Calculating the Leftover Piece

Oct 13, 2025 by wbrum.org 104 views

Introduction

In this article, we will explore a problem that involves basic arithmetic operations, specifically subtraction and conversion between units of measurement. The problem is presented in a real-world scenario, where a carpenter cuts three shelves from a 14-foot board, each shelf being 4 feet 6 inches long. We will calculate the length of the leftover piece and provide a step-by-step solution to the problem.

Understanding the Problem

To solve this problem, we need to understand the measurements involved. The board is 14 feet long, and each shelf is 4 feet 6 inches long. We need to convert the length of each shelf to a single unit of measurement, such as feet, to make the calculation easier.

Converting Measurements

To convert 4 feet 6 inches to feet, we need to convert the inches to feet. There are 12 inches in 1 foot, so we can convert 6 inches to feet by dividing by 12.

6 inches / 12 = 0.5 feet

Now, we can add the converted inches to the feet to get the total length of each shelf in feet.

4 feet + 0.5 feet = 4.5 feet

Calculating the Leftover Piece

To calculate the leftover piece, we need to subtract the total length of the three shelves from the length of the board.

Length of the board = 14 feet Length of each shelf = 4.5 feet Number of shelves = 3

Total length of the shelves = 4.5 feet x 3 = 13.5 feet

Now, we can subtract the total length of the shelves from the length of the board to get the length of the leftover piece.

Length of the leftover piece = 14 feet - 13.5 feet = 0.5 feet

Conclusion

In this article, we solved a problem that involved basic arithmetic operations and conversion between units of measurement. We calculated the length of the leftover piece after a carpenter cut three shelves from a 14-foot board, each shelf being 4 feet 6 inches long. The length of the leftover piece is 0.5 feet.

Additional Information

To convert inches to feet, we can divide the number of inches by 12.
To convert feet to inches, we can multiply the number of feet by 12.
When subtracting a negative number, we can add the absolute value of the number instead.
When subtracting a positive number, we can subtract the number directly.

Real-World Applications

This problem has real-world applications in various fields, such as:

Carpentry: When cutting wood for shelves, it's essential to calculate the leftover piece to ensure accurate measurements.
Construction: When building a structure, it's crucial to calculate the leftover materials to avoid waste and ensure a smooth construction process.
Engineering: When designing a system or a product, it's essential to calculate the leftover materials to ensure accurate measurements and avoid errors.

Final Thoughts

In conclusion, this problem is a great example of how basic arithmetic operations and conversion between units of measurement can be applied to real-world scenarios. By following the step-by-step solution, we can calculate the length of the leftover piece and provide accurate measurements for various applications.

Frequently Asked Questions

Q: How do I convert inches to feet?
A: To convert inches to feet, we can divide the number of inches by 12.
Q: How do I convert feet to inches?
A: To convert feet to inches, we can multiply the number of feet by 12.
Q: What is the length of the leftover piece?
A: The length of the leftover piece is 0.5 feet.

References

[1] "Conversion between units of measurement." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Conversion_between_units_of_measurement.
[2] "Basic arithmetic operations." Khan Academy, Khan Academy, www.khanacademy.org/math/basic-math/basic-math-arithmetic.
[3] "Carpentry and construction." The Spruce Crafts, The Spruce, www.thesprucecrafts.com/carpentry-and-construction-4126541.

Q&A: A Carpenter Cut Three Shelves, Each 4 Feet 6 Inches Long, from a 14-Foot Board. How Long is the Leftover Piece?

Q: What is the problem about?

A: The problem is about a carpenter who cut three shelves, each 4 feet 6 inches long, from a 14-foot board. We need to calculate the length of the leftover piece.

Q: What are the measurements involved in the problem?

A: The measurements involved are:

The length of the board: 14 feet
The length of each shelf: 4 feet 6 inches
The number of shelves: 3

Q: How do we convert 4 feet 6 inches to feet?

A: To convert 4 feet 6 inches to feet, we need to convert the inches to feet. There are 12 inches in 1 foot, so we can convert 6 inches to feet by dividing by 12. 6 inches / 12 = 0.5 feet Now, we can add the converted inches to the feet to get the total length of each shelf in feet. 4 feet + 0.5 feet = 4.5 feet

Q: How do we calculate the total length of the shelves?

A: To calculate the total length of the shelves, we need to multiply the length of each shelf by the number of shelves. Length of each shelf = 4.5 feet Number of shelves = 3 Total length of the shelves = 4.5 feet x 3 = 13.5 feet

Q: How do we calculate the length of the leftover piece?

A: To calculate the length of the leftover piece, we need to subtract the total length of the shelves from the length of the board. Length of the board = 14 feet Total length of the shelves = 13.5 feet Length of the leftover piece = 14 feet - 13.5 feet = 0.5 feet

Q: What is the length of the leftover piece?

A: The length of the leftover piece is 0.5 feet.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as:

Carpentry: When cutting wood for shelves, it's essential to calculate the leftover piece to ensure accurate measurements.
Construction: When building a structure, it's crucial to calculate the leftover materials to avoid waste and ensure a smooth construction process.
Engineering: When designing a system or a product, it's essential to calculate the leftover materials to ensure accurate measurements and avoid errors.

Q: How do we convert inches to feet?

A: To convert inches to feet, we can divide the number of inches by 12.

Q: How do we convert feet to inches?

A: To convert feet to inches, we can multiply the number of feet by 12.

Q: What is the difference between subtracting a negative number and subtracting a positive number?

A: When subtracting a negative number, we can add the absolute value of the number instead. When subtracting a positive number, we can subtract the number directly.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem are:

Not converting the measurements to a single unit of measurement.
Not multiplying the length of each shelf by the number of shelves.
Not subtracting the total length of the shelves from the length of the board.

Q: How can we apply this problem to real-world scenarios?

A: We can apply this problem to real-world scenarios by considering the following:

When cutting wood for shelves, it's essential to calculate the leftover piece to ensure accurate measurements.
When building a structure, it's crucial to calculate the leftover materials to avoid waste and ensure a smooth construction process.
When designing a system or a product, it's essential to calculate the leftover materials to ensure accurate measurements and avoid errors.

Additional Resources

[1] "Conversion between units of measurement." Wikipedia, Wikimedia Foundation, 10 Mar. 2023, en.wikipedia.org/wiki/Conversion_between_units_of_measurement.
[2] "Basic arithmetic operations." Khan Academy, Khan Academy, www.khanacademy.org/math/basic-math/basic-math-arithmetic.
[3] "Carpentry and construction." The Spruce Crafts, The Spruce, www.thesprucecrafts.com/carpentry-and-construction-4126541.