Solving the Expression xy - x/y for Given Values: A Comprehensive Guide

Introduction

In algebra, solving expressions involves substituting given values into the expression to find a result. This article will guide you through the process of solving the expression xy - x/y for a specific case where x 100 and y 10. We will break down the steps involved in solving such an expression and provide a detailed explanation to ensure a thorough understanding of the concept.

Expression Evaluation Step-by-Step

Let's start by examining the given expression: xy - x/y. We are given the values of x and y, which are 100 and 10, respectively. Our task is to substitute these values into the expression and simplify it to find the result.

Step 1: Substitution

Substitute the values of x and y into the expression:

xy - x/y 100 * 10 - 100/10

Step 2: Simplify the Expression

First, simplify the multiplication part of the expression:

100 * 10 1000

Next, simplify the division part of the expression:

100/10 10

Now, substitute the simplified values back into the expression:

1000 - 10

Finally, perform the subtraction:

1000 - 10 990

Conclusion

Therefore, the value of the expression xy - x/y when x 100 and y 10 is 990.

Further Explanation and Applications

Understanding how to solve expressions like xy - x/y is essential in many areas of mathematics, including algebra and calculus. This type of expression is often used in real-world applications, such as financial calculations, physics, and engineering. Here are a few examples of how such expressions can be applied in these fields:

Real-World Applications

1. Finance: In finance, similar expressions might be used to calculate interests, dividends, or other financial metrics. For instance, if x represents the total amount invested and y represents the interest rate, the expression xy - x/y could help in calculating the net gain or loss. 2. Physics: In physics, expressions involving multiplication and division might be used to calculate velocities, accelerations, or other physical quantities. For example, velocity can be calculated as distance divided by time, and in some cases, you might need to subtract or add such division results to find a more complex physical quantity. 3. Engineering: In engineering, expressions can be used to calculate various parameters of mechanical systems, electrical circuits, or control systems. The expression xy - x/y might be used to determine the overall efficiency of a system, where x and y represent different components of the system.

Conclusion

In this article, we have discussed how to solve the expression xy - x/y for given values of x and y. By substituting the given values into the expression and simplifying it step by step, we found that the value of the expression when x 100 and y 10 is 990. This example demonstrates the importance of understanding and accurately solving algebraic expressions, a fundamental skill in various fields of science, technology, engineering, and mathematics (STEM).

Key Takeaways

- Understanding how to solve expressions by substituting given values - The step-by-step process of simplifying expressions - Applications of such expressions in real-world scenarios such as finance, physics, and engineering

References

- Example Calculations for further practice: - Further Reading: Following these steps and concepts, you can confidently solve similar expressions and apply them in various practical situations.