Simplifying 18*(-6+4)/9 A Step-by-Step Guide
In the realm of mathematics, simplifying expressions is a fundamental skill. This article delves into the simplification of the expression 18(-6+4)/9, offering a step-by-step guide to ensure clarity and understanding. This exploration is crucial for anyone looking to enhance their mathematical proficiency, whether you are a student, educator, or simply a math enthusiast. By breaking down each step, we aim to provide a comprehensive explanation that makes the process accessible to all. The process of simplifying expressions involves applying the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order dictates the sequence in which operations should be performed to arrive at the correct answer. Let’s embark on this mathematical journey, unraveling the intricacies of simplifying the expression 18(-6+4)/9. By understanding each step, you’ll gain not just the answer, but also a deeper appreciation for the underlying principles of mathematical operations. This knowledge is invaluable for tackling more complex problems in the future.
Step 1: Simplifying the Parentheses
The cornerstone of simplifying any mathematical expression lies in addressing the parentheses first. Within the given expression, 18(-6+4)/9*, the parentheses enclose the operation -6+4. This is where our simplification journey begins. -6+4 involves adding a negative number to a positive number. To simplify this, think of it as starting at -6 on a number line and moving 4 units to the right. This movement results in landing at -2. Therefore, -6+4 simplifies to -2. This initial simplification is crucial because it transforms the original expression into a more manageable form. Understanding how to handle negative numbers within parentheses is a fundamental skill in algebra and arithmetic. It sets the stage for the subsequent steps in the simplification process. By correctly simplifying the parentheses, we ensure that the rest of the expression is handled with precision. This step-by-step approach is what makes complex mathematical problems approachable and solvable. Mastering the art of simplifying parentheses is not just about getting the right answer; it's about building a solid foundation for more advanced mathematical concepts. It’s the first step in a chain of operations, each dependent on the one before it. Therefore, accuracy in this initial stage is paramount for the overall correctness of the solution. This careful attention to detail is what distinguishes a novice from a proficient mathematician. So, let's proceed with the confidence that we've correctly handled the first step, paving the way for a smooth and accurate simplification process.
Step 2: Multiplication
Following the order of operations (PEMDAS), after simplifying the parentheses, the next operation to tackle in the expression 18(-2)/9* is multiplication. Specifically, we need to multiply 18 by -2. Multiplication involving a positive number and a negative number always results in a negative product. In this case, 18 * -2 equals -36. This step is crucial as it further reduces the complexity of the expression, bringing us closer to the final simplified form. Understanding the rules of multiplication with negative numbers is essential in algebra and arithmetic. It's a basic concept that underpins more advanced mathematical operations. The product -36 now replaces the multiplication part of the original expression, transforming it into a simpler division problem. This highlights the power of stepwise simplification in mathematics. By breaking down a complex expression into smaller, manageable parts, we can systematically arrive at the solution. Each step builds upon the previous one, ensuring accuracy and clarity. This method is not only effective but also fosters a deeper understanding of the underlying mathematical principles. Mastering multiplication, especially with negative numbers, is a key skill that will benefit you in various mathematical contexts. It’s a building block for more complex operations and problem-solving. Therefore, ensuring a solid grasp of this concept is vital for your mathematical journey. The transition from multiplication to the next step, division, is seamless once we have accurately calculated the product. This progression demonstrates the elegance and orderliness of mathematical operations, where each step logically follows the preceding one.
Step 3: Division
With the expression now simplified to -36/9, the final step in our simplification journey involves division. We need to divide -36 by 9. Dividing a negative number by a positive number yields a negative quotient. In this instance, -36 ÷ 9 equals -4. This division completes the simplification process, giving us the final answer. Understanding the rules of division with negative numbers is as crucial as understanding multiplication. It's another fundamental concept that helps in solving various mathematical problems. The result, -4, represents the simplified form of the original expression 18(-6+4)/9*. This outcome demonstrates the effectiveness of following the order of operations (PEMDAS). By systematically addressing the parentheses, multiplication, and then division, we have successfully simplified a seemingly complex expression into a single, concise number. This process not only provides the answer but also reinforces the importance of structured problem-solving in mathematics. Division is the inverse operation of multiplication, and mastering both is essential for mathematical fluency. This final step solidifies our understanding of how different operations interact and contribute to the overall solution. The journey from the initial complex expression to the final simple answer highlights the power of simplification in making mathematical problems more approachable and solvable. This skill is not just important for academic success but also for practical applications in everyday life. So, with the division complete, we arrive at the final answer, confident in our understanding of each step taken.
Final Answer: -4
In conclusion, by meticulously following the order of operations (PEMDAS), we have successfully simplified the expression 18(-6+4)/9*. The journey began with simplifying the parentheses, followed by multiplication, and culminated in division. Each step was crucial in reducing the complexity and arriving at the final answer. The final simplified answer is -4. This process underscores the importance of a systematic approach in mathematics. Breaking down a problem into manageable steps not only makes it easier to solve but also enhances understanding. The ability to simplify expressions is a fundamental skill that underpins more advanced mathematical concepts. It’s a building block for algebra, calculus, and beyond. This exercise demonstrates how mathematical operations work in harmony, each playing a specific role in achieving the final result. The negative sign in the answer is a testament to the rules governing operations with negative numbers, a crucial aspect of mathematical proficiency. This simplification process is not just about finding the answer; it's about understanding the underlying principles and developing problem-solving skills. It's about building confidence in your ability to tackle mathematical challenges. So, with the final answer of -4, we have not only solved the problem but also reinforced our understanding of mathematical simplification. This knowledge will serve as a valuable asset in future mathematical endeavors. The satisfaction of arriving at the correct answer through a clear, step-by-step process is a reward in itself, encouraging further exploration and mastery of mathematical concepts.
Summary
To summarize, the simplification of the expression 18(-6+4)/9* involved a structured approach using the order of operations (PEMDAS). First, we tackled the parentheses, simplifying -6+4 to -2. Then, we performed the multiplication, calculating 18 * -2 to be -36. Finally, we completed the process with division, dividing -36 by 9 to arrive at the final answer of -4. This step-by-step method not only provides the correct solution but also reinforces the importance of following mathematical rules and conventions. The negative sign in the final answer is a crucial detail, highlighting the significance of understanding operations with negative numbers. This simplification exercise serves as a practical example of how complex expressions can be broken down into manageable steps, making mathematics more accessible and understandable. The process emphasizes the interconnectedness of mathematical operations, where each step builds upon the previous one. The final answer of -4 is a testament to the power of systematic problem-solving in mathematics. This skill is not just valuable in academic settings but also in various real-world scenarios where logical thinking and numerical reasoning are required. Therefore, mastering the art of simplifying expressions is a worthwhile endeavor for anyone seeking to enhance their mathematical abilities. The confidence gained from successfully simplifying such expressions can motivate further learning and exploration in the field of mathematics. So, with the final answer reaffirmed, we celebrate the successful completion of this mathematical journey, armed with a deeper understanding of simplification techniques.