Breaking down complex problems into smaller parts

Oct 13, 2025 by wbrum.org 10 views

Introduction

Deon, a book enthusiast, has a vast collection of graphic novels that he treasures dearly. Among his collection, he has stored one-third of the graphic novels in a cabinet, which has 4 shelves. Each shelf is equally filled with graphic novels, sparking a question: what fraction of Deon's collection can be found on the top shelf? In this article, we will delve into the world of mathematics to find the answer.

Understanding the Problem

To begin, let's break down the information provided. Deon has stored one-third of his graphic novels in a cabinet with 4 shelves. This means that the remaining two-thirds of his collection is not stored in the cabinet. Since each shelf is equally filled, we can assume that the number of graphic novels on each shelf is the same.

Calculating the Number of Graphic Novels on Each Shelf

Let's denote the total number of graphic novels in Deon's collection as x. Since one-third of the collection is stored in the cabinet, the number of graphic novels in the cabinet is x/3. Since there are 4 shelves in the cabinet, and each shelf has an equal number of graphic novels, the number of graphic novels on each shelf is (x/3)/4 = x/12.

Finding the Fraction of Deon's Collection on the Top Shelf

Since the number of graphic novels on each shelf is x/12, the number of graphic novels on the top shelf is also x/12. To find the fraction of Deon's collection that can be found on the top shelf, we need to divide the number of graphic novels on the top shelf by the total number of graphic novels in the collection.

Mathematical Representation

Let's represent the fraction of Deon's collection on the top shelf as a mathematical expression:

Fraction = (Number of graphic novels on the top shelf) / (Total number of graphic novels in the collection) = (x/12) / x = 1/12

Conclusion

Based on the mathematical representation, we can conclude that the fraction of Deon's collection that can be found on the top shelf is 1/12. This means that one-twelfth of Deon's graphic novel collection is stored on the top shelf of the cabinet.

Real-World Applications

This problem may seem trivial, but it has real-world applications in various fields, such as:

Inventory Management: In a retail store, the manager may want to know the fraction of products stored on a particular shelf to optimize inventory levels.
Supply Chain Management: In a warehouse, the manager may want to know the fraction of products stored on a particular shelf to ensure efficient storage and retrieval.
Data Analysis: In data analysis, the fraction of data stored in a particular database or file system can be used to optimize data storage and retrieval.

Tips and Tricks

Use Visual Aids: When solving problems involving fractions, it's helpful to use visual aids such as diagrams or charts to represent the situation.
Break Down the Problem: Break down the problem into smaller, manageable parts to make it easier to solve.
Check Your Work: Always check your work to ensure that the solution is correct and makes sense in the context of the problem.

Frequently Asked Questions

Q: What if the cabinet has more than 4 shelves? A: If the cabinet has more than 4 shelves, the number of graphic novels on each shelf would be (x/3)/(number of shelves), and the fraction of Deon's collection on the top shelf would be (x/3)/(number of shelves).
Q: What if Deon has a different number of graphic novels in his collection? A: If Deon has a different number of graphic novels in his collection, the fraction of Deon's collection on the top shelf would be (number of graphic novels on the top shelf)/(total number of graphic novels in the collection).

Conclusion

In conclusion, Deon's graphic novel collection is a fascinating example of how mathematics can be applied to real-world problems. By breaking down the problem into smaller parts and using mathematical representations, we can find the fraction of Deon's collection that can be found on the top shelf. This problem has real-world applications in various fields, and by understanding the mathematical concepts involved, we can optimize inventory levels, supply chain management, and data analysis.

Introduction

In our previous article, we explored the world of mathematics to find the fraction of Deon's graphic novel collection that can be found on the top shelf. We broke down the problem into smaller parts, used mathematical representations, and applied real-world applications to optimize inventory levels, supply chain management, and data analysis. In this article, we will answer some frequently asked questions related to Deon's graphic novel collection.

Q&A

Q: What if Deon has a different number of graphic novels in his collection?

A: If Deon has a different number of graphic novels in his collection, the fraction of Deon's collection on the top shelf would be (number of graphic novels on the top shelf)/(total number of graphic novels in the collection). For example, if Deon has 100 graphic novels in his collection and 20 of them are stored on the top shelf, the fraction of Deon's collection on the top shelf would be 20/100 = 1/5.

Q: What if the cabinet has more than 4 shelves?

A: If the cabinet has more than 4 shelves, the number of graphic novels on each shelf would be (x/3)/(number of shelves), and the fraction of Deon's collection on the top shelf would be (x/3)/(number of shelves). For example, if the cabinet has 6 shelves and Deon has 100 graphic novels in his collection, the number of graphic novels on each shelf would be (100/3)/6 = 5.56, and the fraction of Deon's collection on the top shelf would be (100/3)/6 = 1/10.8.

Q: What if Deon has a different number of graphic novels on each shelf?

A: If Deon has a different number of graphic novels on each shelf, the fraction of Deon's collection on the top shelf would be (number of graphic novels on the top shelf)/(total number of graphic novels in the collection). For example, if Deon has 100 graphic novels in his collection and 20 of them are stored on the top shelf, while 30 are stored on the second shelf, and 50 are stored on the third shelf, the fraction of Deon's collection on the top shelf would be 20/100 = 1/5.

Q: Can we apply this problem to other real-world scenarios?

A: Yes, this problem can be applied to other real-world scenarios, such as:

Inventory Management: In a retail store, the manager may want to know the fraction of products stored on a particular shelf to optimize inventory levels.
Supply Chain Management: In a warehouse, the manager may want to know the fraction of products stored on a particular shelf to ensure efficient storage and retrieval.
Data Analysis: In data analysis, the fraction of data stored in a particular database or file system can be used to optimize data storage and retrieval.

Q: How can we use this problem to teach mathematics to students?

A: This problem can be used to teach mathematics to students by:

Breaking down complex problems into smaller parts: This problem can be used to teach students how to break down complex problems into smaller parts and solve them step-by-step.
Using real-world applications: This problem can be used to teach students how to apply mathematical concepts to real-world scenarios.
Encouraging critical thinking: This problem can be used to encourage students to think critically and come up with creative solutions to problems.