Tomás Is Cutting A Board Into $\frac{1}{4}$-yard Pieces. If The Board Is 3 Yards Long, How Many Pieces Can Tomás Cut?Choose The Equation That Represents The Problem.A. $\frac{1}{4} \div 3=\frac{1}{12}$ B. $1 \div

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Tomás' Cutting Conundrum: A Math Problem of Division

Tomás is a skilled craftsman with a passion for woodworking. He has a 3-yard long board that he wants to cut into smaller pieces, each measuring $\frac{1}{4}$ yard. The question is, how many pieces can Tomás cut from the board? To solve this problem, we need to use division, a fundamental concept in mathematics.

The problem states that Tomás has a 3-yard long board and wants to cut it into $\frac{1}{4}$-yard pieces. To find the number of pieces he can cut, we need to divide the total length of the board (3 yards) by the length of each piece ($\frac{1}{4}$ yard).

There are two equations provided to represent the problem:

A. $\frac{1}{4} \div 3=\frac{1}{12}$ B. $1 \div \frac{1}{4} = 4$

Let's analyze each equation to determine which one represents the problem.

Equation A: $\frac{1}{4} \div 3=\frac{1}{12}$

Equation A represents the division of $\frac{1}{4}$ by 3. However, this equation is incorrect because it is dividing a fraction by a whole number. To divide a fraction by a whole number, we need to multiply the fraction by the reciprocal of the whole number.

Equation B: $1 \div \frac{1}{4} = 4$

Equation B represents the division of 1 by $\frac{1}{4}$. To divide 1 by a fraction, we can multiply 1 by the reciprocal of the fraction. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$, which is equal to 4. Therefore, $1 \div \frac{1}{4} = 1 \times 4 = 4$.

Based on our analysis, the correct equation that represents the problem is:

1÷14=41 \div \frac{1}{4} = 4

This equation correctly represents the division of 1 by $\frac{1}{4}$, which is equal to 4. Therefore, Tomás can cut 4 pieces from the 3-yard long board, each measuring $\frac{1}{4}$ yard.

To solve the problem, we can use the correct equation:

1÷14=41 \div \frac{1}{4} = 4

This equation tells us that Tomás can cut 4 pieces from the 3-yard long board, each measuring $\frac{1}{4}$ yard.

To calculate the number of pieces Tomás can cut, we can multiply the number of pieces (4) by the length of each piece ($\frac{1}{4}$ yard):

4×14=14 \times \frac{1}{4} = 1

This calculation tells us that Tomás can cut 1 piece from the 3-yard long board, each measuring $\frac{1}{4}$ yard.

In conclusion, the correct equation that represents the problem is:

1÷14=41 \div \frac{1}{4} = 4

This equation correctly represents the division of 1 by $\frac{1}{4}$, which is equal to 4. Therefore, Tomás can cut 4 pieces from the 3-yard long board, each measuring $\frac{1}{4}$ yard.

The final answer is 4.
Tomás' Cutting Conundrum: A Math Problem of Division - Q&A

In our previous article, we explored the problem of Tomás cutting a 3-yard long board into $\frac{1}{4}$-yard pieces. We determined that the correct equation to represent the problem is:

1÷14=41 \div \frac{1}{4} = 4

This equation tells us that Tomás can cut 4 pieces from the 3-yard long board, each measuring $\frac{1}{4}$ yard. In this article, we will answer some frequently asked questions related to this problem.

Q: What is the length of each piece that Tomás can cut?

A: The length of each piece that Tomás can cut is $\frac{1}{4}$ yard.

Q: How many pieces can Tomás cut from the 3-yard long board?

A: Tomás can cut 4 pieces from the 3-yard long board, each measuring $\frac{1}{4}$ yard.

Q: What is the total length of the board that Tomás has?

A: The total length of the board that Tomás has is 3 yards.

Q: Why is the equation $\frac{1}{4} \div 3=\frac{1}{12}$ incorrect?

A: The equation $\frac{1}{4} \div 3=\frac{1}{12}$ is incorrect because it is dividing a fraction by a whole number. To divide a fraction by a whole number, we need to multiply the fraction by the reciprocal of the whole number.

Q: How do we divide a fraction by a whole number?

A: To divide a fraction by a whole number, we need to multiply the fraction by the reciprocal of the whole number. For example, to divide $\frac{1}{4}$ by 3, we can multiply $\frac{1}{4}$ by $\frac{1}{3}$.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$, which is equal to 4.

Q: How do we multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, we can multiply the numerator of the fraction by the whole number. For example, to multiply $\frac{1}{4}$ by 3, we can multiply 1 by 3, which gives us $\frac{3}{4}$.

In conclusion, we have answered some frequently asked questions related to the problem of Tomás cutting a 3-yard long board into $\frac{1}{4}$-yard pieces. We hope that this Q&A article has provided you with a better understanding of the problem and its solution.

The final answer is 4.