Evaluate (2x)/y - 10/y For X=5 And Y=2 A Step-by-Step Guide
Introduction
In mathematics, evaluating expressions is a fundamental skill. It involves substituting given values for variables and simplifying the expression using the order of operations. This article will guide you through the process of evaluating the expression $\frac{2x}{y} - \frac{10}{y}$ for $x = 5$ and $y = 2$. We will break down each step, ensuring a clear understanding of the concepts involved. Mastering expression evaluation is crucial for success in algebra and beyond. By understanding the core principles and working through examples, you can build a solid foundation in mathematical problem-solving. This article will help you not only evaluate this specific expression but also equip you with the knowledge to tackle similar problems with confidence. The key to success lies in careful substitution, adherence to the order of operations, and a systematic approach to simplification. Let's dive into the process and learn how to accurately evaluate algebraic expressions.
Understanding the Expression
The expression we need to evaluate is $\frac{2x}{y} - \frac{10}{y}$. This is an algebraic expression involving two variables, x and y. The expression consists of two terms, both of which are fractions. The first term is $ rac{2x}{y}$, and the second term is $ rac{10}{y}$. Both terms have the same denominator, which is y. This is an important observation because it simplifies the process of combining the terms. Understanding the structure of the expression is the first step towards evaluating it. We need to substitute the given values for x and y and then perform the necessary arithmetic operations. Before we jump into the substitution, let's take a moment to appreciate the importance of understanding expressions. Algebraic expressions are the building blocks of equations and formulas, and the ability to manipulate and evaluate them is essential in various fields, including science, engineering, and economics. By understanding the components of an expression, we can approach the evaluation process with a clear plan and avoid common mistakes. The expression at hand is relatively simple, but the same principles apply to more complex expressions as well.
Step 1: Substitute the Values
The first step in evaluating the expression is to substitute the given values for the variables. We are given that $x = 5$ and $y = 2$. We will replace x with 5 and y with 2 in the expression $\frac2x}{y} - \frac{10}{y}$. After substitution, the expression becomes{2} - \frac{10}{2}$ This step is crucial because it transforms the algebraic expression into a numerical expression, which we can then simplify using arithmetic operations. Substitution is a fundamental technique in algebra, and it's important to be meticulous in this step to avoid errors. Double-check that you have replaced each variable with its correct value. In this case, we have replaced x with 5 and y with 2. The parentheses around the 5 in 2(5) indicate multiplication. This notation is common in algebra and helps to avoid confusion. Now that we have substituted the values, we have a numerical expression that we can simplify. The next step is to perform the multiplication in the first term and then simplify the fractions.
Step 2: Simplify the First Term
Now that we have substituted the values, the expression looks like this: $\frac2(5)}{2} - \frac{10}{2}$ The first term is $\frac{2(5)}{2}$. We need to simplify this term by performing the multiplication in the numerator. 2 multiplied by 5 is 10, so the first term becomes $\frac{10}{2}$. This is a simple fraction that we can further simplify by dividing the numerator by the denominator. 10 divided by 2 is 5. Therefore, the first term simplifies to 5. It's important to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions. In this case, we performed the multiplication before the division. Simplifying the first term makes the overall expression easier to manage. We now have a simpler expression to work with. Simplifying terms one at a time helps to reduce the chances of making errors. After simplifying the first term, the expression now becomes{2}$ We are one step closer to the final answer. The next step is to simplify the second term, which is also a fraction.
Step 3: Simplify the Second Term
After simplifying the first term, our expression is now: $5 - \frac{10}{2}$ The second term is $ rac{10}{2}$. This is a fraction that can be simplified by dividing the numerator by the denominator. 10 divided by 2 is 5. Therefore, the second term simplifies to 5. Simplifying fractions is a fundamental skill in mathematics. It involves dividing the numerator and the denominator by their greatest common divisor. In this case, the greatest common divisor of 10 and 2 is 2, so we divided both by 2 to get 5. Simplifying fractions makes it easier to perform other operations, such as addition and subtraction. Now that we have simplified the second term, our expression becomes: $5 - 5$ This is a simple subtraction problem. We are subtracting 5 from 5. The next step is to perform this subtraction to get the final answer.
Step 4: Perform the Subtraction
Our expression has now been simplified to: $5 - 5$ This is a straightforward subtraction problem. 5 minus 5 is 0. Therefore, the final result of evaluating the expression is 0. Subtraction is one of the basic arithmetic operations, and it's essential to be able to perform it accurately. In this case, we are subtracting two equal numbers, which results in 0. This completes the evaluation of the expression. We have substituted the given values, simplified each term, and performed the necessary operations to arrive at the final answer. It's important to review the steps we took to ensure that we understand the process. We started with the expression $\frac{2x}{y} - \frac{10}{y}$, substituted $x = 5$ and $y = 2$, simplified the terms, and performed the subtraction to get the final answer of 0. This systematic approach can be applied to evaluating other expressions as well.
Final Answer
After substituting the values $x = 5$ and $y = 2$ into the expression $\frac2x}{y} - \frac{10}{y}$, and simplifying, we arrive at the final answer{2} - \frac{10}{2} = \frac{10}{2} - \frac{10}{2} = 5 - 5 = 0$ Therefore, the value of the expression when $x = 5$ and $y = 2$ is 0. This result demonstrates the importance of following the correct order of operations and simplifying expressions step by step. The final answer is a single numerical value that represents the value of the expression for the given values of the variables. In this case, the final answer is 0, which means that the expression evaluates to zero when x is 5 and y is 2. This is a clear and concise way to communicate the result of the evaluation. Understanding how to evaluate expressions is a fundamental skill in algebra and is essential for solving more complex mathematical problems. By practicing these steps, you can build confidence in your ability to evaluate expressions accurately and efficiently.
Conclusion
In this article, we have successfully evaluated the expression $\frac{2x}{y} - \frac{10}{y}$ for $x = 5$ and $y = 2$. We followed a step-by-step approach, which included substituting the given values, simplifying the terms, and performing the necessary arithmetic operations. The final answer we obtained was 0. Evaluating expressions is a crucial skill in mathematics, and it forms the basis for solving equations and other algebraic problems. By understanding the process and practicing regularly, you can improve your mathematical abilities and tackle more challenging problems. The key takeaways from this article are the importance of careful substitution, following the order of operations, and simplifying expressions systematically. These principles can be applied to a wide range of mathematical problems. Remember to double-check your work and ensure that you have followed each step correctly. With practice, you will become more confident and proficient in evaluating expressions. This skill will be invaluable as you progress in your mathematical journey. We encourage you to try evaluating other expressions with different values to further enhance your understanding and skills.
