, and a firm grasp of basic operations is crucial for tackling more complex problems. In this comprehensive guide, we will delve into the step-by-step solution of the arithmetic expression 3 - (-3) + 7 - 4. This seemingly simple equation encapsulates several key concepts, including the handling of negative numbers and the order of operations. By meticulously dissecting each step, we aim to provide a clear and thorough understanding, suitable for students, educators, and anyone looking to refresh their mathematical skills. This article will not only provide the solution but also offer insights into the underlying principles, ensuring a robust grasp of basic arithmetic. Understanding these principles is not just about getting the right answer; it's about building a strong mathematical foundation for future learning and problem-solving.

The given expression is 3 - (-3) + 7 - 4. At first glance, it involves a series of additions and subtractions, but the presence of a negative number being subtracted (the -(-3) term) adds a layer of complexity. To solve this accurately, we need to follow the order of operations, which in this case, involves performing the operations from left to right. The key to mastering arithmetic expressions lies in understanding how negative numbers interact with subtraction and addition. Subtracting a negative number is equivalent to adding its positive counterpart, a concept that will be central to our solution. Let’s break down each part of the expression to ensure we understand the logic behind each step. This approach will not only help solve this particular problem but also equip you with the skills to tackle similar expressions with confidence. By focusing on the fundamentals, we can build a solid mathematical base.

To solve the expression 3 - (-3) + 7 - 4, we'll proceed step-by-step, focusing on clarity and precision.

Step 1: Dealing with the Negative

The first part of the expression, 3 - (-3), involves subtracting a negative number. A fundamental rule in arithmetic is that subtracting a negative number is the same as adding its positive counterpart. Therefore, 3 - (-3) becomes 3 + 3. This transformation is crucial for simplifying the expression. Many students find this concept initially confusing, but with practice, it becomes second nature. Remember, subtracting a negative is like removing a debt, which increases your balance. In this case, removing the "debt" of -3 is equivalent to adding 3. This simple yet powerful rule is essential for solving a wide range of mathematical problems.

Step 2: Performing the Addition

Now that we've transformed 3 - (-3) into 3 + 3, we can easily perform the addition. 3 + 3 equals 6. So, the expression now simplifies to 6 + 7 - 4. This step highlights the importance of dealing with negative numbers first to avoid confusion. By breaking the problem down into smaller, manageable steps, we make the entire process less daunting. This incremental approach is a valuable strategy for tackling any mathematical problem, especially those involving multiple operations. By focusing on one operation at a time, we minimize the chance of error and increase our understanding.

Step 3: Continuing the Addition

Next, we move on to the addition of 6 and 7. Adding 6 and 7 gives us 13. The expression is now further simplified to 13 - 4. At this stage, we've reduced the original expression to a simple subtraction problem. Each step we've taken has brought us closer to the final solution. This methodical approach underscores the importance of patience and precision in mathematics. Rushing through steps can lead to errors, so taking the time to perform each operation carefully is crucial. The ability to break down complex problems into simpler steps is a hallmark of a strong mathematical thinker.

Step 4: Final Subtraction

Finally, we perform the subtraction: 13 - 4. Subtracting 4 from 13 results in 9. Therefore, the final answer to the expression 3 - (-3) + 7 - 4 is 9. This concludes our step-by-step solution. By following the order of operations and carefully handling negative numbers, we have arrived at the correct answer. This process demonstrates the power of systematic problem-solving in mathematics. Each step builds upon the previous one, leading us to the final solution. The sense of accomplishment in solving a problem like this comes not just from the answer itself but from the understanding gained along the way.

In conclusion, the solution to the arithmetic expression 3 - (-3) + 7 - 4 is 9. This step-by-step breakdown highlights the importance of understanding the order of operations and the rules for handling negative numbers. By carefully working through each step, we arrived at the correct answer and reinforced our understanding of basic arithmetic principles. This exercise serves as a reminder that even seemingly simple mathematical problems can offer valuable learning opportunities. The key to success in mathematics lies in a solid understanding of the fundamentals and a commitment to careful, methodical problem-solving. This approach not only yields correct answers but also builds confidence and competence in mathematical reasoning. We hope this detailed explanation has provided clarity and insight into solving similar arithmetic expressions. Keep practicing, and you'll find these concepts becoming second nature.

  • A. 12 - Incorrect
  • B. 14 - Incorrect
  • C. 2 - Incorrect
  • D. 9 - Correct

Arithmetic Expression, Negative Numbers, Order of Operations, Step-by-Step Solution, Basic Mathematics