Understanding the Product of Two Numbers and Their Relationship Through a Practical Example
In mathematics, the product of two numbers is a fundamental concept that involves multiplying them together to find the result. This article will delve into a practical example wherein the product of two numbers is known, and one of the numbers is given. We will explore how to find the other number through algebraic manipulation. This understanding is crucial for solving equations and enhances algebraic problem-solving skills.
The Problem at Hand
The problem presented is: xy -120 If one number is 40, what is the other number?
Step-by-Step Solution
Given that the product of two numbers is -120, and one of the numbers is 40, we can set up the equation as follows:
xy -120
Knowing that one of the numbers (let's call it x) is 40, we substitute this value into the equation:
40y -120
Isolating the Unknown Variable
To solve for the unknown variable y, we need to isolate it on one side of the equation. We do this by dividing both sides of the equation by 40:
y frac{-120}{40} -30
Conclusion
Therefore, the other number is -30. This example illustrates the importance of algebraic manipulation in solving problems involving the product of two numbers. By following these steps, we can easily find the missing number in such scenarios.
Practical Applications
Understanding the product of two numbers and how to solve for an unknown variable can be applied in various real-world situations, such as:
Financial calculations: Determining the other factor in a finance problem where the total amount and one known factor are provided.
Scientific research: Calculating concentrations or dilutions in laboratory settings.
Engineering: Solving structural or mechanical problems where quantities and their relationships are critical.
Further Reading and Resources
To delve deeper into similar problems and enhance your understanding, consider the following resources:
Textbooks on algebra and basic mathematics.
Online tutorials and video explanations on algebraic equations.
Practice problems and exercises available on educational websites and platforms.
By mastering the concept of solving for the product of two numbers, you are laying a solid foundation for more advanced mathematical concepts and real-world applications.