Finding One Fifth Of A Number When One Fourth Is Known A Step By Step Solution
Unraveling mathematical puzzles can be an exciting journey, especially when we break down complex problems into smaller, manageable steps. This article delves into a fascinating question: Which of the following numbers is one-fifth of a given number if one-fourth of that same number is 20? We will explore the problem-solving process, understand the underlying concepts, and arrive at the correct solution. Let's embark on this mathematical adventure together!
Understanding the Problem: Laying the Foundation
Before we dive into calculations, let's thoroughly understand the question. The problem presents us with a scenario where we have an unknown number. We are given a crucial piece of information: one-fourth (1/4) of this number is equal to 20. Our ultimate goal is to find one-fifth (1/5) of the same number. This requires us to first determine the original number and then calculate its one-fifth value. By carefully dissecting the problem, we can formulate a clear strategy for solving it.
Understanding the relationship between fractions and whole numbers is paramount in solving this problem. The statement "one-fourth of a number is 20" implies that if we divide the original number into four equal parts, each part will be equal to 20. This provides us with a direct pathway to finding the original number. Similarly, finding one-fifth of a number means dividing it into five equal parts and identifying the value of one such part. By grasping these fundamental concepts, we can confidently approach the problem and navigate towards the solution.
To further solidify our understanding, let's rephrase the problem in simpler terms. Imagine you have a pie, and one-fourth of that pie weighs 20 ounces. The question asks: what would be the weight of one-fifth of the same pie? By visualizing the problem in this manner, we can intuitively grasp the relationships between the fractions and the whole. This conceptual clarity will be invaluable as we proceed with the calculations.
Finding the Original Number: The First Step
The key to solving this problem lies in first determining the original number. We know that one-fourth of the number is 20. Mathematically, we can represent this as:
(1/4) * Original Number = 20
To find the original number, we need to isolate it on one side of the equation. We can achieve this by multiplying both sides of the equation by 4. This is because multiplying a fraction by its reciprocal cancels out the fraction, leaving us with the whole number. Performing this operation, we get:
4 * (1/4) * Original Number = 4 * 20
This simplifies to:
Original Number = 80
Therefore, the original number is 80. This crucial piece of information now allows us to proceed to the next step: finding one-fifth of this number. By successfully calculating the original number, we have laid a solid foundation for solving the remainder of the problem.
It is important to emphasize the logic behind multiplying by 4. Since one-fourth of the number is 20, it logically follows that the whole number must be four times that value. This intuitive understanding reinforces the mathematical operation we performed and helps us avoid rote memorization. By connecting the mathematical steps to the underlying concepts, we can develop a deeper and more meaningful understanding of the problem-solving process.
Calculating One-Fifth: The Final Stretch
Now that we know the original number is 80, we can easily calculate one-fifth of it. To find one-fifth of a number, we simply divide the number by 5 or multiply it by 1/5. Let's express this mathematically:
(1/5) * 80 = ?
Alternatively,
80 / 5 = ?
Performing the calculation, we find that:
(1/5) * 80 = 16
Or,
80 / 5 = 16
Therefore, one-fifth of the original number (80) is 16. This is our final answer. By carefully following the steps and applying the correct mathematical operations, we have successfully solved the problem.
It is worthwhile to reflect on the relationship between the two fractions in the problem. We were given one-fourth of the number and asked to find one-fifth of the same number. Since one-fifth is a smaller fraction than one-fourth, we intuitively expect the final answer (16) to be smaller than the given value (20). This kind of reasoning can serve as a valuable check on our calculations and help us avoid making errors.
The Answer: D. 16
Comparing our result with the given options, we find that the correct answer is:
D. 16
We have successfully navigated the problem, identified the original number, calculated its one-fifth value, and arrived at the correct solution. This demonstrates the power of breaking down complex problems into smaller, manageable steps and applying the fundamental concepts of mathematics.
Conclusion: Mastering the Art of Problem-Solving
This mathematical journey has taken us through the process of dissecting a problem, identifying key information, applying relevant mathematical concepts, and arriving at the correct solution. We have learned the importance of understanding the relationship between fractions and whole numbers, the power of algebraic manipulation, and the value of logical reasoning in problem-solving.
The question, "Which of the following numbers is one-fifth of a given number if one-fourth of that same number is 20?" serves as an excellent example of how mathematical problems can be approached systematically. By understanding the underlying principles and practicing problem-solving techniques, we can enhance our mathematical skills and build confidence in our ability to tackle complex challenges.
Remember, mathematics is not just about memorizing formulas and procedures; it is about developing a way of thinking. By embracing the problem-solving process, we can unlock the beauty and power of mathematics and apply it to various aspects of our lives. This journey has not only provided us with the answer to a specific question but has also equipped us with valuable tools for navigating the world of mathematics and beyond. Embrace the challenge, persevere through the difficulties, and celebrate the joy of discovery!
