Solving The Mathematical Expression 1.7 × 2 – (9 + 2)
Introduction
In the realm of mathematics, expressions often present themselves as puzzles, inviting us to unravel their intricacies and arrive at a solution. The expression 1.7 × 2 – (9 + 2) is one such puzzle, a combination of arithmetic operations that requires careful consideration and a systematic approach to solve. This article delves into the step-by-step process of solving this expression, highlighting the order of operations and the application of fundamental mathematical principles. Understanding the order of operations, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is paramount to correctly solving any mathematical expression. PEMDAS provides a clear roadmap, ensuring that calculations are performed in the correct sequence, leading to an accurate and unambiguous answer. By adhering to this order, we can navigate the complexities of the expression and arrive at the final result with confidence.
The expression 1.7 × 2 – (9 + 2) serves as a valuable exercise in applying mathematical concepts and honing problem-solving skills. It not only reinforces the understanding of arithmetic operations but also underscores the importance of precision and attention to detail in mathematical calculations. As we embark on this journey of solving the expression, we will break it down into manageable steps, explaining each operation and its rationale. This methodical approach will not only lead us to the solution but also equip us with the tools to tackle similar mathematical challenges in the future. So, let us delve into the world of numbers and operations, and together, we will unravel the solution to this intriguing mathematical expression.
Step 1: Parentheses First
The first step in solving the expression 1.7 × 2 – (9 + 2) is to address the operation within the parentheses. According to the order of operations (PEMDAS), parentheses take precedence over other operations, so we must simplify the expression inside the parentheses before proceeding further. The expression within the parentheses is (9 + 2), which is a simple addition operation. Adding 9 and 2 together, we get 11. Therefore, the expression within the parentheses simplifies to 11. This step is crucial as it sets the stage for the subsequent operations. By simplifying the expression within the parentheses first, we reduce the complexity of the overall expression and pave the way for a more straightforward calculation. The result of this step is a simplified expression: 1.7 × 2 – 11. Now, we can move on to the next operation in the order of operations, which is multiplication.
Parentheses, in mathematical expressions, act as containers, grouping terms and operations that need to be evaluated as a single unit. They dictate the order in which calculations are performed, ensuring that the intended meaning of the expression is preserved. Without parentheses, the order of operations might lead to a different result, highlighting the significance of these seemingly simple symbols. In our expression, the parentheses around (9 + 2) clearly indicate that this addition must be performed before any other operation. This step not only simplifies the expression but also demonstrates the importance of adhering to the established rules of mathematical operations. As we proceed to the next step, remember that the foundation laid by simplifying the parentheses is crucial for arriving at the correct solution. By carefully addressing each step in the order of operations, we ensure that our calculations are accurate and our final answer is precise.
Step 2: Multiplication
With the parentheses simplified, the next operation to tackle in the expression 1.7 × 2 – 11 is multiplication. According to the order of operations (PEMDAS), multiplication and division take precedence over addition and subtraction. In this case, we have the multiplication operation 1.7 × 2. To perform this multiplication, we multiply 1.7 by 2, which yields 3.4. This step effectively reduces the expression further, making it easier to manage and solve. Multiplication is a fundamental arithmetic operation that involves repeated addition. In this context, multiplying 1.7 by 2 is equivalent to adding 1.7 to itself twice. The result, 3.4, represents the product of these two numbers. Now, with the multiplication completed, our expression has been simplified to 3.4 – 11. We are now left with a simple subtraction operation, which will lead us to the final solution.
Multiplication, in mathematics, is not merely a mechanical process; it is a powerful tool for scaling quantities and understanding relationships between numbers. In this expression, the multiplication of 1.7 by 2 represents a scaling of the value 1.7 by a factor of 2. This scaling is crucial for accurately evaluating the expression and arriving at the correct answer. As we move forward, it is important to recognize the role that each operation plays in shaping the overall result. By carefully performing each step, we ensure that our calculations are sound and our final answer is reliable. The transition from multiplication to subtraction marks a significant step in solving the expression. With only one operation remaining, we are on the verge of uncovering the final solution. So, let us proceed with confidence and complete the calculation with precision.
Step 3: Subtraction
The final step in solving the expression 3.4 – 11 is subtraction. With the parentheses and multiplication operations completed, we are left with a simple subtraction problem. Subtracting 11 from 3.4, we get -7.6. This is the final solution to the expression. Subtraction is the arithmetic operation that involves finding the difference between two numbers. In this case, we are finding the difference between 3.4 and 11. Since 11 is greater than 3.4, the result is a negative number. The negative sign indicates that the result is less than zero. This final step brings our mathematical journey to a successful conclusion. By meticulously following the order of operations and performing each calculation with care, we have arrived at the correct solution.
Subtraction, in mathematics, is not just about taking away; it is about understanding the relationship between numbers and their relative positions on the number line. In this expression, the subtraction of 11 from 3.4 highlights the concept of negative numbers and their significance in mathematical calculations. The result, -7.6, represents a value that is 7.6 units less than zero. This understanding is crucial for interpreting the solution in the context of the original expression. As we reflect on the steps we have taken, we can appreciate the power of mathematical operations to transform expressions and reveal their underlying values. The final solution, -7.6, is not just a number; it is the culmination of a series of calculations, each contributing to the overall result. By mastering these operations, we equip ourselves with the tools to solve a wide range of mathematical problems and explore the fascinating world of numbers.
Conclusion
In conclusion, by meticulously following the order of operations (PEMDAS), we have successfully solved the expression 1.7 × 2 – (9 + 2). The steps involved simplifying the parentheses first, then performing the multiplication, and finally carrying out the subtraction. This systematic approach led us to the final answer of -7.6. This exercise not only reinforces the importance of adhering to the order of operations but also highlights the power of mathematics to solve complex problems in a clear and concise manner. Understanding the order of operations is crucial for accuracy in mathematical calculations. PEMDAS serves as a guide, ensuring that we perform operations in the correct sequence, avoiding errors and arriving at the correct solution.
Mathematics is more than just a collection of formulas and equations; it is a language, a tool, and a way of thinking. By mastering mathematical concepts, we empower ourselves to solve problems, make informed decisions, and understand the world around us. The expression 1.7 × 2 – (9 + 2) serves as a microcosm of the larger world of mathematics, demonstrating the importance of precision, logic, and a systematic approach. As we continue our mathematical journey, let us remember the lessons learned from this exercise and apply them to new challenges. With a solid understanding of fundamental principles and a commitment to careful calculation, we can unlock the power of mathematics and achieve success in our endeavors.
