Frank Cuts A Board Into Equal-sized Pieces That Are 3 4 \frac{3}{4} 4 3 ​ Foot Long. If He Was Able To Cut Exactly 8 Pieces From The Board With Nothing Left Over, How Long Was The Board?A. 24 32 \frac{24}{32} 32 24 ​ FootB. 24 4 \frac{24}{4} 4 24 ​ FeetC.

Introduction

In this article, we will delve into a mathematical problem that involves finding the length of a board cut into equal-sized pieces. The problem states that Frank cuts a board into pieces that are $\frac{3}{4}$ foot long, and he is able to cut exactly 8 pieces from the board with nothing left over. Our goal is to determine the length of the original board.

Understanding the Problem

To solve this problem, we need to understand the relationship between the length of the board and the number of pieces cut from it. Since each piece is $\frac{3}{4}$ foot long, we can calculate the total length of the board by multiplying the length of each piece by the number of pieces.

Calculating the Length of the Board

Let's denote the length of the board as $L$. Since Frank cuts exactly 8 pieces from the board, we can set up the following equation:

$$L = 8 \times \frac{3}{4}$$

To solve for $L$, we can multiply the number of pieces by the length of each piece:

$$L = 8 \times \frac{3}{4} = \frac{24}{4}$$

Simplifying the Fraction

The fraction $\frac{24}{4}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This gives us:

$$L = \frac{24}{4} = 6$$

Conclusion

Therefore, the length of the board is 6 feet. This solution makes sense, as we are able to cut exactly 8 pieces from the board with nothing left over, and each piece is $\frac{3}{4}$ foot long.

Why This Problem Matters

This problem is a great example of how mathematical concepts can be applied to real-world situations. By understanding the relationship between the length of the board and the number of pieces cut from it, we can solve for the length of the board. This type of problem is essential in various fields, such as carpentry, engineering, and architecture, where accurate measurements are crucial.

Real-World Applications

In the real world, this type of problem can arise in various situations, such as:

• A carpenter needs to cut a board into equal-sized pieces for a furniture project.
• An engineer needs to calculate the length of a beam for a construction project.
• An architect needs to determine the length of a wall for a building design.

Tips and Tricks

When solving problems like this, it's essential to:

• Read the problem carefully and understand what is being asked.
• Identify the key variables and relationships between them.
• Use mathematical concepts and formulas to solve for the unknown variable.
• Check your solution to ensure it makes sense in the context of the problem.

Conclusion

Introduction

In our previous article, we solved the problem of finding the length of a board cut into equal-sized pieces. The problem stated that Frank cuts a board into pieces that are $\frac{3}{4}$ foot long, and he is able to cut exactly 8 pieces from the board with nothing left over. In this article, we will provide a Q&A section to further clarify the solution and provide additional insights.

Q: What is the relationship between the length of the board and the number of pieces cut from it?

A: The relationship between the length of the board and the number of pieces cut from it is that the total length of the board is equal to the number of pieces multiplied by the length of each piece. In this case, the length of each piece is $\frac{3}{4}$ foot, and the number of pieces is 8.

Q: How do you calculate the length of the board?

A: To calculate the length of the board, we multiply the number of pieces by the length of each piece. In this case, we multiply 8 by $\frac{3}{4}$ to get the total length of the board.

Q: What is the formula for calculating the length of the board?

A: The formula for calculating the length of the board is:

$$L = n \times \frac{3}{4}$$

where $L$ is the length of the board, $n$ is the number of pieces, and $\frac{3}{4}$ is the length of each piece.

Q: Can you provide an example of how to use the formula?

A: Yes, let's say we have a board that we want to cut into 6 pieces, and each piece is $\frac{1}{2}$ foot long. We can use the formula to calculate the length of the board as follows:

$$L = 6 \times \frac{1}{2} = 3$$

Q: What if we have a board that we want to cut into fractional pieces? How do we calculate the length of the board?

A: If we have a board that we want to cut into fractional pieces, we can use the formula to calculate the length of the board. For example, let's say we have a board that we want to cut into $\frac{1}{3}$ foot pieces, and we want to cut 9 pieces from the board. We can use the formula to calculate the length of the board as follows:

$$L = 9 \times \frac{1}{3} = 3$$

Q: Can you provide a real-world example of how this problem can arise?

A: Yes, a real-world example of how this problem can arise is in carpentry. A carpenter may need to cut a board into equal-sized pieces for a furniture project. For example, let's say a carpenter needs to cut a board into 8 pieces, and each piece is $\frac{3}{4}$ foot long. The carpenter can use the formula to calculate the length of the board as follows:

$$L = 8 \times \frac{3}{4} = 6$$

Conclusion

In conclusion, this Q&A section provides additional insights and examples to further clarify the solution to the problem of finding the length of a board cut into equal-sized pieces. By understanding the relationship between the length of the board and the number of pieces cut from it, we can solve for the length of the board using the formula.